Early language and executive skills predict variations in number and arithmetic skills in children at family-risk of dyslexia and typically developing controls

PubMed Central

Moll, Kristina; Snowling, Margaret J.; Göbel, Silke M.; Hulme, Charles

2015-01-01

Two important foundations for learning are language and executive skills. Data from a longitudinal study tracking the development of 93 children at family-risk of dyslexia and 76 controls was used to investigate the influence of these skills on the development of arithmetic. A two-group longitudinal path model assessed the relationships between language and executive skills at 3–4 years, verbal number skills (counting and number knowledge) and phonological processing skills at 4–5 years, and written arithmetic in primary school. The same cognitive processes accounted for variability in arithmetic skills in both groups. Early language and executive skills predicted variations in preschool verbal number skills, which in turn, predicted arithmetic skills in school. In contrast, phonological awareness was not a predictor of later arithmetic skills. These results suggest that verbal and executive processes provide the foundation for verbal number skills, which in turn influence the development of formal arithmetic skills. Problems in early language development may explain the comorbidity between reading and mathematics disorder. PMID:26412946

Syntactic Awareness and Arithmetic Word Problem Solving in Children With and Without Learning Disabilities.

PubMed

Peake, Christian; Jiménez, Juan E; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca

2015-01-01

Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in elementary education were formed: children with arithmetic learning disabilities (ALD), children with reading learning disabilities (RLD), and children with comorbid arithmetic and reading learning disabilities (ARLD). Mediation analysis confirmed that SA was a mediator variable for both groups of children with reading disabilities when solving AWPs, but not for children in the ALD group. All groups performed below the control group in the problem solving task. When SA was controlled for, semantic structure and position of the unknown set were variables that affected both groups with ALD. Specifically, children with ALD only were more affected by the place of the unknown set. © Hammill Institute on Disabilities 2014.

Microarray-based Resequencing of Multiple Bacillus anthracis Isolates

DTIC Science & Technology

2004-12-17

generated an Unweighted Pair Group Method Arithmetic Mean ( UPGMA ) tree (see methods [56]; Figure 3). The strains group together in a manner broadly similar...was created using DNADIST, plotted as a UPGMA tree using NEIGHBOR and the tree plotted using DRAWGRAM [56]. The B1 strain A0465 was used as an...distance matrix was created using DNADIST, plotted as a UPGMA tree using NEIGHBOR and the tree plotted using DRAWGRAM [57]. Additional data files The

The functional anatomy of single-digit arithmetic in children with developmental dyslexia.

PubMed

Evans, Tanya M; Flowers, D Lynn; Napoliello, Eileen M; Olulade, Olumide A; Eden, Guinevere F

2014-11-01

Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in the bilateral intraparietal sulcus, the right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in the right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading. Copyright © 2014 Elsevier Inc. All rights reserved.

The Functional Anatomy of Single-Digit Arithmetic in Children with Developmental Dyslexia

PubMed Central

Evans, Tanya M.; Flowers, D. Lynn; Napoliello, Eileen M.; Olulade, Olumide A.; Eden, Guinevere F.

2014-01-01

Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in bilateral intraparietal sulcus, right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading. PMID:25067820

Differences in Arithmetic Performance between Chinese and German Children Are Accompanied by Differences in Processing of Symbolic Numerical Magnitude

PubMed Central

Lonnemann, Jan; Linkersdörfer, Janosch; Hasselhorn, Marcus; Lindberg, Sven

2016-01-01

Symbolic numerical magnitude processing skills are assumed to be fundamental to arithmetic learning. It is, however, still an open question whether better arithmetic skills are reflected in symbolic numerical magnitude processing skills. To address this issue, Chinese and German third graders were compared regarding their performance in arithmetic tasks and in a symbolic numerical magnitude comparison task. Chinese children performed better in the arithmetic tasks and were faster in deciding which one of two Arabic numbers was numerically larger. The group difference in symbolic numerical magnitude processing was fully mediated by the performance in arithmetic tasks. We assume that a higher degree of familiarity with arithmetic in Chinese compared to German children leads to a higher speed of retrieving symbolic numerical magnitude knowledge. PMID:27630606

Mathematical learning disabilities and attention deficit and/or hyperactivity disorder: A study of the cognitive processes involved in arithmetic problem solving.

PubMed

Iglesias-Sarmiento, Valentín; Deaño, Manuel; Alfonso, Sonia; Conde, Ángeles

2017-02-01

The purpose of this study was to examine the contribution of cognitive functioning to arithmetic problem solving and to explore the cognitive profiles of children with attention deficit and/or hyperactivity disorder (ADHD) and with mathematical learning disabilities (MLD). The sample was made up of a total of 90 students of 4th, 5th, and 6th grade organized in three: ADHD (n=30), MLD (n=30) and typically achieving control (TA; n=30) group. Assessment was conducted in two sessions in which the PASS processes and arithmetic problem solving were evaluated. The ADHD group's performance in planning and attention was worse than that of the control group. Children with MLD obtained poorer results than the control group in planning and simultaneous and successive processing. Executive processes predicted arithmetic problem solving in the ADHD group whereas simultaneous processing was the unique predictor in the MLD sample. Children with ADHD and with MLD showed characteristic cognitive profiles. Groups' problem-solving performance can be predicted from their cognitive functioning. Copyright © 2016 Elsevier Ltd. All rights reserved.

Arithmetic Performance of Children with Cerebral Palsy: The Influence of Cognitive and Motor Factors

ERIC Educational Resources Information Center

van Rooijen, Maaike; Verhoeven, Ludo; Smits, Dirk-Wouter; Ketelaar, Marjolijn; Becher, Jules G.; Steenbergen, Bert

2012-01-01

Children diagnosed with cerebral palsy (CP) often show difficulties in arithmetic compared to their typically developing peers. The present study explores whether cognitive and motor variables are related to arithmetic performance of a large group of primary school children with CP. More specifically, the relative influence of non-verbal…

A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing

NASA Technical Reports Server (NTRS)

Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo

2009-01-01

The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.

Spatial Working Memory and Arithmetic Deficits in Children with Nonverbal Learning Difficulties

ERIC Educational Resources Information Center

Mammarella, Irene Cristina; Lucangeli, Daniela; Cornoldi, Cesare

2010-01-01

Visuospatial working memory and its involvement in arithmetic were examined in two groups of 7- to 11-year-olds: one comprising children described by teachers as displaying symptoms of nonverbal learning difficulties (N = 21), the other a control group without learning disabilities (N = 21). The two groups were matched for verbal abilities, age,…

Cognitive Impairments of Children with Severe Arithmetic Difficulties: Cognitive Deficit or Developmental Lag?

ERIC Educational Resources Information Center

Berg, Derek H.

2008-01-01

An age-matched/achievement-matched design was utilized to examine the cognitive functioning of children with severe arithmetic difficulties. A battery of cognitive tasks was administered to three groups of elementary aged children: 20 children with severe arithmetic difficulties (SAD), 20 children matched in age (CAM) to the children with SAD, and…

Evaluation of a Computer-Based Training Program for Enhancing Arithmetic Skills and Spatial Number Representation in Primary School Children.

PubMed

Rauscher, Larissa; Kohn, Juliane; Käser, Tanja; Mayer, Verena; Kucian, Karin; McCaskey, Ursina; Esser, Günter; von Aster, Michael

2016-01-01

Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6-8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation.

The effects of auditory stimulation on the arithmetic performance of children with ADHD and nondisabled children.

PubMed

Abikoff, H; Courtney, M E; Szeibel, P J; Koplewicz, H S

1996-05-01

This study evaluated the impact of extra-task stimulation on the academic task performance of children with attention-deficit/hyperactivity disorder (ADHD). Twenty boys with ADHD and 20 nondisabled boys worked on an arithmetic task during high stimulation (music), low stimulation (speech), and no stimulation (silence). The music "distractors" were individualized for each child, and the arithmetic problems were at each child's ability level. A significant Group x Condition interaction was found for number of correct answers. Specifically, the nondisabled youngsters performed similarly under all three auditory conditions. In contrast, the children with ADHD did significantly better under the music condition than speech or silence conditions. However, a significant Group x Order interaction indicated that arithmetic performance was enhanced only for those children with ADHD who received music as the first condition. The facilitative effects of salient auditory stimulation on the arithmetic performance of the children with ADHD provide some support for the underarousal/optimal stimulation theory of ADHD.

Differences in arithmetic performance between Chinese and German adults are accompanied by differences in processing of non-symbolic numerical magnitude

PubMed Central

Lonnemann, Jan; Li, Su; Zhao, Pei; Li, Peng; Linkersdörfer, Janosch; Lindberg, Sven; Hasselhorn, Marcus; Yan, Song

2017-01-01

Human beings are assumed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information. The ANS is assumed to be fundamental to arithmetic learning and has been shown to be associated with arithmetic performance. It is, however, still a matter of debate whether better arithmetic skills are reflected in the ANS. To address this issue, Chinese and German adults were compared regarding their performance in simple arithmetic tasks and in a non-symbolic numerical magnitude comparison task. Chinese participants showed a better performance in solving simple arithmetic tasks and faster reaction times in the non-symbolic numerical magnitude comparison task without making more errors than their German peers. These differences in performance could not be ascribed to differences in general cognitive abilities. Better arithmetic skills were thus found to be accompanied by a higher speed of retrieving non-symbolic numerical magnitude knowledge but not by a higher precision of non-symbolic numerical magnitude representations. The group difference in the speed of retrieving non-symbolic numerical magnitude knowledge was fully mediated by the performance in arithmetic tasks, suggesting that arithmetic skills shape non-symbolic numerical magnitude processing skills. PMID:28384191

THE SMALLEST FIELD OF DEFINITION OF A SUBGROUP OF THE GROUP \\mathrm{PSL}_2

NASA Astrophysics Data System (ADS)

Vinberg, È. B.

1995-02-01

As previously proved by the author, for each semisimple algebraic group of adjoint type that is dense in the Zariski topology there exists a smallest field of definition which is an invariant of the class of commensurable subgroups. In the present paper an algorithm is given for finding the smallest field of definition of a dense finitely generated subgroup of the group \\mathrm{PSL}_2(\\mathbb{C}). A criterion for arithmeticity of a lattice in \\mathrm{PSL}_2(\\mathbb{R}) or \\mathrm{PSL}_2(\\mathbb{C}) in terms of this field is presented.Bibliography: 7 titles.

The Posing of Arithmetic Problems by Mathematically Talented Students

ERIC Educational Resources Information Center

Espinoza González, Johan; Lupiáñez Gómez, José Luis; Segovia Alex, Isidoro

2016-01-01

Introduction: This paper analyzes the arithmetic problems posed by a group of mathematically talented students when given two problem-posing tasks, and compares these students' responses to those given by a standard group of public school students to the same tasks. Our analysis focuses on characterizing and identifying the differences between the…

Psychological Stress Can Be Decreased by Traditional Thai Massage.

PubMed

Sripongngam, Thanarat; Eungpinichpong, Wichai; Sirivongs, Dhavee; Kanpittaya, Jaturat; Tangvoraphonkchai, Kamonwan; Chanaboon, Sutin

2015-06-01

The purpose of this study was to investigate the immediate effects of traditional Thai massage (TTM) on psychological stress and heart rate variability (HRV). Thirty healthy participants were randomly allocated in two groups, a TTM group (n = 15) who received a 1-hour session with moderate pressure of whole body TTM or a control group (n=15) who rested on the bedfor 1 hour All ofthem were given a 10-minute mental arithmetic test to induce psychological stress after which they received a 1-hour session of TTM or bed rest. Psychological stress and HR V were measured at baseline and immediately after mental arithmetic test, and immediately after TTM or bed rest. The studyfound that psychological stress was signficantly increased (p<0.05) after mental arithmetic test in both groups. Comparison on these measures between immediately after mental arithmetic test and after TTM or bed rest revealed that psychological stress was significantly decreased (p<0.05) and HR Vwas significantly increased (p<0.05) in both groups. Root mean square of successive differences (RMSSD) and low frequency were significantly increased (p<0.05) only in the TTM group. However; all of these measures were found without significant difference when groups were compared. TTM and bed rest could decrease psychological stress and HRV

Neurofunctional Differences Associated with Arithmetic Processing in Turner Syndrome

PubMed Central

Kesler, Shelli R.; Menon, Vinod; Reiss, Allan L.

2011-01-01

Turner syndrome (TS) is a neurogenetic disorder characterized by the absence of one X chromosome in a phenotypic female. Individuals with TS are at risk for impairments in mathematics. We investigated the neural mechanisms underlying arithmetic processing in TS. Fifteen subjects with TS and 15 age-matched typically developing controls were scanned using functional MRI while they performed easy (two-operand) and difficult (three-operand) versions of an arithmetic processing task. Both groups activated fronto-parietal regions involved in arithmetic processing during the math tasks. Compared with controls, the TS group recruited additional neural resources in frontal and parietal regions during the easier, two-operand math task. During the more difficult three-operand task, individuals with TS demonstrated significantly less activation in frontal, parietal and subcortical regions than controls. However, the TS group’s performance on both math tasks was comparable to controls. Individuals with TS demonstrate activation differences in fronto-parietal areas during arithmetic tasks compared with controls. They must recruit additional brain regions during a relatively easy task and demonstrate a potentially inefficient response to increased task difficulty compared with controls. PMID:16135780

Children learn spurious associations in their math textbooks: Examples from fraction arithmetic.

PubMed

Braithwaite, David W; Siegler, Robert S

2018-04-26

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge-rather than understanding of mathematical concepts and procedures-to guide choices of solution strategies. They further proposed that this associative knowledge reflects distributional characteristics of the fraction arithmetic problems children encounter. To test these hypotheses, we examined textbooks and middle school children in the United States (Experiments 1 and 2) and China (Experiment 3). We asked the children to predict which arithmetic operation would accompany a specified pair of operands, to generate operands to accompany a specified arithmetic operation, and to match operands and operations. In both countries, children's responses indicated that they associated operand pairs having equal denominators with addition and subtraction, and operand pairs having a whole number and a fraction with multiplication and division. The children's associations paralleled the textbook input in both countries, which was consistent with the hypothesis that children learned the associations from the practice problems. Differences in the effects of such associative knowledge on U.S. and Chinese children's fraction arithmetic performance are discussed, as are implications of these differences for educational practice. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Concurrent error detecting codes for arithmetic processors

NASA Technical Reports Server (NTRS)

Lim, R. S.

1979-01-01

A method of concurrent error detection for arithmetic processors is described. Low-cost residue codes with check-length l and checkbase m = 2 to the l power - 1 are described for checking arithmetic operations of addition, subtraction, multiplication, division complement, shift, and rotate. Of the three number representations, the signed-magnitude representation is preferred for residue checking. Two methods of residue generation are described: the standard method of using modulo m adders and the method of using a self-testing residue tree. A simple single-bit parity-check code is described for checking the logical operations of XOR, OR, and AND, and also the arithmetic operations of complement, shift, and rotate. For checking complement, shift, and rotate, the single-bit parity-check code is simpler to implement than the residue codes.

The effects of reciprocal peer tutoring and group contingencies on the academic performance of elementary school children.

PubMed Central

Pigott, H E; Fantuzzo, J W; Clement, P W

1986-01-01

We evaluated the effects of reciprocal peer tutoring combined with group reinforcement contingencies on the arithmetic performance of 12 underachieving fifth-grade students. Results indicated that the intervention increased the students' arithmetic performance to a level indistinguishable from their classmates during treatment and 12-week follow-up phases. Pre-, post-, and follow-up sociometric data indicated that the students who participated in the treatment groups increased their amount of peer affiliation with other treatment group members. PMID:3710952

Representing Numbers as Continued Fractions and an N-Spire. tns Document to Do Some Basic Continued Fraction Arithmetic

ERIC Educational Resources Information Center

Leinbach, L. Carl

2015-01-01

This paper illustrates a TI N-Spire .tns file created by the author for generating continued fraction representations of real numbers and doing arithmetic with them. The continued fraction representation provides an alternative to the decimal representation. The .tns file can be used as tool for studying continued fractions and their properties as…

Visuo–spatial working memory is an important source of domain-general vulnerability in the development of arithmetic cognition

PubMed Central

Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Metcalfe, Arron W.S.; Swigart, Anna G.; Menon, Vinod

2014-01-01

The study of developmental disorders can provide a unique window into the role of domain-general cognitive abilities and neural systems in typical and atypical development. Mathematical disabilities (MD) are characterized by marked difficulty in mathematical cognition in the presence of preserved intelligence and verbal ability. Although studies of MD have most often focused on the role of core deficits in numerical processing, domain-general cognitive abilities, in particular working memory (WM), have also been implicated. Here we identify specific WM components that are impaired in children with MD and then examine their role in arithmetic problem solving. Compared to typically developing (TD) children, the MD group demonstrated lower arithmetic performance and lower visuo-spatial working memory (VSWM) scores with preserved abilities on the phonological and central executive components of WM. Whole brain analysis revealed that, during arithmetic problem solving, left posterior parietal cortex, bilateral dorsolateral and ventrolateral prefrontal cortex, cingulate gyrus and precuneus, and fusiform gyrus responses were positively correlated with VSWM ability in TD children, but not in the MD group. Additional analyses using a priori posterior parietal cortex regions previously implicated in WM tasks, demonstrated a convergent pattern of results during arithmetic problem solving. These results suggest that MD is characterized by a common locus of arithmetic and VSWM deficits at both the cognitive and functional neuroanatomical levels. Unlike TD children, children with MD do not use VSWM resources appropriately during arithmetic problem solving. This work advances our understanding of VSWM as an important domain-general cognitive process in both typical and atypical mathematical skill development. PMID:23896444

Relation between arithmetic performance and phonological working memory in children.

PubMed

Silva, Kelly da; Zuanetti, Patrícia Aparecida; Borcat, Vanessa Trombini Ribeiro; Guedes-Granzotti, Raphaela Barroso; Kuroishi, Rita Cristina Sadako; Domenis, Daniele Ramos; Fukuda, Marisa Tomoe Hebihara

2017-08-17

To compare the results of Loop Phonological Working Memory (LPWM) in children without global learning alterations, with lower and average/higher arithmetic performance. The study was conducted with 30 children, between the ages of seven and nine years old, who attended the second or third grade of elementary school in the public network. Exclusion criteria were children with suggestive signs of hearing loss, neurological disorders, poor performance in the reading comprehension test or in speech therapy. The children included in the study were submitted to the subtest of arithmetic of Academic Achievement Test for division into two groups (G1 and G2). The G1 was composed of children with low performance in arithmetic and G2 for children with average/higher performance in arithmetic. All children were submitted to PWM assessment through the repetition of pseudowords test. Statistical analysis was performed using the Mann-Whitney test and a p-value <0.05 was considered significant. The study included 20 girls and 10 boys, mean age 8.7 years. The G1 was composed of 17 children and G2 of 13 children. There was a statistically significant difference between the groups studied for the repetition of pseudowords with three and four syllables. The results of this study provide support for the hypothesis that changes in phonological working memory are related to difficulties in arithmetic tests.

Environmental Gradient Analysis, Ordination, and Classification in Environmental Impact Assessments.

DTIC Science & Technology

1987-09-01

agglomerative clustering algorithms for mainframe computers: (1) the unweighted pair-group method that V uses arithmetic averages ( UPGMA ), (2) the...hierarchical agglomerative unweighted pair-group method using arithmetic averages ( UPGMA ), which is also called average linkage clustering. This method was...dendrograms produced by weighted clustering (93). Sneath and Sokal (94), Romesburg (84), and Seber• (90) also strongly recommend the UPGMA . A dendrogram

The behaviour of resonances in Hecke triangular billiards under deformation

NASA Astrophysics Data System (ADS)

Howard, P. J.; O'Mahony, P. F.

2007-08-01

The right-hand boundary of Artin's billiard on the Poincaré half-plane is continuously deformed to generate a class of chaotic billiards which includes fundamental domains of the Hecke groups Γ(2, n) at certain values of the deformation parameter. The quantum scattering problem in these open chaotic billiards is described and the distributions of both real and imaginary parts of the resonant eigenvalues are investigated. The transitions to arithmetic chaos in the cases n ∈ {4, 6} are closely examined and the explicit analytic form for the scattering matrix is given together with the Fourier coefficients for the scattered wavefunction. The n = 4 and 6 cases have an additional set of regular equally spaced resonances compared to Artin's billiard (n = 3). For a general deformation, a numerical procedure is presented which generates the resonance eigenvalues and the evolution of the eigenvalues is followed as the boundary is varied continuously which leads to dramatic changes in their distribution. For deformations away from the non-generic arithmetic cases, including that of the tiling Hecke triangular billiard n = 5, the distributions of the positions and widths of the resonances are consistent with the predictions of a random matrix theory.

Sulfate Reducing Bacteria and Mycobacteria Dominate the Biofilm Communities in a Chloraminated Drinking Water Distribution System.

PubMed

Gomez-Smith, C Kimloi; LaPara, Timothy M; Hozalski, Raymond M

2015-07-21

The quantity and composition of bacterial biofilms growing on 10 water mains from a full-scale chloraminated water distribution system were analyzed using real-time PCR targeting the 16S rRNA gene and next-generation, high-throughput Illumina sequencing. Water mains with corrosion tubercles supported the greatest amount of bacterial biomass (n = 25; geometric mean = 2.5 × 10(7) copies cm(-2)), which was significantly higher (P = 0.04) than cement-lined cast-iron mains (n = 6; geometric mean = 2.0 × 10(6) copies cm(-2)). Despite spatial variation of community composition and bacterial abundance in water main biofilms, the communities on the interior main surfaces were surprisingly similar, containing a core group of operational taxonomic units (OTUs) assigned to only 17 different genera. Bacteria from the genus Mycobacterium dominated all communities at the main wall-bulk water interface (25-78% of the community), regardless of main age, estimated water age, main material, and the presence of corrosion products. Further sequencing of the mycobacterial heat shock protein gene (hsp65) provided species-level taxonomic resolution of mycobacteria. The two dominant Mycobacteria present, M. frederiksbergense (arithmetic mean = 85.7% of hsp65 sequences) and M. aurum (arithmetic mean = 6.5% of hsp65 sequences), are generally considered to be nonpathogenic. Two opportunistic pathogens, however, were detected at low numbers: M. hemophilum (arithmetic mean = 1.5% of hsp65 sequences) and M. abscessus (arithmetic mean = 0.006% of hsp65 sequences). Sulfate-reducing bacteria from the genus Desulfovibrio, which have been implicated in microbially influenced corrosion, dominated all communities located underneath corrosion tubercules (arithmetic mean = 67.5% of the community). This research provides novel insights into the quantity and composition of biofilms in full-scale drinking water distribution systems, which is critical for assessing the risks to public health and to the water supply infrastructure.

Comorbidity of Arithmetic and Reading Disorder: Basic Number Processing and Calculation in Children with Learning Impairments

ERIC Educational Resources Information Center

Raddatz, Julia; Kuhn, Jörg-Tobias; Holling, Heinz; Moll, Kristina; Dobel, Christian

2017-01-01

The aim of the present study was to investigate the cognitive profiles of primary school children (age 82-133 months) on a battery of basic number processing and calculation tasks. The sample consisted of four groups matched for age and IQ: arithmetic disorder only (AD; n = 20), reading disorder only (RD; n = 40), a comorbid group (n = 27), and an…

Classified one-step high-radix signed-digit arithmetic units

NASA Astrophysics Data System (ADS)

Cherri, Abdallah K.

1998-08-01

High-radix number systems enable higher information storage density, less complexity, fewer system components, and fewer cascaded gates and operations. A simple one-step fully parallel high-radix signed-digit arithmetic is proposed for parallel optical computing based on new joint spatial encodings. This reduces hardware requirements and improves throughput by reducing the space-bandwidth produce needed. The high-radix signed-digit arithmetic operations are based on classifying the neighboring input digit pairs into various groups to reduce the computation rules. A new joint spatial encoding technique is developed to present both the operands and the computation rules. This technique increases the spatial bandwidth product of the spatial light modulators of the system. An optical implementation of the proposed high-radix signed-digit arithmetic operations is also presented. It is shown that our one-step trinary signed-digit and quaternary signed-digit arithmetic units are much simpler and better than all previously reported high-radix signed-digit techniques.

Specific arithmetic calculation deficits in children with Turner syndrome.

PubMed

Rovet, J; Szekely, C; Hockenberry, M N

1994-12-01

Study 1 compared arithmetic processing skills on the WRAT-R in 45 girls with Turner syndrome (TS) and 92 age-matched female controls. Results revealed significant underachievement by subjects with TS, which reflected their poorer performance on problems requiring the retrieval of addition and multiplication facts and procedural knowledge for addition and division operations. TS subjects did not differ qualitatively from controls in type of procedural error committed. Study 2, which compared the performance of 10 subjects with TS and 31 controls on the Keymath Diagnostic Arithmetic Test, showed that the TS group had less adequate knowledge of arithmetic, subtraction, and multiplication procedures but did not differ from controls on Fact items. Error analyses revealed that TS subjects were more likely to confuse component steps or fail to separate intermediate steps or to complete problems. TS subjects relied to a greater degree on verbal than visual-spatial abilities in arithmetic processing while their visual-spatial abilities were associated with retrieval of simple multidigit addition facts and knowledge of subtraction, multiplication, and division procedures. Differences between the TS and control groups increased with age for Keymath, but not WRAT-R, procedures. Discrepant findings are related to the different task constraints (timed vs. untimed, single vs. alternate versions, size of item pool) and the use of different strategies (counting vs. fact retrieval). It is concluded that arithmetic difficulties in females with TS are due to less adequate procedural skills, combined with poorer fact retrieval in timed testing situations, rather than to inadequate visual-spatial abilities.

Discrete mathematical physics and particle modeling

NASA Astrophysics Data System (ADS)

Greenspan, D.

The theory and application of the arithmetic approach to the foundations of both Newtonian and special relativistic mechanics are explored. Using only arithmetic, a reformulation of the Newtonian approach is given for: gravity; particle modeling of solids, liquids, and gases; conservative modeling of laminar and turbulent fluid flow, heat conduction, and elastic vibration; and nonconservative modeling of heat convection, shock-wave generation, the liquid drop problem, porous flow, the interface motion of a melting solid, soap films, string vibrations, and solitons. An arithmetic reformulation of special relativistic mechanics is given for theory in one space dimension, relativistic harmonic oscillation, and theory in three space dimensions. A speculative quantum mechanical model of vibrations in the water molecule is also discussed.

Group differences in adult simple arithmetic: good retrievers, not-so-good retrievers, and perfectionists.

PubMed

Hecht, Steven A

2006-01-01

We used the choice/no-choice methodology in two experiments to examine patterns of strategy selection and execution in groups of undergraduates. Comparisons between choice and no-choice trials revealed three groups. Some participants good retrievers) were consistently able to use retrieval to solve almost all arithmetic problems. Other participants (perfectionists) successfully used retrieval substantially less often in choice-allowed trials than when strategy choices were prohibited. Not-so-good retrievers retrieved correct answers less often than the other participants in both the choice-allowed and no-choice conditions. No group differences emerged with respect to time needed to search and access answers from long-term memory; however, not-so-good retrievers were consistently slower than the other subgroups at executing fact-retrieval processes that are peripheral to memory search and access. Theoretical models of simple arithmetic, such as the Strategy Choice and Discovery Simulation (Shrager & Siegler, 1998), should be updated to include the existence of both perfectionist and not-so-good retriever adults.

Brain Activation during Addition and Subtraction Tasks In-Noise and In-Quiet

PubMed Central

Abd Hamid, Aini Ismafairus; Yusoff, Ahmad Nazlim; Mukari, Siti Zamratol-Mai Sarah; Mohamad, Mazlyfarina

2011-01-01

Background: In spite of extensive research conducted to study how human brain works, little is known about a special function of the brain that stores and manipulates information—the working memory—and how noise influences this special ability. In this study, Functional magnetic resonance imaging (fMRI) was used to investigate brain responses to arithmetic problems solved in noisy and quiet backgrounds. Methods: Eighteen healthy young males performed simple arithmetic operations of addition and subtraction with in-quiet and in-noise backgrounds. The MATLAB-based Statistical Parametric Mapping (SPM8) was implemented on the fMRI datasets to generate and analyse the activated brain regions. Results: Group results showed that addition and subtraction operations evoked extended activation in the left inferior parietal lobe, left precentral gyrus, left superior parietal lobe, left supramarginal gyrus, and left middle temporal gyrus. This supported the hypothesis that the human brain relatively activates its left hemisphere more compared with the right hemisphere when solving arithmetic problems. The insula, middle cingulate cortex, and middle frontal gyrus, however, showed more extended right hemispheric activation, potentially due to the involvement of attention, executive processes, and working memory. For addition operations, there was extensive left hemispheric activation in the superior temporal gyrus, inferior frontal gyrus, and thalamus. In contrast, subtraction tasks evoked a greater activation of similar brain structures in the right hemisphere. For both addition and subtraction operations, the total number of activated voxels was higher for in-noise than in-quiet conditions. Conclusion: These findings suggest that when arithmetic operations were delivered auditorily, the auditory, attention, and working memory functions were required to accomplish the executive processing of the mathematical calculation. The respective brain activation patterns appear to be modulated by the noisy background condition. PMID:22135581

[Effect of mental arithmetic and verbal fluency on blood flow velocity in the middle cerebral arteries].

PubMed

Amrein, Ilona; Pálvölgyi, László; Debreczeni, Róbert; Kamondi, Anita; Szirmai, Imre

2004-01-20

Using transcranial Doppler sonography (TCD), changes in blood flow velocity (BFV) can be measured in the Medial Cerebral Artery (MCA) during cognitive effort. Our goal was to define the time-course and laterality of BFV in healthy volunteers during arithmetic and verbal fluency tasks according to handedness. Twelve subjects (8 right-handed, 4 left-handed) were assessed. The TCD registered BFV in both MCA simultaneously. Heart rate was also recorded using TCD. Finally we included a 16-channel EEG. BFV laterality index (LI) was calculated. Participants were asked to count silently and generate words beginning with a specified letter. To estimate hemispheric differences in BFV, two-tailed Wilcoxon tests were utilized along with correlational analyses. During cognitive effort the BFV changed in a tri-phasic manner in all participants. A 6-8% elevation of BFV was observed in MCAs without latency at the time of the evoking signal. Laterality of BFV developed after 5-13 seconds during cognitive effort in right-, and several seconds later in left-handed subjects. During tasks the BFV increased in the dominant hemisphere up to 2.6-4.7% compared to the subdominant one. We also calculated the LI. During the verbal task the LI agreed with the handedness in 9 out of 12 subjects. During the mental arithmetic task, agreement was found in 6 out of 12 subjects. According to LI results we found a discrepancy between verbal and arithmetic tests in 3 out of 12 subjects. Cognitive effort elicites significant bilateral BFV increases in the MCAs, which suggests fast neurogenic regulation. The course of BFV during mental arithmetic proved to be different from course BFV assessed during the word fluency task. Based on the laterality of the BFV, the word-generation task was more sensitive in determining the dominant hemisphere when compared to the mental arithmetic task. The use of LI may help to estimate hemispheric functions even in pathologic circumstances.

Mental exercises for cognitive function: clinical evidence.

PubMed

Kawashima, Ryuta

2013-01-01

The purpose of this study was to examine the beneficial effects of a new cognitive intervention program designed for the care and prevention of dementia, namely Learning Therapy. The training program used systematized basic problems in arithmetic and Japanese language as training tasks. In study 1, 16 individuals in the experimental group and 16 in the control group were recruited from a nursing home. In both groups, all individuals were clinically diagnosed with senile dementia of the Alzheimer type. In study 2, we performed a single-blind, randomized controlled trial in our cognitive intervention program of 124 community-dwelling seniors. In both studies, the daily training program using reading and arithmetic tasks was carried out approximately 5 days a week, for 15 to 20 minutes a day in the intervention groups. Neuropsychological measures were determined simultaneously in the groups both prior to and after six months of the intervention. The results of our investigations indicate that our cognitive intervention using reading and arithmetic problems demonstrated a transfer effect and they provide convincing evidence that cognitive training maintains and improves the cognitive functions of dementia patients and healthy seniors.

Arithmetic difficulties in children with cerebral palsy are related to executive function and working memory.

PubMed

Jenks, Kathleen M; de Moor, Jan; van Lieshout, Ernest C D M

2009-07-01

Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and controls in mainstream education (n = 16). Second grade executive function and working memory scores were used to predict third grade arithmetic accuracy and response time. Children with cerebral palsy in special education were less accurate and slower than their peers on all arithmetic tests, even after controlling for IQ, whereas children with cerebral palsy in mainstream education performed as well as controls. Although the performance gap became smaller over time, it did not disappear. Children with cerebral palsy in special education showed evidence of executive function and working memory deficits in shifting, updating, visuospatial sketchpad and phonological loop (for digits, not words) whereas children with cerebral palsy in mainstream education only had a deficit in visuospatial sketchpad. Hierarchical regression revealed that, after controlling for intelligence, components of executive function and working memory explained large proportions of unique variance in arithmetic accuracy and response time and these variables were sufficient to explain group differences in simple, but not complex, arithmetic. Children with cerebral palsy are at risk for specific executive function and working memory deficits that, when present, increase the risk for arithmetic difficulties in these children.

Brain Correlates of Mathematical Competence in Processing Mathematical Representations

PubMed Central

Grabner, Roland H.; Reishofer, Gernot; Koschutnig, Karl; Ebner, Franz

2011-01-01

The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams) is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus (AG) activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left AG activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left AG activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance. PMID:22069387

The Influence of Mathematical Ability and Morning Nutrition on Mental Arithmetic in Preadolescents: An ERP study.

USDA-ARS?s Scientific Manuscript database

The effects of eating or skipping breakfast on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Participants, randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by age [8.8 yrs (B: ...

ERP correlates of mental arithmetic in preadolescents: influence of ability and effects of morning nutrition

USDA-ARS?s Scientific Manuscript database

The effects of morning nutritional status on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Children [right-handed; IQ > 80), randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by...

Deficits in working memory, reading comprehension and arithmetic skills in children with mouth breathing syndrome: analytical cross-sectional study.

PubMed

Kuroishi, Rita Cristina Sadako; Garcia, Ricardo Basso; Valera, Fabiana Cardoso Pereira; Anselmo-Lima, Wilma Terezinha; Fukuda, Marisa Tomoe Hebihara

2015-01-01

Mouth breathing syndrome is very common among school-age children, and it is possibly related to learning difficulties and low academic achievement. In this study, we investigated working memory, reading comprehension and arithmetic skills in children with nasal and mouth breathing. Analytical cross-sectional study with control group conducted in a public university hospital. 42 children (mean age = 8.7 years) who had been identified as mouth breathers were compared with a control group (mean age = 8.4 years) matched for age and schooling. All the participants underwent a clinical interview, tone audiometry, otorhinolaryngological evaluation and cognitive assessment of phonological working memory (numbers and pseudowords), reading comprehension and arithmetic skills. Children with mouth breathing had poorer performance than controls, regarding reading comprehension (P = 0.006), arithmetic (P = 0.025) and working memory for pseudowords (P = 0.002), but not for numbers (P = 0.76). Children with mouth breathing have low academic achievement and poorer phonological working memory than controls. Teachers and healthcare professionals should be aware of the association of mouth breathing with children's physical and cognitive health.

Arabidopsis plants perform arithmetic division to prevent starvation at night

PubMed Central

Scialdone, Antonio; Mugford, Sam T; Feike, Doreen; Skeffington, Alastair; Borrill, Philippa; Graf, Alexander; Smith, Alison M; Howard, Martin

2013-01-01

Photosynthetic starch reserves that accumulate in Arabidopsis leaves during the day decrease approximately linearly with time at night to support metabolism and growth. We find that the rate of decrease is adjusted to accommodate variation in the time of onset of darkness and starch content, such that reserves last almost precisely until dawn. Generation of these dynamics therefore requires an arithmetic division computation between the starch content and expected time to dawn. We introduce two novel chemical kinetic models capable of implementing analog arithmetic division. Predictions from the models are successfully tested in plants perturbed by a night-time light period or by mutations in starch degradation pathways. Our experiments indicate which components of the starch degradation apparatus may be important for appropriate arithmetic division. Our results are potentially relevant for any biological system dependent on a food reserve for survival over a predictable time period. DOI: http://dx.doi.org/10.7554/eLife.00669.001 PMID:23805380

Desynchronization of Theta-Phase Gamma-Amplitude Coupling during a Mental Arithmetic Task in Children with Attention Deficit/Hyperactivity Disorder.

PubMed

Kim, Jun Won; Kim, Bung-Nyun; Lee, Jaewon; Na, Chul; Kee, Baik Seok; Min, Kyung Joon; Han, Doug Hyun; Kim, Johanna Inhyang; Lee, Young Sik

2016-01-01

Theta-phase gamma-amplitude coupling (TGC) measurement has recently received attention as a feasible method of assessing brain functions such as neuronal interactions. The purpose of this electroencephalographic (EEG) study is to understand the mechanisms underlying the deficits in attentional control in children with attention deficit/hyperactivity disorder (ADHD) by comparing the power spectra and TGC at rest and during a mental arithmetic task. Nineteen-channel EEGs were recorded from 97 volunteers (including 53 subjects with ADHD) from a camp for hyperactive children under two conditions (rest and task performance). The EEG power spectra and the TGC data were analyzed. Correlation analyses between the Intermediate Visual and Auditory (IVA) continuous performance test (CPT) scores and EEG parameters were performed. No significant difference in the power spectra was detected between the groups at rest and during task performance. However, TGC was reduced during the arithmetic task in the ADHD group compared with the normal group (F = 16.70, p < 0.001). The TGC values positively correlated with the IVA CPT scores but negatively correlated with theta power. Our findings suggest that desynchronization of TGC occurred during the arithmetic task in ADHD children. TGC in ADHD children is expected to serve as a promising neurophysiological marker of network deactivation during attention-demanding tasks.

Dissociation between arithmetic relatedness and distance effects is modulated by task properties: an ERP study comparing explicit vs. implicit arithmetic processing.

PubMed

Avancini, Chiara; Galfano, Giovanni; Szűcs, Dénes

2014-12-01

Event-related potential (ERP) studies have detected several characteristic consecutive amplitude modulations in both implicit and explicit mental arithmetic tasks. Implicit tasks typically focused on the arithmetic relatedness effect (in which performance is affected by semantic associations between numbers) while explicit tasks focused on the distance effect (in which performance is affected by the numerical difference of to-be-compared numbers). Both task types elicit morphologically similar ERP waves which were explained in functionally similar terms. However, to date, the relationship between these tasks has not been investigated explicitly and systematically. In order to fill this gap, here we examined whether ERP effects and their underlying cognitive processes in implicit and explicit mental arithmetic tasks differ from each other. The same group of participants performed both an implicit number-matching task (in which arithmetic knowledge is task-irrelevant) and an explicit arithmetic-verification task (in which arithmetic knowledge is task-relevant). 129-channel ERP data differed substantially between tasks. In the number-matching task, the arithmetic relatedness effect appeared as a negativity over left-frontal electrodes whereas the distance effect was more prominent over right centro-parietal electrodes. In the verification task, all probe types elicited similar N2b waves over right fronto-central electrodes and typical centro-parietal N400 effects over central electrodes. The distance effect appeared as an early-rising, long-lasting left parietal negativity. We suggest that ERP effects in the implicit task reflect access to semantic memory networks and to magnitude discrimination, respectively. In contrast, effects of expectation violation are more prominent in explicit tasks and may mask more delicate cognitive processes. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

Dissociation between arithmetic relatedness and distance effects is modulated by task properties: An ERP study comparing explicit vs. implicit arithmetic processing

PubMed Central

Avancini, Chiara; Galfano, Giovanni; Szűcs, Dénes

2014-01-01

Event-related potential (ERP) studies have detected several characteristic consecutive amplitude modulations in both implicit and explicit mental arithmetic tasks. Implicit tasks typically focused on the arithmetic relatedness effect (in which performance is affected by semantic associations between numbers) while explicit tasks focused on the distance effect (in which performance is affected by the numerical difference of to-be-compared numbers). Both task types elicit morphologically similar ERP waves which were explained in functionally similar terms. However, to date, the relationship between these tasks has not been investigated explicitly and systematically. In order to fill this gap, here we examined whether ERP effects and their underlying cognitive processes in implicit and explicit mental arithmetic tasks differ from each other. The same group of participants performed both an implicit number-matching task (in which arithmetic knowledge is task-irrelevant) and an explicit arithmetic-verification task (in which arithmetic knowledge is task-relevant). 129-channel ERP data differed substantially between tasks. In the number-matching task, the arithmetic relatedness effect appeared as a negativity over left-frontal electrodes whereas the distance effect was more prominent over right centro-parietal electrodes. In the verification task, all probe types elicited similar N2b waves over right fronto-central electrodes and typical centro-parietal N400 effects over central electrodes. The distance effect appeared as an early-rising, long-lasting left parietal negativity. We suggest that ERP effects in the implicit task reflect access to semantic memory networks and to magnitude discrimination, respectively. In contrast, effects of expectation violation are more prominent in explicit tasks and may mask more delicate cognitive processes. PMID:25450162

Population Structure of the Primary Malaria Vector in South America, Anopheles darlingi, Using Isozyme, Random Amplified Polymorphic DNA, Internal Transcribed Spacer 2, and Morphologic Markers

DTIC Science & Technology

1999-01-01

distances and identities and Roger?’ genetic distances were clustered by the unweighted pair group method using arithmetic average ( UPGMA ) to produce...Seattle, WA) using the NEIGHBOR program with the UPGMA option and a phenogram was produced with DRAWGRAM, also in PHYLIP 3.X RAPDBOOT5’ was used to...generate 100 pseudoreplicate distance matrices, which were collapsed to form 100 trees with UPGMA . The bootstrap consensus tree was derived from the 100

Neural Correlates of Arithmetic and Language Comprehension: A Common Substrate?

ERIC Educational Resources Information Center

Baldo, Juliana V.; Dronkers, Nina F.

2007-01-01

There is debate as to the relationship between mathematical ability and language. Some research has suggested that common processes underlie arithmetic and grammar while other research has suggested that these are distinct processes. The current study aimed to address this issue in a large group of 68 left hemisphere stroke patients who were all…

Learning Arithmetic Outdoors in Junior High School--Influence on Performance and Self-Regulating Skills

ERIC Educational Resources Information Center

Fägerstam, Emilia; Samuelsson, Joakim

2014-01-01

This study aims to explore the influence of outdoor teaching among students, aged 13, on arithmetic performance and self-regulation skills as previous research concerning outdoor mathematics learning is limited. This study had a quasi-experimental design. An outdoor and a traditional group answered a test and a self-regulation skills questionnaire…

Syntactic Awareness and Arithmetic Word Problem Solving in Children with and without Learning Disabilities

ERIC Educational Resources Information Center

Peake, Christian; Jiménez, Juan E.; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca

2015-01-01

Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in…

MGUPGMA: A Fast UPGMA Algorithm With Multiple Graphics Processing Units Using NCCL

PubMed Central

Hua, Guan-Jie; Hung, Che-Lun; Lin, Chun-Yuan; Wu, Fu-Che; Chan, Yu-Wei; Tang, Chuan Yi

2017-01-01

A phylogenetic tree is a visual diagram of the relationship between a set of biological species. The scientists usually use it to analyze many characteristics of the species. The distance-matrix methods, such as Unweighted Pair Group Method with Arithmetic Mean and Neighbor Joining, construct a phylogenetic tree by calculating pairwise genetic distances between taxa. These methods have the computational performance issue. Although several new methods with high-performance hardware and frameworks have been proposed, the issue still exists. In this work, a novel parallel Unweighted Pair Group Method with Arithmetic Mean approach on multiple Graphics Processing Units is proposed to construct a phylogenetic tree from extremely large set of sequences. The experimental results present that the proposed approach on a DGX-1 server with 8 NVIDIA P100 graphic cards achieves approximately 3-fold to 7-fold speedup over the implementation of Unweighted Pair Group Method with Arithmetic Mean on a modern CPU and a single GPU, respectively. PMID:29051701

MGUPGMA: A Fast UPGMA Algorithm With Multiple Graphics Processing Units Using NCCL.

PubMed

Hua, Guan-Jie; Hung, Che-Lun; Lin, Chun-Yuan; Wu, Fu-Che; Chan, Yu-Wei; Tang, Chuan Yi

2017-01-01

A phylogenetic tree is a visual diagram of the relationship between a set of biological species. The scientists usually use it to analyze many characteristics of the species. The distance-matrix methods, such as Unweighted Pair Group Method with Arithmetic Mean and Neighbor Joining, construct a phylogenetic tree by calculating pairwise genetic distances between taxa. These methods have the computational performance issue. Although several new methods with high-performance hardware and frameworks have been proposed, the issue still exists. In this work, a novel parallel Unweighted Pair Group Method with Arithmetic Mean approach on multiple Graphics Processing Units is proposed to construct a phylogenetic tree from extremely large set of sequences. The experimental results present that the proposed approach on a DGX-1 server with 8 NVIDIA P100 graphic cards achieves approximately 3-fold to 7-fold speedup over the implementation of Unweighted Pair Group Method with Arithmetic Mean on a modern CPU and a single GPU, respectively.

Sum of the m-th Powers of n Successive Terms of an Arithmetic Sequence: b[superscript m] + (a + b)[superscript m] + (2a + b)[superscript m] ... + ((n - 1)a + b)[superscript m

ERIC Educational Resources Information Center

Gauthier, N.

2006-01-01

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

Application of Stochastic Learning Theory to Elementary Arithmetic Exercises. Technical Report No. 302. Psychology and Education Series.

ERIC Educational Resources Information Center

Wagner, William J.

The application of a linear learning model, which combines learning theory with a structural analysis of the exercises given to students, to an elementary mathematics curriculum is examined. Elementary arithmetic items taken by about 100 second-grade students on 26 weekly tests form the data base. Weekly predictions of group performance on…

It Pays to Be Organized: Organizing Arithmetic Practice around Equivalent Values Facilitates Understanding of Math Equivalence

ERIC Educational Resources Information Center

McNeil, Nicole M.; Chesney, Dana L.; Matthews, Percival G.; Fyfe, Emily R.; Petersen, Lori A.; Dunwiddie, April E.; Wheeler, Mary C.

2012-01-01

This experiment tested the hypothesis that organizing arithmetic fact practice by equivalent values facilitates children's understanding of math equivalence. Children (M age = 8 years 6 months, N = 104) were randomly assigned to 1 of 3 practice conditions: (a) equivalent values, in which problems were grouped by equivalent sums (e.g., 3 + 4 = 7, 2…

Verbal and nonverbal communication of events in learning-disability subtypes.

PubMed

Loveland, K A; Fletcher, J M; Bailey, V

1990-08-01

This study compared a group of nondisabled children (ND) with groups of learning-disabled children who were primarily impaired in reading and arithmetic skills (Reading-Arithmetic Disabled; RAD) and arithmetic but not reading (Arithmetic Disabled; AD) on a set of tasks involving comprehension and production of verbally and nonverbally presented events. Children viewed videotaped scenarios presented in verbal (narrative) and nonverbal (puppet actors) formats and were asked to describe or enact with puppets the events depicted in the stories. Rourke (1978, 1982) has shown that RAD children have problems with verbal skills, whereas AD children have problems with nonverbal skills. Consequently, it was hypothesized that children's performance in comprehending and reproducing stories would be related to the type of learning disability. Results showed that RAD children made more errors than AD children with verbal presentations and describe-responses, whereas AD children made more errors than RAD children with nonverbal presentations and enact-responses. In addition, learning disabled children were more likely than controls to misinterpret affect and motivation depicted in the stories. These results show that learning disabled children have problems with social communication skills, but that the nature of these problems varies with the type of learning disability.

Individual differences in mathematical competence predict parietal brain activation during mental calculation.

PubMed

Grabner, Roland H; Ansari, Daniel; Reishofer, Gernot; Stern, Elsbeth; Ebner, Franz; Neuper, Christa

2007-11-01

Functional neuroimaging studies have revealed that parietal brain circuits subserve arithmetic problem solving and that their recruitment dynamically changes as a function of training and development. The present study investigated whether the brain activation during mental calculation is also modulated by individual differences in mathematical competence. Twenty-five adult students were selected from a larger pool based on their performance on standardized tests of intelligence and arithmetic and divided into groups of individuals with relatively lower and higher mathematical competence. These groups did not differ in their non-numerical intelligence or age. In an fMRI block-design, participants had to verify the correctness of single-digit and multi-digit multiplication problems. Analyses revealed that the individuals with higher mathematical competence displayed stronger activation of the left angular gyrus while solving both types of arithmetic problems. Additional correlational analyses corroborated the association between individual differences in mathematical competence and angular gyrus activation, even when variability in task performance was controlled for. These findings demonstrate that the recruitment of the left angular gyrus during arithmetic problem solving underlies individual differences in mathematical ability and suggests a stronger reliance on automatic, language-mediated processes in more competent individuals.

Arithmetic memory networks established in childhood are changed by experience in adulthood

PubMed Central

Martinez-Lincoln, Amanda; Cortinas, Christina; Wicha, Nicole Y. Y.

2014-01-01

Adult bilinguals show stronger access to multiplication tables when using the language in which they learned arithmetic during childhood (LA+) than the other language (LA−), implying language-specific encoding of math facts. However, most bilinguals use LA+ throughout their life, confounding the impact of encoding and use. We tested if using arithmetic facts in LA− could reduce this LA− disadvantage. We measured event related brain potentials while bilingual teachers judged the correctness of multiplication problems in each of their languages. Critically, each teacher taught arithmetic in either LA+ or LA−. Earlier N400 peak latency was observed in both groups for the teaching than non-teaching language, showing more efficient access to these facts with use. LA+ teachers maintained an LA+ advantage, while LA− teachers showed equivalent N400 congruency effects (for incorrect versus correct solutions) in both languages. LA− teachers also showed a late positive component that may reflect conflict monitoring between their LA+ and a strong LA−. Thus, the LA− disadvantage for exact arithmetic established in early bilingual education can be mitigated by later use of LA−. PMID:25445361

Arithmetic strategy development and its domain-specific and domain-general cognitive correlates: a longitudinal study in children with persistent mathematical learning difficulties.

PubMed

Vanbinst, Kiran; Ghesquière, Pol; De Smedt, Bert

2014-11-01

Deficits in arithmetic fact retrieval constitute the hallmark of children with mathematical learning difficulties (MLD). It remains, however, unclear which cognitive deficits underpin these difficulties in arithmetic fact retrieval. Many prior studies defined MLD by considering low achievement criteria and not by additionally taking the persistence of the MLD into account. Therefore, the present longitudinal study contrasted children with persistent MLD (MLD-p; mean age: 9 years 2 months) and typically developing (TD) children (mean age: 9 years 6 months) at three time points, to explore whether differences in arithmetic strategy development were associated with differences in numerical magnitude processing, working memory and phonological processing. Our longitudinal data revealed that children with MLD-p had persistent arithmetic fact retrieval deficits at each time point. Children with MLD-p showed persistent impairments in symbolic, but not in nonsymbolic, magnitude processing at each time point. The two groups differed in phonological processing, but not in working memory. Our data indicate that both domain-specific and domain-general cognitive abilities contribute to individual differences in children's arithmetic strategy development, and that the symbolic processing of numerical magnitudes might be a particular risk factor for children with MLD-p. Copyright © 2014 Elsevier Ltd. All rights reserved.

Number Theoretic Background

NASA Astrophysics Data System (ADS)

Rudnick, Z.

Contents: 1. Introduction 2. Divisibility 2.1. Basics on Divisibility 2.2. The Greatest Common Divisor 2.3. The Euclidean Algorithm 2.4. The Diophantine Equation ax+by=c 3. Prime Numbers 3.1. The Fundamental Theorem of Arithmetic 3.2. There Are Infinitely Many Primes 3.3. The Density of Primes 3.4. Primes in Arithmetic Progressions 4. Continued Fractions 5. Modular Arithmetic 5.1. Congruences 5.2. Modular Inverses 5.3. The Chinese Remainder Theorem 5.4. The Structure of the Multiplicative Group (Z/NZ)^* 5.5. Primitive Roots 6. Quadratic Congruences 6.1. Euler's Criterion 6.2. The Legendre Symbol and Quadratic Reciprocity 7. Pell's Equation 7.1. The Group Law 7.2. Integer Solutions 7.3. Finding the Fundamental Solution 8. The Riemann Zeta Function 8.1 Analytic Continuation and Functinal Equation of ζ(s) 8.2 Connecting the Primes and the Zeros of ζ(s) 8.3 The Riemann Hypothesis References

Mathematical abilities in dyslexic children: a diffusion tensor imaging study.

PubMed

Koerte, Inga K; Willems, Anna; Muehlmann, Marc; Moll, Kristina; Cornell, Sonia; Pixner, Silvia; Steffinger, Denise; Keeser, Daniel; Heinen, Florian; Kubicki, Marek; Shenton, Martha E; Ertl-Wagner, Birgit; Schulte-Körne, Gerd

2016-09-01

Dyslexia is characterized by a deficit in language processing which mainly affects word decoding and spelling skills. In addition, children with dyslexia also show problems in mathematics. However, for the latter, the underlying structural correlates have not been investigated. Sixteen children with dyslexia (mean age 9.8 years [0.39]) and 24 typically developing children (mean age 9.9 years [0.29]) group matched for age, gender, IQ, and handedness underwent 3 T MR diffusion tensor imaging as well as cognitive testing. Tract-Based Spatial Statistics were performed to correlate behavioral data with diffusion data. Children with dyslexia performed worse than controls in standardized verbal number tasks, such as arithmetic efficiency tests (addition, subtraction, multiplication, division). In contrast, the two groups did not differ in the nonverbal number line task. Arithmetic efficiency, representing the total score of the four arithmetic tasks, multiplication, and division, correlated with diffusion measures in widespread areas of the white matter, including bilateral superior and inferior longitudinal fasciculi in children with dyslexia compared to controls. Children with dyslexia demonstrated lower performance in verbal number tasks but performed similarly to controls in a nonverbal number task. Further, an association between verbal arithmetic efficiency and diffusion measures was demonstrated in widespread areas of the white matter suggesting compensatory mechanisms in children with dyslexia compared to controls. Taken together, poor fact retrieval in children with dyslexia is likely a consequence of deficits in the language system, which not only affects literacy skills but also impacts on arithmetic skills.

Association between Abacus Training and Improvement in Response Inhibition: A Case-control Study

PubMed Central

Na, Kyoung-Sae; Lee, Soyoung Irene; Park, Jun-Ho; Jung, Han-Yong; Ryu, Jung-Hee

2015-01-01

Objective The abacus, first used in Asian countries more than 800 years ago, enables efficient arithmetic calculation via visuo-spatial configuration. We investigated whether abacus-trained children performed better on cognitive tasks and demonstrated higher levels of arithmetic abilities compared to those without such training. Methods We recruited 75 elementary school children (43 abacus-trained and 32 not so trained). Attention, memory, and arithmetic abilities were measured, and we compared the abacus with the control group. Results Children who had learned to use an abacus committed fewer commission errors and showed better arithmetic ability than did controls. We found no significant differences between children with and without abacus training in other areas of attention. Conclusion We speculate that abacus training improves response inhibition via neuroanatomical alterations of the areas that regulate such functions. Further studies are needed to confirm the association between abacus training and better response inhibition. PMID:26243843

When Generating Answers Benefits Arithmetic Skill: The Importance of Prior Knowledge

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Kmicikewycz, Alexander Oleksij

2008-01-01

People remember information better if they generate the information while studying rather than read the information. However, prior research has not investigated whether this generation effect extends to related but unstudied items and has not been conducted in classroom settings. We compared third graders' success on studied and unstudied…

Mathematics learning disabilities in girls with fragile X or Turner syndrome during late elementary school.

PubMed

Murphy, Melissa M; Mazzocco, Michèle M M

2008-01-01

The present study focuses on math and related skills among 32 girls with fragile X (n = 14) or Turner (n = 18) syndrome during late elementary school. Performance in each syndrome group was assessed relative to Full Scale IQ-matched comparison groups of girls from the general population (n = 32 and n = 89 for fragile X syndrome and Turner syndrome, respectively). Differences between girls with fragile X and their comparison group emerged on untimed arithmetic calculations, mastery of counting skills, and arithmetic problem verification accuracy. Relative to girls in the comparison group, girls with Turner syndrome did not differ on untimed arithmetic calculations or problem verification accuracy, but they had limited mastery of counting skills and longer response times to complete the problem verification task. Girls with fragile X or Turner syndrome also differed from their respective comparison groups on math-related abilities, including visual-spatial, working memory, and reading skills, and the associations between math and those related skills. Together, these findings support the notion that difficulty with math and related skills among girls with fragile X or Turner syndrome continues into late elementary school and that the profile of math and related skill difficulty distinguishes the two syndrome groups from each other.

Neurocognitive Predictors of Mathematical Processing in School-Aged Children with Spina Bifida and Their Typically Developing Peers: Attention, Working Memory, and Fine Motor Skills

PubMed Central

Raghubar, Kimberly P.; Barnes, Marcia A.; Dennis, Maureen; Cirino, Paul T.; Taylor, Heather; Landry, Susan

2015-01-01

Objective Math and attention are related in neurobiological and behavioral models of mathematical cognition. This study employed model-driven assessments of attention and math in children with spina bifida myelomeningocele (SBM), who have known math difficulties and specific attentional deficits, to more directly examine putative relations between attention and mathematical processing. The relation of other domain general abilities and math was also investigated. Method Participants were 9.5-year-old children with SBM (N = 44) and typically developing children (N = 50). Participants were administered experimental exact and approximate arithmetic tasks, and standardized measures of math fluency and calculation. Cognitive measures included the Attention Network Test (ANT), and standardized measures of fine motor skills, verbal working memory (WM), and visual-spatial WM. Results Children with SBM performed similarly to peers on exact arithmetic but more poorly on approximate and standardized arithmetic measures. On the ANT, children with SBM differed from controls on orienting attention but not alerting and executive attention. Multiple mediation models showed that: fine motor skills and verbal WM mediated the relation of group to approximate arithmetic; fine motor skills and visual-spatial WM mediated the relation of group to math fluency; and verbal and visual-spatial WM mediated the relation of group to math calculation. Attention was not a significant mediator of the effects of group for any aspect of math in this study. Conclusions Results are discussed with reference to models of attention, WM, and mathematical cognition. PMID:26011113

Neurocognitive predictors of mathematical processing in school-aged children with spina bifida and their typically developing peers: Attention, working memory, and fine motor skills.

PubMed

Raghubar, Kimberly P; Barnes, Marcia A; Dennis, Maureen; Cirino, Paul T; Taylor, Heather; Landry, Susan

2015-11-01

Math and attention are related in neurobiological and behavioral models of mathematical cognition. This study employed model-driven assessments of attention and math in children with spina bifida myelomeningocele (SBM), who have known math difficulties and specific attentional deficits, to more directly examine putative relations between attention and mathematical processing. The relation of other domain general abilities and math was also investigated. Participants were 9.5-year-old children with SBM (n = 44) and typically developing children (n = 50). Participants were administered experimental exact and approximate arithmetic tasks, and standardized measures of math fluency and calculation. Cognitive measures included the Attention Network Test (ANT), and standardized measures of fine motor skills, verbal working memory (WM), and visual-spatial WM. Children with SBM performed similarly to peers on exact arithmetic, but more poorly on approximate and standardized arithmetic measures. On the ANT, children with SBM differed from controls on orienting attention, but not on alerting and executive attention. Multiple mediation models showed that fine motor skills and verbal WM mediated the relation of group to approximate arithmetic; fine motor skills and visual-spatial WM mediated the relation of group to math fluency; and verbal and visual-spatial WM mediated the relation of group to math calculation. Attention was not a significant mediator of the effects of group for any aspect of math in this study. Results are discussed with reference to models of attention, WM, and mathematical cognition. (c) 2015 APA, all rights reserved).

A software framework for pipelined arithmetic algorithms in field programmable gate arrays

NASA Astrophysics Data System (ADS)

Kim, J. B.; Won, E.

2018-03-01

Pipelined algorithms implemented in field programmable gate arrays are extensively used for hardware triggers in the modern experimental high energy physics field and the complexity of such algorithms increases rapidly. For development of such hardware triggers, algorithms are developed in C++, ported to hardware description language for synthesizing firmware, and then ported back to C++ for simulating the firmware response down to the single bit level. We present a C++ software framework which automatically simulates and generates hardware description language code for pipelined arithmetic algorithms.

The generative basis of natural number concepts.

PubMed

Leslie, Alan M; Gelman, Rochel; Gallistel, C R

2008-06-01

Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes.

Mathematics/Arithmetic Knowledge-Based Way of Thinking and Its Maintenance Needed for Engineers

NASA Astrophysics Data System (ADS)

Harada, Shoji

Examining curriculum among universities revealed that no significant difference in math class or related subjects can be seen. However, amount and depth of those studies, in general, differed depending on content of curriculum and the level of achievement at entrance to individual university. Universalization of higher education shows that students have many problems in learning higher level of traditional math and that the memory of math they learned quickly fades away after passing in exam. It means that further development of higher math knowledgebased engineer after graduation from universities. Under these circumstances, the present author, as one of fun of math, propose how to maintain way of thinking generated by math knowledge. What necessary for engineer is to pay attention to common books, dealing with elementary mathematics or arithmetic- related matters. This surely leads engineer to nourish math/arithmetic knowledge-based way of thinking.

Developmental and Individual Differences in Understanding of Fractions

PubMed Central

Siegler, Robert S.; Pyke, Aryn A.

2014-01-01

We examined developmental and individual differences in 6th and 8th graders’ fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross sectional design. Results indicated that the difference between low achieving and higher achieving children’s fraction arithmetic knowledge, already substantial in 6th grade, was much greater in 8th grade. The fraction arithmetic knowledge of low achieving children was similar in the two grades, whereas higher achieving children showed much greater knowledge in 8th than 6th grade, despite both groups having been in the same classrooms, using the same textbooks, and having the same teachers and classmates. Individual differences in both fraction arithmetic and mathematics achievement test scores were predicted by differences in fraction magnitude knowledge and whole number division, even after the contributions of reading achievement and executive functioning were statistically controlled. Instructional implications of the findings are discussed. PMID:23244401

Efficient Probabilistic Diagnostics for Electrical Power Systems

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Chavira, Mark; Cascio, Keith; Poll, Scott; Darwiche, Adnan; Uckun, Serdar

2008-01-01

We consider in this work the probabilistic approach to model-based diagnosis when applied to electrical power systems (EPSs). Our probabilistic approach is formally well-founded, as it based on Bayesian networks and arithmetic circuits. We investigate the diagnostic task known as fault isolation, and pay special attention to meeting two of the main challenges . model development and real-time reasoning . often associated with real-world application of model-based diagnosis technologies. To address the challenge of model development, we develop a systematic approach to representing electrical power systems as Bayesian networks, supported by an easy-to-use speci.cation language. To address the real-time reasoning challenge, we compile Bayesian networks into arithmetic circuits. Arithmetic circuit evaluation supports real-time diagnosis by being predictable and fast. In essence, we introduce a high-level EPS speci.cation language from which Bayesian networks that can diagnose multiple simultaneous failures are auto-generated, and we illustrate the feasibility of using arithmetic circuits, compiled from Bayesian networks, for real-time diagnosis on real-world EPSs of interest to NASA. The experimental system is a real-world EPS, namely the Advanced Diagnostic and Prognostic Testbed (ADAPT) located at the NASA Ames Research Center. In experiments with the ADAPT Bayesian network, which currently contains 503 discrete nodes and 579 edges, we .nd high diagnostic accuracy in scenarios where one to three faults, both in components and sensors, were inserted. The time taken to compute the most probable explanation using arithmetic circuits has a small mean of 0.2625 milliseconds and standard deviation of 0.2028 milliseconds. In experiments with data from ADAPT we also show that arithmetic circuit evaluation substantially outperforms joint tree propagation and variable elimination, two alternative algorithms for diagnosis using Bayesian network inference.

[Event-related potentials in Chinese characters semantic priming and arithmetic tasks: comparative study between healthy children and children with cognitive disorder].

PubMed

Dong, Xuan; Wang, Su-hong; Yang, Yi-lin; Ren, Yan-ling; Meng, Ping; Yang, Yu-xia

2007-10-30

To explore the cognitive psychological process of healthy children and children with cognitive disorder. Single Chinese character semantic priming and arithmetic tasks were delivered to 20 8-year-old healthy children, and 20 11-year-old healthy children, and 30 children with attention deficit hyperactivity disorder, 23 children with epilepsy, and 22 age-matched normal children as controls. Electroencephalography was used. Event-related potential was distilled by BESA software. (1) During the Chinese character semantic priming, the amplitudes of N2 toward the non-related words and pseudo-words in the 8-year-old group were 12.1 microV and 11.7 microV respectively, both significantly larger than those of the 11-year-old group (3.7 microV and 4.8 microV, respectively, both P<0.05). The amplitudes of N2 and P2 toward the non-related words and pseudo-words among the children with attention deficit hyperactivity disorder were both significantly lower than those in the healthy children (both P<0.05). (2) During the arithmetic task, the latency values of P2 and P3 of addition, subtraction, and multiplication in the 8-year-old group of healthy children were all significantly longer than those of the 11-year-old group of healthy children (all P<0.05). The P3 latency of the children with epilepsy was significantly longer than that of the healthy children (P<0.05). Chinese character and arithmetic cognitive waves are steady. ERP can be used to estimate the healthy children's personality index. Quantitative indicators are helpful in diagnosis and treatment of cognitive and learning disorders.

Mathematical skills in 3- and 5-year-olds with spina bifida and their typically developing peers: a longitudinal approach.

PubMed

Barnes, Marcia A; Stubbs, Allison; Raghubar, Kimberly P; Agostino, Alba; Taylor, Heather; Landry, Susan; Fletcher, Jack M; Smith-Chant, Brenda

2011-05-01

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual-spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual-spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual-spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder.

Mathematical Skills in 3- and 5-Year-Olds with Spina Bifida and Their Typically Developing Peers: A Longitudinal Approach

PubMed Central

Barnes, Marcia A.; Stubbs, Allison; Raghubar, Kimberly P.; Agostino, Alba; Taylor, Heather; Landry, Susan; Fletcher, Jack M.; Smith-Chant, Brenda

2011-01-01

Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual–spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual–spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual–spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder. PMID:21418718

When listening to rain sounds boosts arithmetic ability

PubMed Central

De Benedetto, Francesco; Ferrari, Maria Vittoria; Ferrarini, Giorgia

2018-01-01

Studies in the literature have provided conflicting evidence about the effects of background noise or music on concurrent cognitive tasks. Some studies have shown a detrimental effect, while others have shown a beneficial effect of background auditory stimuli. The aim of this study was to investigate the influence of agitating, happy or touching music, as opposed to environmental sounds or silence, on the ability of non-musician subjects to perform arithmetic operations. Fifty university students (25 women and 25 men, 25 introverts and 25 extroverts) volunteered for the study. The participants were administered 180 easy or difficult arithmetic operations (division, multiplication, subtraction and addition) while listening to heavy rain sounds, silence or classical music. Silence was detrimental when participants were faced with difficult arithmetic operations, as it was associated with significantly worse accuracy and slower RTs than music or rain sound conditions. This finding suggests that the benefit of background stimulation was not music-specific but possibly due to an enhanced cerebral alertness level induced by the auditory stimulation. Introverts were always faster than extroverts in solving mathematical problems, except when the latter performed calculations accompanied by the sound of heavy rain, a condition that made them as fast as introverts. While the background auditory stimuli had no effect on the arithmetic ability of either group in the easy condition, it strongly affected extroverts in the difficult condition, with RTs being faster during agitating or joyful music as well as rain sounds, compared to the silent condition. For introverts, agitating music was associated with faster response times than the silent condition. This group difference may be explained on the basis of the notion that introverts have a generally higher arousal level compared to extroverts and would therefore benefit less from the background auditory stimuli. PMID:29466472

When listening to rain sounds boosts arithmetic ability.

PubMed

Proverbio, Alice Mado; De Benedetto, Francesco; Ferrari, Maria Vittoria; Ferrarini, Giorgia

2018-01-01

Studies in the literature have provided conflicting evidence about the effects of background noise or music on concurrent cognitive tasks. Some studies have shown a detrimental effect, while others have shown a beneficial effect of background auditory stimuli. The aim of this study was to investigate the influence of agitating, happy or touching music, as opposed to environmental sounds or silence, on the ability of non-musician subjects to perform arithmetic operations. Fifty university students (25 women and 25 men, 25 introverts and 25 extroverts) volunteered for the study. The participants were administered 180 easy or difficult arithmetic operations (division, multiplication, subtraction and addition) while listening to heavy rain sounds, silence or classical music. Silence was detrimental when participants were faced with difficult arithmetic operations, as it was associated with significantly worse accuracy and slower RTs than music or rain sound conditions. This finding suggests that the benefit of background stimulation was not music-specific but possibly due to an enhanced cerebral alertness level induced by the auditory stimulation. Introverts were always faster than extroverts in solving mathematical problems, except when the latter performed calculations accompanied by the sound of heavy rain, a condition that made them as fast as introverts. While the background auditory stimuli had no effect on the arithmetic ability of either group in the easy condition, it strongly affected extroverts in the difficult condition, with RTs being faster during agitating or joyful music as well as rain sounds, compared to the silent condition. For introverts, agitating music was associated with faster response times than the silent condition. This group difference may be explained on the basis of the notion that introverts have a generally higher arousal level compared to extroverts and would therefore benefit less from the background auditory stimuli.

Dissociation between exact and approximate addition in developmental dyslexia.

PubMed

Yang, Xiujie; Meng, Xiangzhi

2016-09-01

Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.

A pedagogical example of second-order arithmetic sequences applied to the construction of computer passwords by upper elementary grade students

NASA Astrophysics Data System (ADS)

Coggins, Porter E.

2015-04-01

The purpose of this paper is (1) to present how general education elementary school age students constructed computer passwords using digital root sums and second-order arithmetic sequences, (2) argue that computer password construction can be used as an engaging introduction to generate interest in elementary school students to study mathematics related to computer science, and (3) share additional mathematical ideas accessible to elementary school students that can be used to create computer passwords. This paper serves to fill a current gap in the literature regarding the integration of mathematical content accessible to upper elementary school students and aspects of computer science in general, and computer password construction in particular. In addition, the protocols presented here can serve as a hook to generate further interest in mathematics and computer science. Students learned to create a random-looking computer password by using biometric measurements of their shoe size, height, and age in months and to create a second-order arithmetic sequence, then converted the resulting numbers into characters that become their computer passwords. This password protocol can be used to introduce students to good computer password habits that can serve a foundation for a life-long awareness of data security. A refinement of the password protocol is also presented.

Genetic diversity among silkworm (Bombyx mori L., Lep., Bombycidae) germplasms revealed by microsatellites.

PubMed

Li, Muwang; Shen, Li; Xu, Anying; Miao, Xuexia; Hou, Chengxiang; Sun, Pingjiang; Zhang, Yuehua; Huang, Yongping

2005-10-01

To determine genetic relationships among strains of silkworm, Bombyx mori L., 31 strains with different origins, number of generations per year, number of molts per generation, and morphological characters were studied using simple sequence repeat (SSR) markers. Twenty-six primer pairs flanking microsatellite sequences in the silkworm genome were assayed. All were polymorphic and unambiguously separated silkworm strains from each other. A total of 188 alleles were detected with a mean value of 7.2 alleles/locus (range 2-17). The average heterozygosity value for each SSR locus ranged from 0 to 0.60, and the highest one was 0.96 (Fl0516 in 4013). The mean polymorphism index content (PIC) was 0.66 (range 0.12-0.89). Unweighted pair group method with arithmetic means (UPGMA) cluster analysis of Nei's genetic distance grouped silkworm strains based on their origin. Seven major ecotypic silkworm groups were analyzed. Principal components analysis (PCA) for SSR data support their UPGMA clustering. The results indicated that SSR markers are an efficient tool for fingerprinting cultivars and conducting genetic-diversity studies in the silkworm.

Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation.

PubMed

Rodic, Maja; Cui, Jiaxin; Malykh, Sergey; Zhou, Xinlin; Gynku, Elena I; Bogdanova, Elena L; Zueva, Dina Y; Y Bogdanova, Olga; Kovas, Yulia

2018-06-01

The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations. © 2018 The Authors British Journal of Developmental Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)

2002-01-01

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Triangle geometry processing for surface modeling and cartesian grid generation

DOEpatents

Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY

2002-09-03

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Paranoia.Ada: A diagnostic program to evaluate Ada floating-point arithmetic

NASA Technical Reports Server (NTRS)

Hjermstad, Chris

1986-01-01

Many essential software functions in the mission critical computer resource application domain depend on floating point arithmetic. Numerically intensive functions associated with the Space Station project, such as emphemeris generation or the implementation of Kalman filters, are likely to employ the floating point facilities of Ada. Paranoia.Ada appears to be a valuabe program to insure that Ada environments and their underlying hardware exhibit the precision and correctness required to satisfy mission computational requirements. As a diagnostic tool, Paranoia.Ada reveals many essential characteristics of an Ada floating point implementation. Equipped with such knowledge, programmers need not tremble before the complex task of floating point computation.

Educational skills: long-term outcome and predictors following paediatric traumatic brain injury.

PubMed

Catroppa, Cathy; Anderson, Vicki A; Muscara, Frank; Morse, Sue A; Haritou, Flora; Rosenfeld, Jeffrey V; Heinrich, Liesl M

2009-10-01

Given that reading, spelling and arithmetic skills are acquired through childhood, their development may be compromised following a childhood traumatic brain injury (TBI). The present study examined educational skills (reading accuracy, spelling and arithmetic) at a mean follow-up interval of 6.8 years post-injury in children who had sustained a mild, moderate, or severe TBI at two ages: 'Young' (age at injury: 3-7 years, n = 48) and 'Old': (age at injury: 8-12 years, n = 36). Comparisons between the young and old TBI groups resulted in inconsistent findings. While a dose-response relationship for severity was evident for the young group, this was not always the case for the old group. Significant predictors of outcome included both severity and acute intellectual function.

Efficient Boundary Extraction of BSP Solids Based on Clipping Operations.

PubMed

Wang, Charlie C L; Manocha, Dinesh

2013-01-01

We present an efficient algorithm to extract the manifold surface that approximates the boundary of a solid represented by a Binary Space Partition (BSP) tree. Our polygonization algorithm repeatedly performs clipping operations on volumetric cells that correspond to a spatial convex partition and computes the boundary by traversing the connected cells. We use point-based representations along with finite-precision arithmetic to improve the efficiency and generate the B-rep approximation of a BSP solid. The core of our polygonization method is a novel clipping algorithm that uses a set of logical operations to make it resistant to degeneracies resulting from limited precision of floating-point arithmetic. The overall BSP to B-rep conversion algorithm can accurately generate boundaries with sharp and small features, and is faster than prior methods. At the end of this paper, we use this algorithm for a few geometric processing applications including Boolean operations, model repair, and mesh reconstruction.

Age difference in numeral recognition and calculation: an event-related potential study.

PubMed

Xuan, Dong; Wang, Suhong; Yang, Yilin; Meng, Ping; Xu, Feng; Yang, Wen; Sheng, Wei; Yang, Yuxia

2007-01-01

In this study, we investigated the age difference in numeral recognition and calculation in one group of school-aged children (n = 38) and one of undergraduate students (n = 26) using the event-related potential (ERP) methods. Consistent with previous reports, the age difference was significant in behavioral results. Both numeral recognition and calculation elicited a negativity peaking at about 170-280 ms (N2) and a positivity peaking at 200-470 ms (pSW) in raw ERPs, and a difference potential (dN3) between 360 and 450 ms. The difference between the two age groups indicated that more attention resources were devoted to arithmetical tasks in school-aged children, and that school-aged children and undergraduate students appear to use different strategies to solve arithmetical problems. The analysis of frontal negativity suggested that numeral recognition and mental calculation impose greater load on working memory and executive function in schoolchildren than in undergraduate students. The topography data determined that the parietal regions were responsible for arithmetical function in humans, and there was an age-related difference in the area of cerebral activation.

Design and evaluation of online arithmetic for signal processing applications on FPGAs

NASA Astrophysics Data System (ADS)

Galli, Reto; Tenca, Alexandre F.

2001-11-01

This paper shows the design and the evaluation of on-line arithmetic modules for the most common operators used in DSP applications, using FPGAs as the target technology. The designs are highly optimized for the target technology and the common range of precision in DSP. The results are based on experimental data collected using CAD tools. All designs are synthesized for the same type of devices (Xilinx XC4000) for comparison, avoiding rough estimates of the system performance, and generating a more reliable and detailed comparison of on-line signal processing solutions with other state of the art approaches, such as distributed arithmetic. We show that on-line designs have a hard stand for basic DSP applications that use only addition and multiplication. However, we also show that on-line designs are able to overtake other approaches as the applications become more sophisticated, e.g. when data dependencies exist, or when non constant multiplicands restrict the use of other approaches.

Predicting Arithmetic Abilities: The Role of Preparatory Arithmetic Markers and Intelligence

ERIC Educational Resources Information Center

Stock, Pieter; Desoete, Annemie; Roeyers, Herbert

2009-01-01

Arithmetic abilities acquired in kindergarten are found to be strong predictors for later deficient arithmetic abilities. This longitudinal study (N = 684) was designed to examine if it was possible to predict the level of children's arithmetic abilities in first and second grade from their performance on preparatory arithmetic abilities in…

Word problems: a review of linguistic and numerical factors contributing to their difficulty

PubMed Central

Daroczy, Gabriella; Wolska, Magdalena; Meurers, Walt Detmar; Nuerk, Hans-Christoph

2015-01-01

Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group. PMID:25883575

Magnitude Representation and Working Memory Updating in Children With Arithmetic and Reading Comprehension Disabilities.

PubMed

Pelegrina, Santiago; Capodieci, Agnese; Carretti, Barbara; Cornoldi, Cesare

2015-01-01

It has been argued that children with learning disabilities (LD) encounter severe problems in working memory (WM) tasks, especially when they need to update information stored in their WM. It is not clear, however, to what extent this is due to a generally poor updating ability or to a difficulty specific to the domain to be processed. To examine this issue, two groups of children with arithmetic or reading comprehension LD and a group of typically developing children (9 to 10 years old) were assessed using two updating tasks requiring to select the smallest numbers or objects presented. The results showed that children with an arithmetic disability failed in a number updating task, but not in the object updating task. The opposite was true for the group with poor reading comprehension, whose performance was worse in the object than in the number updating task. It may be concluded that the problem of WM updating in children with LD is also due to a poor representation of the material to be updated. In addition, our findings suggest that the mental representation of the size of objects relates to the semantic representation of the objects' properties and differs from the quantitative representation of numbers. © Hammill Institute on Disabilities 2014.

Genetic fidelity and variability of micropropagated cassava plants (Manihot esculenta Crantz) evaluated using ISSR markers.

PubMed

Vidal, Á M; Vieira, L J; Ferreira, C F; Souza, F V D; Souza, A S; Ledo, C A S

2015-07-14

Molecular markers are efficient for assessing the genetic fidelity of various species of plants after in vitro culture. In this study, we evaluated the genetic fidelity and variability of micropropagated cassava plants (Manihot esculenta Crantz) using inter-simple sequence repeat markers. Twenty-two cassava accessions from the Embrapa Cassava & Fruits Germplasm Bank were used. For each accession, DNA was extracted from a plant maintained in the field and from 3 plants grown in vitro. For DNA amplification, 27 inter-simple sequence repeat primers were used, of which 24 generated 175 bands; 100 of those bands were polymorphic and were used to study genetic variability among accessions of cassava plants maintained in the field. Based on the genetic distance matrix calculated using the arithmetic complement of the Jaccard's index, genotypes were clustered using the unweighted pair group method using arithmetic averages. The number of bands per primer was 2-13, with an average of 7.3. For most micropropagated accessions, the fidelity study showed no genetic variation between plants of the same accessions maintained in the field and those maintained in vitro, confirming the high genetic fidelity of the micropropagated plants. However, genetic variability was observed among different accessions grown in the field, and clustering based on the dissimilarity matrix revealed 7 groups. Inter-simple sequence repeat markers were efficient for detecting the genetic homogeneity of cassava plants derived from meristem culture, demonstrating the reliability of this propagation system.

Cardiovascular and metabolic activity at rest and during psychological and physical challenge in normotensives and subjects with mildly elevated blood pressure.

PubMed

Sims, J; Carroll, D

1990-03-01

Heart rate, systolic and diastolic blood pressure, and respiratory and metabolic activity were recorded prior to and during mental arithmetic and a video game task in 20 young men with mildly elevated casual systolic blood pressures. Twenty-five unambiguously normotensive young men were tested under the same protocol. For pretask baseline physiological activity, group differences emerged for all cardiovascular and metabolic variables; thus the elevated blood pressure group displayed not only higher resting cardiovascular levels than normotensive subjects, but higher levels of metabolic activity too. With regard to change in physiological activity from rest to task, the group with mildly elevated blood pressure showed reliably larger increases in heart rate to the mental arithmetic task than the normotensive subjects. These effects, however, were not paralleled by group differences in metabolic activity increase. Physiological measures were also taken prior to and during graded dynamic exercise. The subsequent calculation of individual heart rate-oxygen consumption exercise regression lines allowed the comparison of actual and predicted heart rates during psychological challenge. The subjects with mildly elevated blood pressure displayed significantly greater discrepancies between actual and predicted heart rate values than normotensives during the psychological tasks in general and mental arithmetic in particular. Group differences in physiological activity during exercise largely reflected the pattern seen at rest. A possible exception here was systolic blood pressure. Not only were systolic blood pressure levels higher throughout the exercise phase for mildly elevated blood pressure subjects, but this group evidenced more of an increase from rest to exercise than the normotensives.

The Arithmetic of Aromaticity.

ERIC Educational Resources Information Center

Glidewell, Christopher; Lloyd, Douglas

1986-01-01

Explores the extent to which, in polycyclic hydrocarbons, the total pi electron population tends to form small (4n plus 2) groups and avoid the formation of 4n groups. Also discusses the relation of this trend to resonance energy stabilizations. (JN)

Students who developed logical reasoning skills reported improved confidence in drug dose calculation: Feedback from remedial maths classes.

PubMed

Shelton, Chris

2016-06-01

The safe administration of drugs is a focus of attention in healthcare. It is regarded as acceptable that a formula card or mnemonic can be used to find the correct dose and fill a prescription even though this removes any requirement for performing the underlying computation. Feedback and discussion in class reveal that confidence in arithmetic skills can be low even when students are able to pass the end of semester drug calculation exam. To see if confidence in the understanding and performance of arithmetic for drug calculations can be increased by emphasising student's innate powers of logical reasoning after reflection. Remedial classes offered for students who have declared a dislike or lack of confidence in arithmetic have been developed from student feedback adopting a reasoning by logical step methodology. Students who gave up two hours of their free learning time were observed to engage seriously with the learning methods, focussing on the innate ability to perform logical reasoning necessary for drug calculation problems. Working in small groups allowed some discussion of the route to the answer and this was followed by class discussion and reflection. The results were recorded as weekly self-assessment scores for confidence in calculation. A self-selecting group who successfully completed the end of semester drug calculation exam reported low to moderate confidence in arithmetic. After four weeks focussing on logical skills a significant increase in self-belief was measured. This continued to rise in students who remained in the classes. Many students hold a negative belief regarding their own mathematical abilities. This restricts the learning of arithmetic skills making alternate routes using mnemonics and memorised steps an attractive alternative. Practising stepwise logical reasoning skills consolidated by personal reflection has been effective in developing student's confidence and awareness of their innate powers of deduction supporting an increase in competence in drug administration. Copyright © 2016 Elsevier Ltd. All rights reserved.

A sparse matrix algorithm on the Boolean vector machine

NASA Technical Reports Server (NTRS)

Wagner, Robert A.; Patrick, Merrell L.

1988-01-01

VLSI technology is being used to implement a prototype Boolean Vector Machine (BVM), which is a large network of very small processors with equally small memories that operate in SIMD mode; these use bit-serial arithmetic, and communicate via cube-connected cycles network. The BVM's bit-serial arithmetic and the small memories of individual processors are noted to compromise the system's effectiveness in large numerical problem applications. Attention is presently given to the implementation of a basic matrix-vector iteration algorithm for space matrices of the BVM, in order to generate over 1 billion useful floating-point operations/sec for this iteration algorithm. The algorithm is expressed in a novel language designated 'BVM'.

Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

PubMed Central

Spelke, Elizabeth S.

2014-01-01

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics. PMID:24462713

Attention Contributes to Arithmetic Deficits in New-Onset Childhood Absence Epilepsy.

PubMed

Cheng, Dazhi; Yan, Xiuxian; Gao, Zhijie; Xu, Keming; Chen, Qian

2017-01-01

Neuropsychological studies indicate that new-onset childhood absence epilepsy (CAE) is associated with deficits in attention and executive functioning. However, the contribution of these deficits to impaired academic performance remains unclear. We aimed to examine whether attention and executive functioning deficits account for the academic difficulties prevalent in patients with new-onset CAE. We analyzed cognitive performance in several domains, including language, mathematics, psychomotor speed, spatial ability, memory, general intelligence, attention, and executive functioning, in 35 children with new-onset CAE and 33 control participants. Patients with new-onset CAE exhibited deficits in mathematics, general intelligence, attention, and executive functioning. Furthermore, attention deficits, as measured by a visual tracing task, accounted for impaired arithmetic performance in the new-onset CAE group. Therefore, attention deficits, rather than impaired general intelligence or executive functioning, may be responsible for arithmetic performance deficits in patients with new-onset CAE.

40 CFR 52.1923 - Best Available Retrofit Requirements (BART) for SO2 and Interstate pollutant transport provisions...

Code of Federal Regulations, 2014 CFR

2014-07-01

... combusted at any time at the steam generating unit. Daily average means the arithmetic average of the hourly... which may include, but is not limited to, monitoring results, review of operating and maintenance...

The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

PubMed

Wong, Terry Tin-Yau

2017-12-01

The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

PubMed

Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard

2018-03-01

A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.

The neuropsychological function of children with achondroplasia.

PubMed

Wigg, Kimberley; Tofts, Louise; Benson, Suzanne; Porter, Melanie

2016-11-01

The current observational study had three specific objectives: (i) to document any neuropsychological impairment in a sample of children with achondroplasia; (ii) to explore individual variability; and (iii) to determine the functional impact of any impairments. Fourteen children aged between 6 and 15 years with a medically confirmed diagnosis of achondroplasia (FGFR 3 mutation positive) underwent a comprehensive standardized neuropsychological evaluation. On average, while generally still within normal limits, significantly lower scores compared to standardized means were identified on: Full-scale IQ, verbal IQ, working memory, arithmetic, attention, executive functioning and aspects of day-to-day emotional, social, and behavioral functioning. Clinically significant levels of impairment at a group level were identified on measures of: arithmetic, attention, and executive functioning. There was variability among the group and for most measures scores ranged from impaired to within normal limits. A high percentage of children were impaired on measures of: verbal IQ, attention and executive functioning. Results of this study suggest a need for individual neuropsychological evaluation and monitoring of children with achondroplasia and suggest verbal IQ, arithmetic, attention, and executive functioning are particularly common areas of impairment. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Differentiation of strains from the Bacillus cereus group by RFLP-PFGE genomic fingerprinting.

PubMed

Otlewska, Anna; Oltuszak-Walczak, Elzbieta; Walczak, Piotr

2013-11-01

Bacillus mycoides, Bacillus pseudomycoides, Bacillus weihenstephanensis, Bacillus anthracis, Bacillus thuringiensis, and Bacillus cereus belong to the B. cereus group. The last three species are characterized by different phenotype features and pathogenicity spectrum, but it has been shown that these species are genetically closely related. The macrorestriction analysis of the genomic DNA with the NotI enzyme was used to generate polymorphism of restriction profiles for 39 food-borne isolates (B. cereus, B. mycoides) and seven reference strains (B. mycoides, B. thuringiensis, B. weihenstephanensis, and B. cereus). The PFGE method was applied to differentiate the examined strains of the B. cereus group. On the basis of the unweighted pair group method with the arithmetic mean method and Dice coefficient, the strains were divided into five clusters (types A-E), and the most numerous group was group A (25 strains). A total of 21 distinct pulsotypes were observed. The RFLP-PFGE analysis was successfully used for the differentiation and characterization of B. cereus and B. mycoides strains isolated from different food products. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Percolation on shopping and cashback electronic commerce networks

NASA Astrophysics Data System (ADS)

Fu, Tao; Chen, Yini; Qin, Zhen; Guo, Liping

2013-06-01

Many realistic networks live in the form of multiple networks, including interacting networks and interdependent networks. Here we study percolation properties of a special kind of interacting networks, namely Shopping and Cashback Electronic Commerce Networks (SCECNs). We investigate two actual SCECNs to extract their structural properties, and develop a mathematical framework based on generating functions for analyzing directed interacting networks. Then we derive the necessary and sufficient condition for the absence of the system-wide giant in- and out- component, and propose arithmetic to calculate the corresponding structural measures in the sub-critical and supercritical regimes. We apply our mathematical framework and arithmetic to those two actual SCECNs to observe its accuracy, and give some explanations on the discrepancies. We show those structural measures based on our mathematical framework and arithmetic are useful to appraise the status of SCECNs. We also find that the supercritical regime of the whole network is maintained mainly by hyperlinks between different kinds of websites, while those hyperlinks between the same kinds of websites can only enlarge the sizes of in-components and out-components.

Implicit Learning of Arithmetic Regularities Is Facilitated by Proximal Contrast

PubMed Central

Prather, Richard W.

2012-01-01

Natural number arithmetic is a simple, powerful and important symbolic system. Despite intense focus on learning in cognitive development and educational research many adults have weak knowledge of the system. In current study participants learn arithmetic principles via an implicit learning paradigm. Participants learn not by solving arithmetic equations, but through viewing and evaluating example equations, similar to the implicit learning of artificial grammars. We expand this to the symbolic arithmetic system. Specifically we find that exposure to principle-inconsistent examples facilitates the acquisition of arithmetic principle knowledge if the equations are presented to the learning in a temporally proximate fashion. The results expand on research of the implicit learning of regularities and suggest that contrasting cases, show to facilitate explicit arithmetic learning, is also relevant to implicit learning of arithmetic. PMID:23119101

Arithmetic Circuit Verification Based on Symbolic Computer Algebra

NASA Astrophysics Data System (ADS)

Watanabe, Yuki; Homma, Naofumi; Aoki, Takafumi; Higuchi, Tatsuo

This paper presents a formal approach to verify arithmetic circuits using symbolic computer algebra. Our method describes arithmetic circuits directly with high-level mathematical objects based on weighted number systems and arithmetic formulae. Such circuit description can be effectively verified by polynomial reduction techniques using Gröbner Bases. In this paper, we describe how the symbolic computer algebra can be used to describe and verify arithmetic circuits. The advantageous effects of the proposed approach are demonstrated through experimental verification of some arithmetic circuits such as multiply-accumulator and FIR filter. The result shows that the proposed approach has a definite possibility of verifying practical arithmetic circuits.

Effect of laughter on salivary flow rates and levels of chromogranin A in young adults and elderly people.

PubMed

Toda, Masahiro; Ichikawa, Hiroe

2012-11-01

Salivary chromogranin A (CgA) levels and salivary flow rates were measured to evaluate the stress relief effect of laughter on the young and the elderly. Thirty healthy volunteers (15 aged 20-25 years; 15 aged 62-83 years) performed a serial arithmetic task for 15 min and then watched a comedy video for 30 min. On a different day, as a control, they watched a non-humorous video after performing a task similar to the first one. Saliva samples were collected immediately before and after the arithmetic task, 30 min after completing the task (immediately after watching the film), and 30 min after watching the film (60 min after completing mental task). Salivary CgA levels were determined by enzyme-linked immunosorbent assay. In the elderly group, salivary flow rates, which had declined by the end of the arithmetic task, were statistically significantly higher after watching the comedy video. In the young group, salivary CgA levels, which had increased by the end of the task, had statistically significantly declined after watching the comedy video. No such post-task changes were apparent in control results; in the young group, there was a statistically significant interprotocol difference in salivary CgA levels. These findings suggest that laughter may relieve stress, particularly in the young people.

The neural circuits for arithmetic principles.

PubMed

Liu, Jie; Zhang, Han; Chen, Chuansheng; Chen, Hui; Cui, Jiaxin; Zhou, Xinlin

2017-02-15

Arithmetic principles are the regularities underlying arithmetic computation. Little is known about how the brain supports the processing of arithmetic principles. The current fMRI study examined neural activation and functional connectivity during the processing of verbalized arithmetic principles, as compared to numerical computation and general language processing. As expected, arithmetic principles elicited stronger activation in bilateral horizontal intraparietal sulcus and right supramarginal gyrus than did language processing, and stronger activation in left middle temporal lobe and left orbital part of inferior frontal gyrus than did computation. In contrast, computation elicited greater activation in bilateral horizontal intraparietal sulcus (extending to posterior superior parietal lobule) than did either arithmetic principles or language processing. Functional connectivity analysis with the psychophysiological interaction approach (PPI) showed that left temporal-parietal (MTG-HIPS) connectivity was stronger during the processing of arithmetic principle and language than during computation, whereas parietal-occipital connectivities were stronger during computation than during the processing of arithmetic principles and language. Additionally, the left fronto-parietal (orbital IFG-HIPS) connectivity was stronger during the processing of arithmetic principles than during computation. The results suggest that verbalized arithmetic principles engage a neural network that overlaps but is distinct from the networks for computation and language processing. Copyright © 2016 Elsevier Inc. All rights reserved.

Comparison of surgically induced astigmatism following different glaucoma operations.

PubMed

Tanito, Masaki; Matsuzaki, Yukari; Ikeda, Yoshifumi; Fujihara, Etsuko

2017-01-01

To compare surgically induced astigmatism (SIA) among glaucomatous eyes treated with trabeculectomy (LEC), EX-PRESS ® shunt (EXP), ab externo trabeculotomy (exLOT), or microhook ab interno trabeculotomy (μLOT). Eighty right eyes of 80 subjects who underwent LEC (n=20), EXP (n=20), exLOT (n=20), or μLOT (n=20) were included. The dataset including the best-corrected visual acuity (BCVA), intraocular pressure (IOP), and keratometry recordings preoperatively and 3 months postoperatively was collected by chart review. The means of the vector magnitude, vector meridian, and arithmetic magnitude of the preoperative and postoperative astigmatism and SIA were calculated. The correlations among the SIA magnitude, postoperative BCVA, and IOP were assessed. The mean astigmatic arithmetic magnitudes did not differ significantly ( P =0.0732) preoperatively among the four groups, but the magnitude was significantly ( P =0.0002) greater in the LEC group than the other groups postoperatively. The mean SIA vectors were calculated to be 1.01 D at 56°, 0.62 D at 74°, 0.23 D at 112°, and 0.12 D at 97° for the LEC, EXP, exLOT, and μLOT groups, respectively. The mean SIA arithmetic magnitudes were significantly ( P <0.0001) greater in the LEC group than the other groups. Three months postoperatively, the SIA magnitude was correlated positively with the logarithm of the minimum angle of resolution (logMAR) BCVA ( r =0.3538) and negatively with the IOP ( r =-0.3265); the logMAR BCVA was correlated negatively with the IOP ( r =-0.3105). EXP, exLOT, and μLOT induce less corneal astigmatism than LEC in the early postoperative period.

Comparison of surgically induced astigmatism following different glaucoma operations

PubMed Central

Tanito, Masaki; Matsuzaki, Yukari; Ikeda, Yoshifumi; Fujihara, Etsuko

2017-01-01

Aim To compare surgically induced astigmatism (SIA) among glaucomatous eyes treated with trabeculectomy (LEC), EX-PRESS® shunt (EXP), ab externo trabeculotomy (exLOT), or microhook ab interno trabeculotomy (μLOT). Subjects and methods Eighty right eyes of 80 subjects who underwent LEC (n=20), EXP (n=20), exLOT (n=20), or μLOT (n=20) were included. The dataset including the best-corrected visual acuity (BCVA), intraocular pressure (IOP), and keratometry recordings preoperatively and 3 months postoperatively was collected by chart review. The means of the vector magnitude, vector meridian, and arithmetic magnitude of the preoperative and postoperative astigmatism and SIA were calculated. The correlations among the SIA magnitude, postoperative BCVA, and IOP were assessed. Results The mean astigmatic arithmetic magnitudes did not differ significantly (P=0.0732) preoperatively among the four groups, but the magnitude was significantly (P=0.0002) greater in the LEC group than the other groups postoperatively. The mean SIA vectors were calculated to be 1.01 D at 56°, 0.62 D at 74°, 0.23 D at 112°, and 0.12 D at 97° for the LEC, EXP, exLOT, and μLOT groups, respectively. The mean SIA arithmetic magnitudes were significantly (P<0.0001) greater in the LEC group than the other groups. Three months postoperatively, the SIA magnitude was correlated positively with the logarithm of the minimum angle of resolution (logMAR) BCVA (r=0.3538) and negatively with the IOP (r=−0.3265); the logMAR BCVA was correlated negatively with the IOP (r=−0.3105). Conclusion EXP, exLOT, and μLOT induce less corneal astigmatism than LEC in the early postoperative period. PMID:29238159

Preverbal and verbal counting and computation.

PubMed

Gallistel, C R; Gelman, R

1992-08-01

We describe the preverbal system of counting and arithmetic reasoning revealed by experiments on numerical representations in animals. In this system, numerosities are represented by magnitudes, which are rapidly but inaccurately generated by the Meck and Church (1983) preverbal counting mechanism. We suggest the following. (1) The preverbal counting mechanism is the source of the implicit principles that guide the acquisition of verbal counting. (2) The preverbal system of arithmetic computation provides the framework for the assimilation of the verbal system. (3) Learning to count involves, in part, learning a mapping from the preverbal numerical magnitudes to the verbal and written number symbols and the inverse mappings from these symbols to the preverbal magnitudes. (4) Subitizing is the use of the preverbal counting process and the mapping from the resulting magnitudes to number words in order to generate rapidly the number words for small numerosities. (5) The retrieval of the number facts, which plays a central role in verbal computation, is mediated via the inverse mappings from verbal and written numbers to the preverbal magnitudes and the use of these magnitudes to find the appropriate cells in tabular arrangements of the answers. (6) This model of the fact retrieval process accounts for the salient features of the reaction time differences and error patterns revealed by experiments on mental arithmetic. (7) The application of verbal and written computational algorithms goes on in parallel with, and is to some extent guided by, preverbal computations, both in the child and in the adult.

Pre-Algebra Groups. Concepts & Applications.

ERIC Educational Resources Information Center

Montgomery County Public Schools, Rockville, MD.

Discussion material and exercises related to pre-algebra groups are provided in this five chapter manual. Chapter 1 (mappings) focuses on restricted domains, order of operations (parentheses and exponents), rules of assignment, and computer extensions. Chapter 2 considers finite number systems, including binary operations, clock arithmetic,…

Genetic analysis of 430 Chinese Cynodon dactylon accessions using sequence-related amplified polymorphism markers.

PubMed

Huang, Chunqiong; Liu, Guodao; Bai, Changjun; Wang, Wenqiang

2014-10-21

Although Cynodon dactylon (C. dactylon) is widely distributed in China, information on its genetic diversity within the germplasm pool is limited. The objective of this study was to reveal the genetic variation and relationships of 430 C. dactylon accessions collected from 22 Chinese provinces using sequence-related amplified polymorphism (SRAP) markers. Fifteen primer pairs were used to amplify specific C. dactylon genomic sequences. A total of 481 SRAP fragments were generated, with fragment sizes ranging from 260-1800 base pairs (bp). Genetic similarity coefficients (GSC) among the 430 accessions averaged 0.72 and ranged from 0.53-0.96. Cluster analysis conducted by two methods, namely the unweighted pair-group method with arithmetic averages (UPGMA) and principle coordinate analysis (PCoA), separated the accessions into eight distinct groups. Our findings verify that Chinese C. dactylon germplasms have rich genetic diversity, which is an excellent basis for C. dactylon breeding for new cultivars.

Knowing, Applying, and Reasoning about Arithmetic: Roles of Domain-General and Numerical Skills in Multiple Domains of Arithmetic Learning

ERIC Educational Resources Information Center

Zhang, Xiao; Räsänen, Pekka; Koponen, Tuire; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik

2017-01-01

The longitudinal relations of domain-general and numerical skills at ages 6-7 years to 3 cognitive domains of arithmetic learning, namely knowing (written computation), applying (arithmetic word problems), and reasoning (arithmetic reasoning) at age 11, were examined for a representative sample of 378 Finnish children. The results showed that…

Children's use of decomposition strategies mediates the visuospatial memory and arithmetic accuracy relation.

PubMed

Foley, Alana E; Vasilyeva, Marina; Laski, Elida V

2017-06-01

This study examined the mediating role of children's use of decomposition strategies in the relation between visuospatial memory (VSM) and arithmetic accuracy. Children (N = 78; Age M = 9.36) completed assessments of VSM, arithmetic strategies, and arithmetic accuracy. Consistent with previous findings, VSM predicted arithmetic accuracy in children. Extending previous findings, the current study showed that the relation between VSM and arithmetic performance was mediated by the frequency of children's use of decomposition strategies. Identifying the role of arithmetic strategies in this relation has implications for increasing the math performance of children with lower VSM. Statement of contribution What is already known on this subject? The link between children's visuospatial working memory and arithmetic accuracy is well documented. Frequency of decomposition strategy use is positively related to children's arithmetic accuracy. Children's spatial skill positively predicts the frequency with which they use decomposition. What does this study add? Short-term visuospatial memory (VSM) positively relates to the frequency of children's decomposition use. Decomposition use mediates the relation between short-term VSM and arithmetic accuracy. Children with limited short-term VSM may struggle to use decomposition, decreasing accuracy. © 2016 The British Psychological Society.

Reading instead of reasoning? Predictors of arithmetic skills in children with cochlear implants.

PubMed

Huber, Maria; Kipman, Ulrike; Pletzer, Belinda

2014-07-01

The aim of the present study was to evaluate whether the arithmetic achievement of children with cochlear implants (CI) was lower or comparable to that of their normal hearing peers and to identify predictors of arithmetic achievement in children with CI. In particular we related the arithmetic achievement of children with CI to nonverbal IQ, reading skills and hearing variables. 23 children with CI (onset of hearing loss in the first 24 months, cochlear implantation in the first 60 months of life, atleast 3 years of hearing experience with the first CI) and 23 normal hearing peers matched by age, gender, and social background participated in this case control study. All attended grades two to four in primary schools. To assess their arithmetic achievement, all children completed the "Arithmetic Operations" part of the "Heidelberger Rechentest" (HRT), a German arithmetic test. To assess reading skills and nonverbal intelligence as potential predictors of arithmetic achievement, all children completed the "Salzburger Lesetest" (SLS), a German reading screening, and the Culture Fair Intelligence Test (CFIT), a nonverbal intelligence test. Children with CI did not differ significantly from hearing children in their arithmetic achievement. Correlation and regression analyses revealed that in children with CI, arithmetic achievement was significantly (positively) related to reading skills, but not to nonverbal IQ. Reading skills and nonverbal IQ were not related to each other. In normal hearing children, arithmetic achievement was significantly (positively) related to nonverbal IQ, but not to reading skills. Reading skills and nonverbal IQ were positively correlated. Hearing variables were not related to arithmetic achievement. Children with CI do not show lower performance in non-verbal arithmetic tasks, compared to normal hearing peers. Copyright © 2014. Published by Elsevier Ireland Ltd.

Calculator Use Need Not Undermine Direct-Access Ability: The Roles of Retrieval, Calculation, and Calculator Use in the Acquisition of Arithmetic Facts

ERIC Educational Resources Information Center

Pyke, Aryn A.; LeFevre, Jo-Anne

2011-01-01

Why is subsequent recall sometimes better for self-generated answers than for answers obtained from an external source (e.g., calculator)? In this study, we explore the relative contribution of 2 processes, recall attempts and self-computation, to this "generation effect" (i.e., enhanced answer recall relative to when problems are practiced with a…

Subpicosecond Optical Digital Computation Using Conjugate Parametric Generators

DTIC Science & Technology

1989-03-31

Using Phase Conjugate Farametric Generators ..... 12. PERSONAL AUTHOR(S) Alfano, Robert- Eichmann . George; Dorsinville. Roger! Li. Yao 13a. TYPE OF...conjugation-based optical residue arithmetic processor," Y. Li, G. Eichmann , R. Dorsinville, and R. R. Alfano, Opt. Lett. 13, (1988). [2] "Parallel ultrafast...optical digital and symbolic computation via optical phase conjugation," Y. Li, G. Eichmann , R. Dorsinville, Appl. Opt. 27, 2025 (1988). [3

Sensory trigeminal ULF-TENS stimulation reduces HRV response to experimentally induced arithmetic stress: A randomized clinical trial.

PubMed

Monaco, Annalisa; Cattaneo, Ruggero; Ortu, Eleonora; Constantinescu, Marian Vladimir; Pietropaoli, Davide

2017-05-01

Ultra Low Frequency Transcutaneous Electric Nervous Stimulation (ULF-TENS) is extensively used for pain relief and for the diagnosis and treatment of temporomandibular disorders (TMD). In addition to its local effects, ULF-TENS acts on the autonomic nervous system (ANS), with particular reference to the periaqueductal gray (PAG), promoting the release of endogenous opioids and modulating descending pain systems. It has been suggested that the PAG participates in the coupling between the emotional stimulus and the appropriate behavioral autonomic response. This function is successfully investigated by HRV. Therefore, our goal is to investigate the effects of trigeminal ULF-TENS stimulation on autonomic behavior in terms of HRV and respiratory parameters during an experimentally-induced arithmetic stress test in healthy subjects. Thirty healthy women between 25 and 35years of age were enrolled and randomly assigned to either the control (TENS stimulation off) or test group (TENS stimulation on). Heart (HR, LF, HF, LF/HF ratio, DET, RMSSD, PNN50, RR) and respiratory (BR) rate were evaluated under basal, T1 (TENS off/on), and stress (mathematical task) conditions. Results showed that HRV parameters and BR significantly changed during the arithmetic stress paradigm (p<0.01). Independently of stress conditions, TENS and control group could be discriminated only by non-linear HRV data, namely RR and DET (p=0.038 and p=0.027, respectively). During the arithmetic task, LF/HF ratio was the most sensitive parameter to discriminate between groups (p=0.019). Our data suggest that trigeminal sensory ULF-TENS reduces the autonomic response in terms of HRV and BR during acute mental stress in healthy subjects. Future directions of our work aim at applying the HRV and BR analysis, with and without TENS stimulation, to individuals with dysfunctional ANS among those with TMD. Copyright © 2017 Elsevier Inc. All rights reserved.

Exploring the relationship between math anxiety and gender through implicit measurement

PubMed Central

Rubinsten, Orly; Bialik, Noam; Solar, Yael

2012-01-01

Math anxiety, defined as a negative affective response to mathematics, is suggested as a strong antecedent for the low visibility of women in the science and engineering workforce. However, the assumption of gender differences in math anxiety is still being studied and results are inconclusive, probably due to the use of explicit measures such as direct questionnaires. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in males and females by using a novel affective priming task as an indirect measure. Specifically, university students (23 males and 30 females) completed a priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative, or related to mathematics). Participants were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication, or division) was true or false. People are typically found to respond to target stimuli more rapidly after presentation of an affectively related prime than after an affectively unrelated one. In the current study, shorter response latencies for positive as compared to negative affective primes were found in the male group. An affective priming effect was found in the female group as well, but with a reversed pattern. That is, significantly shorter response latencies were observed in the female group for negative as compared to positive targets. That is, for females, negative affective primes act as affectively related to simple arithmetic problems. In contrast, males associated positive affect with simple arithmetic. In addition, only females with lower or insignificant negative affect toward arithmetic study at faculties of mathematics and science. We discuss the advantages of examining pure anxiety factors with implicit measures which are free of response factors. In addition it is suggested that environmental factors may enhance the association between math achievements and math anxiety in females. PMID:23087633

Exploring the relationship between math anxiety and gender through implicit measurement.

PubMed

Rubinsten, Orly; Bialik, Noam; Solar, Yael

2012-01-01

Math anxiety, defined as a negative affective response to mathematics, is suggested as a strong antecedent for the low visibility of women in the science and engineering workforce. However, the assumption of gender differences in math anxiety is still being studied and results are inconclusive, probably due to the use of explicit measures such as direct questionnaires. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in males and females by using a novel affective priming task as an indirect measure. Specifically, university students (23 males and 30 females) completed a priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative, or related to mathematics). Participants were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication, or division) was true or false. People are typically found to respond to target stimuli more rapidly after presentation of an affectively related prime than after an affectively unrelated one. In the current study, shorter response latencies for positive as compared to negative affective primes were found in the male group. An affective priming effect was found in the female group as well, but with a reversed pattern. That is, significantly shorter response latencies were observed in the female group for negative as compared to positive targets. That is, for females, negative affective primes act as affectively related to simple arithmetic problems. In contrast, males associated positive affect with simple arithmetic. In addition, only females with lower or insignificant negative affect toward arithmetic study at faculties of mathematics and science. We discuss the advantages of examining pure anxiety factors with implicit measures which are free of response factors. In addition it is suggested that environmental factors may enhance the association between math achievements and math anxiety in females.

Math Wonders to Inspire Teachers and Students.

ERIC Educational Resources Information Center

Posamentier, Alfred S.

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

Genetic Diversity Analysis of Medicinally Important Horticultural Crop Aegle marmelos by ISSR Markers.

PubMed

Mujeeb, Farina; Bajpai, Preeti; Pathak, Neelam; Verma, Smita Rastogi

2017-01-01

Inter simple sequence repeat (ISSR) markers help in identifying and determining the extent of genetic diversity in cultivars. Here, we describe their application in determining the genetic diversity of bael (Aegle marmelos Corr.). Universal ISSR primers are selected and their marker characteristics such as polymorphism information content, effective multiplex ratio and marker index have been evaluated. ISSR-PCR is then performed using universal ISSR primers to generate polymorphic bands. This information is used to determine the degree of genetic similarity among the bael varieties/accessions by cluster analysis using unweighted pair-group method with arithmetic averages (UPGMA). This technology is valuable for biodiversity conservation and for making an efficient choice of parents in breeding programs.

On the classification of weakly integral modular categories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruillard, Paul; Galindo, César; Ng, Siu-Hung

In this paper we classify all modular categories of dimension 4m, where m is an odd square-free integer, and all rank 6 and rank 7 weakly integral modular categories. This completes the classification of weakly integral modular categories through rank 7. In particular, our results imply that all integral modular categories of rank at most 7 are pointed (that is, every simple object has dimension 1). All the non-integral (but weakly integral) modular categories of ranks 6 and 7 have dimension 4m, with m an odd square free integer, so their classification is an application of our main result. Themore » classification of rank 7 integral modular categories is facilitated by an analysis of the two group actions on modular categories: the Galois group of the field generated by the entries of the S-matrix and the group of invertible isomorphism classes of objects. We derive some valuable arithmetic consequences from these actions.« less

Assessing hemispheric specialization for processing arithmetic skills in adults: A functional transcranial doppler ultrasonography (fTCD) study.

PubMed

Connaughton, Veronica M; Amiruddin, Azhani; Clunies-Ross, Karen L; French, Noel; Fox, Allison M

2017-05-01

A major model of the cerebral circuits that underpin arithmetic calculation is the triple-code model of numerical processing. This model proposes that the lateralization of mathematical operations is organized across three circuits: a left-hemispheric dominant verbal code; a bilateral magnitude representation of numbers and a bilateral Arabic number code. This study simultaneously measured the blood flow of both middle cerebral arteries using functional transcranial Doppler ultrasonography to assess hemispheric specialization during the performance of both language and arithmetic tasks. The propositions of the triple-code model were assessed in a non-clinical adult group by measuring cerebral blood flow during the performance of multiplication and subtraction problems. Participants were 17 adults aged between 18-27 years. We obtained laterality indices for each type of mathematical operation and compared these in participants with left-hemispheric language dominance. It was hypothesized that blood flow would lateralize to the left hemisphere during the performance of multiplication operations, but would not lateralize during the performance of subtraction operations. Hemispheric blood flow was significantly left lateralized during the multiplication task, but was not lateralized during the subtraction task. Compared to high spatial resolution neuroimaging techniques previously used to measure cerebral lateralization, functional transcranial Doppler ultrasonography is a cost-effective measure that provides a superior temporal representation of arithmetic cognition. These results provide support for the triple-code model of arithmetic processing and offer complementary evidence that multiplication operations are processed differently in the adult brain compared to subtraction operations. Copyright © 2017 Elsevier B.V. All rights reserved.

Unpacking symbolic number comparison and its relation with arithmetic in adults.

PubMed

Sasanguie, Delphine; Lyons, Ian M; De Smedt, Bert; Reynvoet, Bert

2017-08-01

Symbolic number - or digit - comparison has been a central tool in the domain of numerical cognition for decades. More recently, individual differences in performance on this task have been shown to robustly relate to individual differences in more complex math processing - a result that has been replicated across many different age groups. In this study, we 'unpack' the underlying components of digit comparison (i.e. digit identification, digit to number-word matching, digit ordering and general comparison) in a sample of adults. In a first experiment, we showed that digit comparison performance was most strongly related to digit ordering ability - i.e., the ability to judge whether symbolic numbers are in numerical order. Furthermore, path analyses indicated that the relation between digit comparison and arithmetic was partly mediated by digit ordering and fully mediated when non-numerical (letter) ordering was also entered into the model. In a second experiment, we examined whether a general order working memory component could account for the relation between digit comparison and arithmetic. It could not. Instead, results were more consistent with the notion that fluent access and activation of long-term stored associations between numbers explains the relation between arithmetic and both digit comparison and digit ordering tasks. Copyright © 2017 Elsevier B.V. All rights reserved.

Working memory and arithmetic calculation in children: the contributory roles of processing speed, short-term memory, and reading.

PubMed

Berg, Derek H

2008-04-01

The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing speed, short-term memory, working memory, and reading to arithmetic calculation in children. Results suggested four important findings. First, processing speed emerged as a significant contributor of arithmetic calculation only in relation to age-related differences in the general sample. Second, processing speed and short-term memory did not eliminate the contribution of working memory to arithmetic calculation. Third, individual working memory components--verbal working memory and visual-spatial working memory--each contributed unique variance to arithmetic calculation in the presence of all other variables. Fourth, a full model indicated that chronological age remained a significant contributor to arithmetic calculation in the presence of significant contributions from all other variables. Results are discussed in terms of directions for future research on working memory in arithmetic calculation.

Computational Performance of Group IV Personnel in Vocational Training Programs. Final Report.

ERIC Educational Resources Information Center

Main, Ray E.; Harrigan, Robert J.

The document evaluates Navy Group Four personnel gains in basic arithmetic skills after taking experimental courses in linear measurement and recipe conversion. Categorized as Mental Group Four by receiving scores from the 10th to the 30th percentile of the Armed Forces Qualification Test, trainees received instruction tailored to the level of…

IQ of four-year-olds who go on to develop dyslexia.

PubMed

van Bergen, Elsje; de Jong, Peter F; Maassen, Ben; Krikhaar, Evelien; Plakas, Anna; van der Leij, Aryan

2014-01-01

Do children who go on to develop dyslexia show normal verbal and nonverbal development before reading onset? According to the aptitude-achievement discrepancy model, dyslexia is defined as a discrepancy between intelligence and reading achievement. One of the underlying assumptions is that the general cognitive development of children who fail to learn to read has been normal. The current study tests this assumption. In addition, we investigated whether possible IQ deficits are uniquely related to later reading or are also related to arithmetic. Four-year-olds (N = 212) with and without familial risk for dyslexia were assessed on 10 IQ subtests. Reading and arithmetic skills were measured 4 years later, at the end of Grade 2. Relative to the controls, the at-risk group without dyslexia had subtle impairments only in the verbal domain, whereas the at-risk group with dyslexia lagged behind across IQ tasks. Nonverbal IQ was associated with both reading and arithmetic, whereas verbal IQ was uniquely related to later reading. The children who went on to develop dyslexia performed relatively poorly in both verbal and nonverbal abilities at age 4, which challenges the discrepancy model. Furthermore, we discuss possible causal and epiphenomenal models explaining the links between early IQ and later reading. © Hammill Institute on Disabilities 2013.

Visuospatial and Mathematical Dysfunction in Major Depressive Disorder and/or Panic Disorder: A Study of Parietal Functioning

PubMed Central

Nelson, Brady D.; Shankman, Stewart A.

2015-01-01

The parietal cortex is critical for several different cognitive functions, including visuospatial processing and mathematical abilities. There is strong evidence indicating parietal dysfunction in depression. However, it is less clear whether anxiety is associated with parietal dysfunction, and whether comorbid depression and anxiety is associated with greater impairment. The present study compared participants with major depression (MDD), panic disorder (PD), comorbid MDD/PD, and controls on neuropsychological measures of visuospatial processing, Judgment of Line Orientation (JLO), and mathematical abilities, Wide Range Achievement Arithmetic (WRAT-Arithmetic). Only comorbid MDD/PD was associated with decreased performance on JLO, whereas all psychopathological groups exhibited comparably decreased performance on WRAT-Arithmetic. Furthermore, the results were not accounted for by other comorbid disorders, medication use, or psychopathology severity. The present study suggests comorbid depression and anxious arousal is associated with impairment in visuospatial processing and provides novel evidence indicating mathematical deficits across depression and/or anxiety. Implications for understanding parietal dysfunction in internalizing psychopathology are discussed. PMID:25707308

Subitizing and Counting in Typical and Atypical Development

ERIC Educational Resources Information Center

Schleifer, Patrick; Landerl, Karin

2011-01-01

Enumeration performance in standard dot counting paradigms was investigated for different age groups with typical and atypically poor development of arithmetic skills. Experiment 1 showed a high correspondence between response times and saccadic frequencies for four age groups with typical development. Age differences were more marked for the…

What basic number processing measures in kindergarten explain unique variability in first-grade arithmetic proficiency?

PubMed

Bartelet, Dimona; Vaessen, Anniek; Blomert, Leo; Ansari, Daniel

2014-01-01

Relations between children's mathematics achievement and their basic number processing skills have been reported in both cross-sectional and longitudinal studies. Yet, some key questions are currently unresolved, including which kindergarten skills uniquely predict children's arithmetic fluency during the first year of formal schooling and the degree to which predictors are contingent on children's level of arithmetic proficiency. The current study assessed kindergarteners' non-symbolic and symbolic number processing efficiency. In addition, the contribution of children's underlying magnitude representations to differences in arithmetic achievement was assessed. Subsequently, in January of Grade 1, their arithmetic proficiency was assessed. Hierarchical regression analysis revealed that children's efficiency to compare digits, count, and estimate numerosities uniquely predicted arithmetic differences above and beyond the non-numerical factors included. Moreover, quantile regression analysis indicated that symbolic number processing efficiency was consistently a significant predictor of arithmetic achievement scores regardless of children's level of arithmetic proficiency, whereas their non-symbolic number processing efficiency was not. Finally, none of the task-specific effects indexing children's representational precision was significantly associated with arithmetic fluency. The implications of the results are 2-fold. First, the findings indicate that children's efficiency to process symbols is important for the development of their arithmetic fluency in Grade 1 above and beyond the influence of non-numerical factors. Second, the impact of children's non-symbolic number processing skills does not depend on their arithmetic achievement level given that they are selected from a nonclinical population. Copyright © 2013 Elsevier Inc. All rights reserved.

Measuring Arithmetic: A Psychometric Approach to Understanding Formatting Effects and Domain Specificity

ERIC Educational Resources Information Center

Rhodes, Katherine T.; Branum-Martin, Lee; Washington, Julie A.; Fuchs, Lynn S.

2017-01-01

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

Personal Experience and Arithmetic Meaning in Semantic Dementia

ERIC Educational Resources Information Center

Julien, Camille L.; Neary, David; Snowden, Julie S.

2010-01-01

Arithmetic skills are generally claimed to be preserved in semantic dementia (SD), suggesting functional independence of arithmetic knowledge from other aspects of semantic memory. However, in a recent case series analysis we showed that arithmetic performance in SD is not entirely normal. The finding of a direct association between severity of…

Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia.

PubMed

Kucian, Karin; Zuber, Isabelle; Kohn, Juliane; Poltz, Nadine; Wyschkon, Anne; Esser, Günter; von Aster, Michael

2018-01-01

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (= negative math priming effect ).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task.

Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia

PubMed Central

Kucian, Karin; Zuber, Isabelle; Kohn, Juliane; Poltz, Nadine; Wyschkon, Anne; Esser, Günter; von Aster, Michael

2018-01-01

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (=negative math priming effect).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task. PMID:29755376

A Two-Minute Paper-and-Pencil Test of Symbolic and Nonsymbolic Numerical Magnitude Processing Explains Variability in Primary School Children's Arithmetic Competence

PubMed Central

Nosworthy, Nadia; Bugden, Stephanie; Archibald, Lisa; Evans, Barrie; Ansari, Daniel

2013-01-01

Recently, there has been a growing emphasis on basic number processing competencies (such as the ability to judge which of two numbers is larger) and their role in predicting individual differences in school-relevant math achievement. Children’s ability to compare both symbolic (e.g. Arabic numerals) and nonsymbolic (e.g. dot arrays) magnitudes has been found to correlate with their math achievement. The available evidence, however, has focused on computerized paradigms, which may not always be suitable for universal, quick application in the classroom. Furthermore, it is currently unclear whether both symbolic and nonsymbolic magnitude comparison are related to children’s performance on tests of arithmetic competence and whether either of these factors relate to arithmetic achievement over and above other factors such as working memory and reading ability. In order to address these outstanding issues, we designed a quick (2 minute) paper-and-pencil tool to assess children’s ability to compare symbolic and nonsymbolic numerical magnitudes and assessed the degree to which performance on this measure explains individual differences in achievement. Children were required to cross out the larger of two, single-digit numerical magnitudes under time constraints. Results from a group of 160 children from grades 1–3 revealed that both symbolic and nonsymbolic number comparison accuracy were related to individual differences in arithmetic achievement. However, only symbolic number comparison performance accounted for unique variance in arithmetic achievement. The theoretical and practical implications of these findings are discussed which include the use of this measure as a possible tool for identifying students at risk for future difficulties in mathematics. PMID:23844126

Early but not late blindness leads to enhanced arithmetic and working memory abilities.

PubMed

Dormal, Valérie; Crollen, Virginie; Baumans, Christine; Lepore, Franco; Collignon, Olivier

2016-10-01

Behavioural and neurophysiological evidence suggest that vision plays an important role in the emergence and development of arithmetic abilities. However, how visual deprivation impacts on the development of arithmetic processing remains poorly understood. We compared the performances of early (EB), late blind (LB) and sighted control (SC) individuals during various arithmetic tasks involving addition, subtraction and multiplication of various complexities. We also assessed working memory (WM) performances to determine if they relate to a blind person's arithmetic capacities. Results showed that EB participants performed better than LB and SC in arithmetic tasks, especially in conditions in which verbal routines and WM abilities are needed. Moreover, EB participants also showed higher WM abilities. Together, our findings demonstrate that the absence of developmental vision does not prevent the development of refined arithmetic skills and can even trigger the refinement of these abilities in specific tasks. Copyright © 2016 Elsevier Ltd. All rights reserved.

The cognitive foundations of early arithmetic skills: It is counting and number judgment, but not finger gnosis, that count.

PubMed

Long, Imogen; Malone, Stephanie A; Tolan, Anne; Burgoyne, Kelly; Heron-Delaney, Michelle; Witteveen, Kate; Hulme, Charles

2016-12-01

Following on from ideas developed by Gerstmann, a body of work has suggested that impairments in finger gnosis may be causally related to children's difficulties in learning arithmetic. We report a study with a large sample of typically developing children (N=197) in which we assessed finger gnosis and arithmetic along with a range of other relevant cognitive predictors of arithmetic skills (vocabulary, counting, and symbolic and nonsymbolic magnitude judgments). Contrary to some earlier claims, we found no meaningful association between finger gnosis and arithmetic skills. Counting and symbolic magnitude comparison were, however, powerful predictors of arithmetic skills, replicating a number of earlier findings. Our findings seriously question theories that posit either a simple association or a causal connection between finger gnosis and the development of arithmetic skills. Crown Copyright © 2016. Published by Elsevier Inc. All rights reserved.

Effects of Classification Exposure upon Numerical Achievement of Educable Mentally Retarded Children.

ERIC Educational Resources Information Center

Funk, Kerri L.; Tseng, M. S.

Two groups of 32 educable mentally retarded children (ages 7 to 14 years) were compared as to their arithmetic and classification performances attributable to the presence or absence of a 4 1/2 week exposure to classification tasks. The randomized block pretest-posttest design was used. The experimental group and the control group were matched on…

[Acquisition of arithmetic knowledge].

PubMed

Fayol, Michel

2008-01-01

The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3).

The Development of Arithmetic Principle Knowledge: How Do We Know What Learners Know?

ERIC Educational Resources Information Center

Prather, Richard W.; Alibali, Martha W.

2009-01-01

This paper reviews research on learners' knowledge of three arithmetic principles: "Commutativity", "Relation to Operands", and "Inversion." Studies of arithmetic principle knowledge vary along several dimensions, including the age of the participants, the context in which the arithmetic is presented, and most importantly, the type of knowledge…

How to interpret cognitive training studies: A reply to Lindskog & Winman

PubMed Central

Park, Joonkoo; Brannon, Elizabeth M.

2017-01-01

In our previous studies, we demonstrated that repeated training on an approximate arithmetic task selectively improves symbolic arithmetic performance (Park & Brannon, 2013, 2014). We proposed that mental manipulation of quantity is the common cognitive component between approximate arithmetic and symbolic arithmetic, driving the causal relationship between the two. In a commentary to our work, Lindskog and Winman argue that there is no evidence of performance improvement during approximate arithmetic training and that this challenges the proposed causal relationship between approximate arithmetic and symbolic arithmetic. Here, we argue that causality in cognitive training experiments is interpreted from the selectivity of transfer effects and does not hinge upon improved performance in the training task. This is because changes in the unobservable cognitive elements underlying the transfer effect may not be observable from performance measures in the training task. We also question the validity of Lindskog and Winman’s simulation approach for testing for a training effect, given that simulations require a valid and sufficient model of a decision process, which is often difficult to achieve. Finally we provide an empirical approach to testing the training effects in adaptive training. Our analysis reveals new evidence that approximate arithmetic performance improved over the course of training in Park and Brannon (2014). We maintain that our data supports the conclusion that approximate arithmetic training leads to improvement in symbolic arithmetic driven by the common cognitive component of mental quantity manipulation. PMID:26972469

The neural correlates of mental arithmetic in adolescents: a longitudinal fNIRS study.

PubMed

Artemenko, Christina; Soltanlou, Mojtaba; Ehlis, Ann-Christine; Nuerk, Hans-Christoph; Dresler, Thomas

2018-03-10

Arithmetic processing in adults is known to rely on a frontal-parietal network. However, neurocognitive research focusing on the neural and behavioral correlates of arithmetic development has been scarce, even though the acquisition of arithmetic skills is accompanied by changes within the fronto-parietal network of the developing brain. Furthermore, experimental procedures are typically adjusted to constraints of functional magnetic resonance imaging, which may not reflect natural settings in which children and adolescents actually perform arithmetic. Therefore, we investigated the longitudinal neurocognitive development of processes involved in performing the four basic arithmetic operations in 19 adolescents. By using functional near-infrared spectroscopy, we were able to use an ecologically valid task, i.e., a written production paradigm. A common pattern of activation in the bilateral fronto-parietal network for arithmetic processing was found for all basic arithmetic operations. Moreover, evidence was obtained for decreasing activation during subtraction over the course of 1 year in middle and inferior frontal gyri, and increased activation during addition and multiplication in angular and middle temporal gyri. In the self-paced block design, parietal activation in multiplication and left angular and temporal activation in addition were observed to be higher for simple than for complex blocks, reflecting an inverse effect of arithmetic complexity. In general, the findings suggest that the brain network for arithmetic processing is already established in 12-14 year-old adolescents, but still undergoes developmental changes.

Practising Arithmetic Using Educational Video Games with an Interpersonal Computer

ERIC Educational Resources Information Center

Beserra, Vagner; Nussbaum, Miguel; Zeni, Ricardo; Rodriguez, Werner; Wurman, Gabriel

2014-01-01

Studies show the positive effects that video games can have on student performance and attitude towards learning. In the past few years, strategies have been generated to optimize the use of technological resources with the aim of facilitating widespread adoption of technology in the classroom. Given its low acquisition and maintenance costs, the…

Text-interpreter language for flexible generation of patient notes and instructions.

PubMed

Forker, T S

1992-01-01

An interpreted computer language has been developed along with a windowed user interface and multi-printer-support formatter to allow preparation of documentation of patient visits, including progress notes, prescriptions, excuses for work/school, outpatient laboratory requisitions, and patient instructions. Input is by trackball or mouse with little or no keyboard skill required. For clinical problems with specific protocols, the clinician can be prompted with problem-specific items of history, exam, and lab data to be gathered and documented. The language implements a number of text-related commands as well as branching logic and arithmetic commands. In addition to generating text, it is simple to implement arithmetic calculations such as weight-specific drug dosages; multiple branching decision-support protocols for paramedical personnel (or physicians); and calculation of clinical scores (e.g., coma or trauma scores) while simultaneously documenting the status of each component of the score. ASCII text files produced by the interpreter are available for computerized quality audit. Interpreter instructions are contained in text files users can customize with any text editor.

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

PubMed Central

Szkudlarek, Emily; Brannon, Elizabeth M.

2018-01-01

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children (n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic training improves early informal, but not formal, math skills. PMID:29867624

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers.

PubMed

Szkudlarek, Emily; Brannon, Elizabeth M

2018-01-01

Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children ( n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic training improves early informal, but not formal, math skills.

Application of a Taxonomical Structure for Classifying Goods Procured by the Federal Government

DTIC Science & Technology

1991-12-01

between all pairs of objects. Also called a "tree" or "phenogram". "• UPGMA Clustering Method- (Un--weighted pair-group method using weighted averages...clustering arrangement, specifically, the unweighted pair-group method using arithmetic averages ( UPGMA ) (more commonly known as the 49 average linkage method

Numerical and arithmetical cognition: a longitudinal study of process and concept deficits in children with learning disability.

PubMed

Geary, D C; Hamson, C O; Hoard, M K

2000-11-01

Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade = 82 months), children with IQ scores in the low-average to high-average range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD). These children (n = 42), a group of children who showed variable achievement test performance across grades (n = 16), and a control group of academically normal peers (n = 35) were administered a series of experimental and psychometric tasks. The tasks assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, the ease of activation of phonetic representations of words and numbers, and spatial abilities. The children with variable achievement test performance did not differ from the academically normal children in any cognitive domain, whereas the children in the LD groups showed specific patterns of cognitive deficit, above and beyond the influence of IQ. Discussion focuses on the similarities and differences across the groups of LD children. Copyright 2000 Academic Press.

Conclusiveness of natural languages and recognition of images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wojcik, Z.M.

1983-01-01

The conclusiveness is investigated using recognition processes and one-one correspondence between expressions of a natural language and graphs representing events. The graphs, as conceived in psycholinguistics, are obtained as a result of perception processes. It is possible to generate and process the graphs automatically, using computers and then to convert the resulting graphs into expressions of a natural language. Correctness and conclusiveness of the graphs and sentences are investigated using the fundamental condition for events representation processes. Some consequences of the conclusiveness are discussed, e.g. undecidability of arithmetic, human brain assymetry, correctness of statistical calculations and operations research. It ismore » suggested that the group theory should be imposed on mathematical models of any real system. Proof of the fundamental condition is also presented. 14 references.« less

CADNA: a library for estimating round-off error propagation

NASA Astrophysics Data System (ADS)

Jézéquel, Fabienne; Chesneaux, Jean-Marie

2008-06-01

The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed. CADNA provides new numerical types on which round-off errors can be estimated. Slight modifications are required to control a code with CADNA, mainly changes in variable declarations, input and output. This paper describes the features of the CADNA library and shows how to interpret the information it provides concerning round-off error propagation in a code. Program summaryProgram title:CADNA Catalogue identifier:AEAT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAT_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:53 420 No. of bytes in distributed program, including test data, etc.:566 495 Distribution format:tar.gz Programming language:Fortran Computer:PC running LINUX with an i686 or an ia64 processor, UNIX workstations including SUN, IBM Operating system:LINUX, UNIX Classification:4.14, 6.5, 20 Nature of problem:A simulation program which uses floating-point arithmetic generates round-off errors, due to the rounding performed at each assignment and at each arithmetic operation. Round-off error propagation may invalidate the result of a program. The CADNA library enables one to estimate round-off error propagation in any simulation program and to detect all numerical instabilities that may occur at run time. Solution method:The CADNA library [1] implements Discrete Stochastic Arithmetic [2-4] which is based on a probabilistic model of round-off errors. The program is run several times with a random rounding mode generating different results each time. From this set of results, CADNA estimates the number of exact significant digits in the result that would have been computed with standard floating-point arithmetic. Restrictions:CADNA requires a Fortran 90 (or newer) compiler. In the program to be linked with the CADNA library, round-off errors on complex variables cannot be estimated. Furthermore array functions such as product or sum must not be used. Only the arithmetic operators and the abs, min, max and sqrt functions can be used for arrays. Running time:The version of a code which uses CADNA runs at least three times slower than its floating-point version. This cost depends on the computer architecture and can be higher if the detection of numerical instabilities is enabled. In this case, the cost may be related to the number of instabilities detected. References:The CADNA library, URL address: http://www.lip6.fr/cadna. J.-M. Chesneaux, L'arithmétique Stochastique et le Logiciel CADNA, Habilitation á diriger des recherches, Université Pierre et Marie Curie, Paris, 1995. J. Vignes, A stochastic arithmetic for reliable scientific computation, Math. Comput. Simulation 35 (1993) 233-261. J. Vignes, Discrete stochastic arithmetic for validating results of numerical software, Numer. Algorithms 37 (2004) 377-390.

An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

ERIC Educational Resources Information Center

Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

2016-01-01

This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

Non-symbolic arithmetic in adults and young children.

PubMed

Barth, Hilary; La Mont, Kristen; Lipton, Jennifer; Dehaene, Stanislas; Kanwisher, Nancy; Spelke, Elizabeth

2006-01-01

Five experiments investigated whether adults and preschool children can perform simple arithmetic calculations on non-symbolic numerosities. Previous research has demonstrated that human adults, human infants, and non-human animals can process numerical quantities through approximate representations of their magnitudes. Here we consider whether these non-symbolic numerical representations might serve as a building block of uniquely human, learned mathematics. Both adults and children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Success at these tasks did not depend on non-numerical continuous quantities, modality-specific quantity information, the adoption of alternative non-arithmetic strategies, or learned symbolic arithmetic knowledge. Abstract numerical quantity representations therefore are computationally functional and may provide a foundation for formal mathematics.

Common brain regions underlying different arithmetic operations as revealed by conjunct fMRI-BOLD activation.

PubMed

Fehr, Thorsten; Code, Chris; Herrmann, Manfred

2007-10-03

The issue of how and where arithmetic operations are represented in the brain has been addressed in numerous studies. Lesion studies suggest that a network of different brain areas are involved in mental calculation. Neuroimaging studies have reported inferior parietal and lateral frontal activations during mental arithmetic using tasks of different complexities and using different operators (addition, subtraction, etc.). Indeed, it has been difficult to compare brain activation across studies because of the variety of different operators and different presentation modalities used. The present experiment examined fMRI-BOLD activity in participants during calculation tasks entailing different arithmetic operations -- addition, subtraction, multiplication and division -- of different complexities. Functional imaging data revealed a common activation pattern comprising right precuneus, left and right middle and superior frontal regions during all arithmetic operations. All other regional activations were operation specific and distributed in prominently frontal, parietal and central regions when contrasting complex and simple calculation tasks. The present results largely confirm former studies suggesting that activation patterns due to mental arithmetic appear to reflect a basic anatomical substrate of working memory, numerical knowledge and processing based on finger counting, and derived from a network originally related to finger movement. We emphasize that in mental arithmetic research different arithmetic operations should always be examined and discussed independently of each other in order to avoid invalid generalizations on arithmetics and involved brain areas.

Examining the relationship between rapid automatized naming and arithmetic fluency in Chinese kindergarten children.

PubMed

Cui, Jiaxin; Georgiou, George K; Zhang, Yiyun; Li, Yixun; Shu, Hua; Zhou, Xinlin

2017-02-01

Rapid automatized naming (RAN) has been found to predict mathematics. However, the nature of their relationship remains unclear. Thus, the purpose of this study was twofold: (a) to examine how RAN (numeric and non-numeric) predicts a subdomain of mathematics (arithmetic fluency) and (b) to examine what processing skills may account for the RAN-arithmetic fluency relationship. A total of 160 third-year kindergarten Chinese children (83 boys and 77 girls, mean age=5.11years) were assessed on RAN (colors, objects, digits, and dice), nonverbal IQ, visual-verbal paired associate learning, phonological awareness, short-term memory, speed of processing, approximate number system acuity, and arithmetic fluency (addition and subtraction). The results indicated first that RAN was a significant correlate of arithmetic fluency and the correlations did not vary as a function of type of RAN or arithmetic fluency tasks. In addition, RAN continued to predict addition and subtraction fluency even after controlling for all other processing skills. Taken together, these findings challenge the existing theoretical accounts of the RAN-arithmetic fluency relationship and suggest that, similar to reading fluency, multiple processes underlie the RAN-arithmetic fluency relationship. Copyright © 2016 Elsevier Inc. All rights reserved.

Non-verbal numerical cognition: from reals to integers.

PubMed

Gallistel; Gelman

2000-02-01

Data on numerical processing by verbal (human) and non-verbal (animal and human) subjects are integrated by the hypothesis that a non-verbal counting process represents discrete (countable) quantities by means of magnitudes with scalar variability. These appear to be identical to the magnitudes that represent continuous (uncountable) quantities such as duration. The magnitudes representing countable quantity are generated by a discrete incrementing process, which defines next magnitudes and yields a discrete ordering. In the case of continuous quantities, the continuous accumulation process does not define next magnitudes, so the ordering is also continuous ('dense'). The magnitudes representing both countable and uncountable quantity are arithmetically combined in, for example, the computation of the income to be expected from a foraging patch. Thus, on the hypothesis presented here, the primitive machinery for arithmetic processing works with real numbers (magnitudes).

When generating answers benefits arithmetic skill: the importance of prior knowledge.

PubMed

Rittle-Johnson, Bethany; Kmicikewycz, Alexander Oleksij

2008-09-01

People remember information better if they generate the information while studying rather than read the information. However, prior research has not investigated whether this generation effect extends to related but unstudied items and has not been conducted in classroom settings. We compared third graders' success on studied and unstudied multiplication problems after they spent a class period generating answers to problems or reading the answers from a calculator. The effect of condition interacted with prior knowledge. Students with low prior knowledge had higher accuracy in the generate condition, but as prior knowledge increased, the advantage of generating answers decreased. The benefits of generating answers may extend to unstudied items and to classroom settings, but only for learners with low prior knowledge.

Nonanalytic function generation routines for 16-bit microprocessors

NASA Technical Reports Server (NTRS)

Soeder, J. F.; Shaufl, M.

1980-01-01

Interpolation techniques for three types (univariate, bivariate, and map) of nonanalytic functions are described. These interpolation techniques are then implemented in scaled fraction arithmetic on a representative 16 bit microprocessor. A FORTRAN program is described that facilitates the scaling, documentation, and organization of data for use by these routines. Listings of all these programs are included in an appendix.

The Y2K Problem: Will It Just Be Another New Year's Eve?

ERIC Educational Resources Information Center

Iwanowski, Jay

1998-01-01

Potential problems for college and university computing functions posed by arrival of the year 2000 (Y2K) are discussed, including arithmetic calculations and sorting functions based on two-digit year dates, embedding of two-digit dates in archival data, system coordination for data exchange, unique number generation, and leap year calculations. A…

Individual structural differences in left inferior parietal area are associated with schoolchildrens' arithmetic scores

PubMed Central

Li, Yongxin; Hu, Yuzheng; Wang, Yunqi; Weng, Jian; Chen, Feiyan

2013-01-01

Arithmetic skill is of critical importance for academic achievement, professional success and everyday life, and childhood is the key period to acquire this skill. Neuroimaging studies have identified that left parietal regions are a key neural substrate for representing arithmetic skill. Although the relationship between functional brain activity in left parietal regions and arithmetic skill has been studied in detail, it remains unclear about the relationship between arithmetic achievement and structural properties in left inferior parietal area in schoolchildren. The current study employed a combination of voxel-based morphometry (VBM) for high-resolution T1-weighted images and fiber tracking on diffusion tensor imaging (DTI) to examine the relationship between structural properties in the inferior parietal area and arithmetic achievement in 10-year-old schoolchildren. VBM of the T1-weighted images revealed that individual differences in arithmetic scores were significantly and positively correlated with the gray matter (GM) volume in the left intraparietal sulcus (IPS). Fiber tracking analysis revealed that the forceps major, left superior longitudinal fasciculus (SLF), bilateral inferior longitudinal fasciculus (ILF) and inferior fronto-occipital fasciculus (IFOF) were the primary pathways connecting the left IPS with other brain areas. Furthermore, the regression analysis of the probabilistic pathways revealed a significant and positive correlation between the fractional anisotropy (FA) values in the left SLF, ILF and bilateral IFOF and arithmetic scores. The brain structure-behavior correlation analyses indicated that the GM volumes in the left IPS and the FA values in the tract pathways connecting left IPS were both related to children's arithmetic achievement. The present findings provide evidence that individual structural differences in the left IPS are associated with arithmetic scores in schoolchildren. PMID:24367320

Analysis of mitochondrial genetic diversity of Ustilago maydis in Mexico.

PubMed

Jiménez-Becerril, María F; Hernández-Delgado, Sanjuana; Solís-Oba, Myrna; González Prieto, Juan M

2018-01-01

The current understanding of the genetic diversity of the phytopathogenic fungus Ustilago maydis is limited. To determine the genetic diversity and structure of U. maydis, 48 fungal isolates were analyzed using mitochondrial simple sequence repeats (SSRs). Tumours (corn smut or 'huitlacoche') were collected from different Mexican states with diverse environmental conditions. Using bioinformatic tools, five microsatellites were identified within intergenic regions of the U. maydis mitochondrial genome. SSRMUM4 was the most polymorphic marker. The most common repeats were hexanucleotides. A total of 12 allelic variants were identified, with a mean of 2.4 alleles per locus. An estimate of the genetic diversity using analysis of molecular variance (AMOVA) revealed that the highest variance component is within states (84%), with moderate genetic differentiation between states (16%) (F ST  = 0.158). A dendrogram generated using the unweighted paired-grouping method with arithmetic averages (UPGMA) and the Bayesian analysis of population structure grouped the U. maydis isolates into two subgroups (K = 2) based on their shared SSRs.

Genetic Analysis of 430 Chinese Cynodon dactylon Accessions Using Sequence-Related Amplified Polymorphism Markers

PubMed Central

Huang, Chunqiong; Liu, Guodao; Bai, Changjun; Wang, Wenqiang

2014-01-01

Although Cynodon dactylon (C. dactylon) is widely distributed in China, information on its genetic diversity within the germplasm pool is limited. The objective of this study was to reveal the genetic variation and relationships of 430 C. dactylon accessions collected from 22 Chinese provinces using sequence-related amplified polymorphism (SRAP) markers. Fifteen primer pairs were used to amplify specific C. dactylon genomic sequences. A total of 481 SRAP fragments were generated, with fragment sizes ranging from 260–1800 base pairs (bp). Genetic similarity coefficients (GSC) among the 430 accessions averaged 0.72 and ranged from 0.53–0.96. Cluster analysis conducted by two methods, namely the unweighted pair-group method with arithmetic averages (UPGMA) and principle coordinate analysis (PCoA), separated the accessions into eight distinct groups. Our findings verify that Chinese C. dactylon germplasms have rich genetic diversity, which is an excellent basis for C. dactylon breeding for new cultivars. PMID:25338051

Age-related changes in strategic variations during arithmetic problem solving: The role of executive control.

PubMed

Hinault, T; Lemaire, P

2016-01-01

In this review, we provide an overview of how age-related changes in executive control influence aging effects in arithmetic processing. More specifically, we consider the role of executive control in strategic variations with age during arithmetic problem solving. Previous studies found that age-related differences in arithmetic performance are associated with strategic variations. That is, when they accomplish arithmetic problem-solving tasks, older adults use fewer strategies than young adults, use strategies in different proportions, and select and execute strategies less efficiently. Here, we review recent evidence, suggesting that age-related changes in inhibition, cognitive flexibility, and working memory processes underlie age-related changes in strategic variations during arithmetic problem solving. We discuss both behavioral and neural mechanisms underlying age-related changes in these executive control processes. © 2016 Elsevier B.V. All rights reserved.

Right-Brain/Left-Brain Integrated Associative Processor Employing Convertible Multiple-Instruction-Stream Multiple-Data-Stream Elements

NASA Astrophysics Data System (ADS)

Hayakawa, Hitoshi; Ogawa, Makoto; Shibata, Tadashi

2005-04-01

A very large scale integrated circuit (VLSI) architecture for a multiple-instruction-stream multiple-data-stream (MIMD) associative processor has been proposed. The processor employs an architecture that enables seamless switching from associative operations to arithmetic operations. The MIMD element is convertible to a regular central processing unit (CPU) while maintaining its high performance as an associative processor. Therefore, the MIMD associative processor can perform not only on-chip perception, i.e., searching for the vector most similar to an input vector throughout the on-chip cache memory, but also arithmetic and logic operations similar to those in ordinary CPUs, both simultaneously in parallel processing. Three key technologies have been developed to generate the MIMD element: associative-operation-and-arithmetic-operation switchable calculation units, a versatile register control scheme within the MIMD element for flexible operations, and a short instruction set for minimizing the memory size for program storage. Key circuit blocks were designed and fabricated using 0.18 μm complementary metal-oxide-semiconductor (CMOS) technology. As a result, the full-featured MIMD element is estimated to be 3 mm2, showing the feasibility of an 8-parallel-MIMD-element associative processor in a single chip of 5 mm× 5 mm.

Cognitive Processes that Account for Mental Addition Fluency Differences between Children Typically Achieving in Arithmetic and Children At-Risk for Failure in Arithmetic

ERIC Educational Resources Information Center

Berg, Derek H.; Hutchinson, Nancy L.

2010-01-01

This study investigated whether processing speed, short-term memory, and working memory accounted for the differential mental addition fluency between children typically achieving in arithmetic (TA) and children at-risk for failure in arithmetic (AR). Further, we drew attention to fluency differences in simple (e.g., 5 + 3) and complex (e.g., 16 +…

Functional Neuroanatomy Involved in Automatic order Mental Arithmetic and Recitation of the Multiplication Table

NASA Astrophysics Data System (ADS)

Wang, Li-Qun; Saito, Masao

We used 1.5T functional magnetic resonance imaging (fMRI) to explore that which brain areas contribute uniquely to numeric computation. The BOLD effect activation pattern of metal arithmetic task (successive subtraction: actual calculation task) was compared with multiplication tables repetition task (rote verbal arithmetic memory task) response. The activation found in right parietal lobule during metal arithmetic task suggested that quantitative cognition or numeric computation may need the assistance of sensuous convert, such as spatial imagination and spatial sensuous convert. In addition, this mechanism may be an ’analog algorithm’ in the simple mental arithmetic processing.

Multiple task performance as a predictor of the potential of air traffic controller trainees.

DOT National Transportation Integrated Search

1972-01-01

Two hundred and twenty-nine air traffic controller trainees were tested on the CAMI Multiple Task Performance Battery. The battery provides objective measures of monitoring, arithmetical skills, visual discrimination, and group problem solving. The c...

Teachers’ Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic

PubMed Central

Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

2016-01-01

The current study investigated early elementary school teachers’ beliefs and practices regarding the role of Executive Functions (EFs) in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1) beliefs regarding the contribution of EFs to reading and arithmetic, (2) pedagogical practices, and (3) a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe EFs affect students’ performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers’ scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices. PMID:27799917

Teachers' Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic.

PubMed

Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami

2016-01-01

The current study investigated early elementary school teachers' beliefs and practices regarding the role of Executive Functions (EFs) in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1) beliefs regarding the contribution of EFs to reading and arithmetic, (2) pedagogical practices, and (3) a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe EFs affect students' performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers' scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices.

A new version of the CADNA library for estimating round-off error propagation in Fortran programs

NASA Astrophysics Data System (ADS)

Jézéquel, Fabienne; Chesneaux, Jean-Marie; Lamotte, Jean-Luc

2010-11-01

The CADNA library enables one to estimate, using a probabilistic approach, round-off error propagation in any simulation program. CADNA provides new numerical types, the so-called stochastic types, on which round-off errors can be estimated. Furthermore CADNA contains the definition of arithmetic and relational operators which are overloaded for stochastic variables and the definition of mathematical functions which can be used with stochastic arguments. On 64-bit processors, depending on the rounding mode chosen, the mathematical library associated with the GNU Fortran compiler may provide incorrect results or generate severe bugs. Therefore the CADNA library has been improved to enable the numerical validation of programs on 64-bit processors. New version program summaryProgram title: CADNA Catalogue identifier: AEAT_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAT_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 28 488 No. of bytes in distributed program, including test data, etc.: 463 778 Distribution format: tar.gz Programming language: Fortran NOTE: A C++ version of this program is available in the Library as AEGQ_v1_0 Computer: PC running LINUX with an i686 or an ia64 processor, UNIX workstations including SUN, IBM Operating system: LINUX, UNIX Classification: 6.5 Catalogue identifier of previous version: AEAT_v1_0 Journal reference of previous version: Comput. Phys. Commun. 178 (2008) 933 Does the new version supersede the previous version?: Yes Nature of problem: A simulation program which uses floating-point arithmetic generates round-off errors, due to the rounding performed at each assignment and at each arithmetic operation. Round-off error propagation may invalidate the result of a program. The CADNA library enables one to estimate round-off error propagation in any simulation program and to detect all numerical instabilities that may occur at run time. Solution method: The CADNA library [1-3] implements Discrete Stochastic Arithmetic [4,5] which is based on a probabilistic model of round-off errors. The program is run several times with a random rounding mode generating different results each time. From this set of results, CADNA estimates the number of exact significant digits in the result that would have been computed with standard floating-point arithmetic. Reasons for new version: On 64-bit processors, the mathematical library associated with the GNU Fortran compiler may provide incorrect results or generate severe bugs with rounding towards -∞ and +∞, which the random rounding mode is based on. Therefore a particular definition of mathematical functions for stochastic arguments has been included in the CADNA library to enable its use with the GNU Fortran compiler on 64-bit processors. Summary of revisions: If CADNA is used on a 64-bit processor with the GNU Fortran compiler, mathematical functions are computed with rounding to the nearest, otherwise they are computed with the random rounding mode. It must be pointed out that the knowledge of the accuracy of the stochastic argument of a mathematical function is never lost. Restrictions: CADNA requires a Fortran 90 (or newer) compiler. In the program to be linked with the CADNA library, round-off errors on complex variables cannot be estimated. Furthermore array functions such as product or sum must not be used. Only the arithmetic operators and the abs, min, max and sqrt functions can be used for arrays. Additional comments: In the library archive, users are advised to read the INSTALL file first. The doc directory contains a user guide named ug.cadna.pdf which shows how to control the numerical accuracy of a program using CADNA, provides installation instructions and describes test runs. The source code, which is located in the src directory, consists of one assembly language file (cadna_rounding.s) and eighteen Fortran language files. cadna_rounding.s is a symbolic link to the assembly file corresponding to the processor and the Fortran compiler used. This assembly file contains routines which are frequently called in the CADNA Fortran files to change the rounding mode. The Fortran language files contain the definition of the stochastic types on which the control of accuracy can be performed, CADNA specific functions (for instance to enable or disable the detection of numerical instabilities), the definition of arithmetic and relational operators which are overloaded for stochastic variables and the definition of mathematical functions which can be used with stochastic arguments. The examples directory contains seven test runs which illustrate the use of the CADNA library and the benefits of Discrete Stochastic Arithmetic. Running time: The version of a code which uses CADNA runs at least three times slower than its floating-point version. This cost depends on the computer architecture and can be higher if the detection of numerical instabilities is enabled. In this case, the cost may be related to the number of instabilities detected.

The Effect of Various Reinforcement Contingencies on the Accuracy of Children's Self-Reports. Technical Report #46.

ERIC Educational Resources Information Center

Speidel, Gisela E.

This study, part of the Kamehameha Early Education Program (KEEP), investigated the accuracy of children's self reports under various contingencies. Sixteen first grade arithmetic students were randomly assigned to two groups, A and B. It was found that both groups learned to check their own work and report it fairly accurately when no…

Residual performance effects of simulated sonic booms introduced during sleep.

DOT National Transportation Integrated Search

1972-05-01

Twenty-four male subjects were tested on a complex performance device involving monitoring, mental arithmetic, and pattern discrimination. Three age-groups were used: 20 to 26, 40 to 45, and 60 to 72. Subjects were tested for 30 minutes each morning ...

The Slow Learner in Mathematics: Aids and Activities

ERIC Educational Resources Information Center

Maletsky, Evan M.

1973-01-01

Specific examples of effective use of multisensory aids are given. All can easily and inexpensively be made by the teacher or the students. Examples are grouped under the following major headings: number patterns, arithmetic skills, geometric concepts, algebraic concepts, and models. (LS)

Prospective relations between resting-state connectivity of parietal subdivisions and arithmetic competence.

PubMed

Price, Gavin R; Yeo, Darren J; Wilkey, Eric D; Cutting, Laurie E

2018-04-01

The present study investigates the relation between resting-state functional connectivity (rsFC) of cytoarchitectonically defined subdivisions of the parietal cortex at the end of 1st grade and arithmetic performance at the end of 2nd grade. Results revealed a dissociable pattern of relations between rsFC and arithmetic competence among subdivisions of intraparietal sulcus (IPS) and angular gyrus (AG). rsFC between right hemisphere IPS subdivisions and contralateral IPS subdivisions positively correlated with arithmetic competence. In contrast, rsFC between the left hIP1 and the right medial temporal lobe, and rsFC between the left AG and left superior frontal gyrus, were negatively correlated with arithmetic competence. These results suggest that strong inter-hemispheric IPS connectivity is important for math development, reflecting either neurocognitive mechanisms specific to arithmetic processing, domain-general mechanisms that are particularly relevant to arithmetic competence, or structural 'cortical maturity'. Stronger connectivity between IPS, and AG, subdivisions and frontal and temporal cortices, however, appears to be negatively associated with math development, possibly reflecting the ability to disengage suboptimal problem-solving strategies during mathematical processing, or to flexibly reorient task-based networks. Importantly, the reported results pertain even when controlling for reading, spatial attention, and working memory, suggesting that the observed rsFC-behavior relations are specific to arithmetic competence. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Genetic diversity of Iranian honey bee (Apis mellifera meda Skorikow, 1829) populations based on ISSR markers.

PubMed

Rahimi, A; Mirmoayedi, A; Kahrizi, D; Zarei, L; Jamali, S

2016-04-30

Honey bee is one of the most important insects considering its role in agriculture,ecology and economy as a whole. In this study, the genetic diversity of different Iranian honey bee populations was evaluated using inter simple sequence repeat (ISSR) markers. During May to September 2014, 108 young worker honey bees were collected from six different populations in 30 different geoclimatic locations from Golestan, Mazendaran, Guilan, West Azerbaijan, East Azerbaijan, Ardebil provinces of Iran. DNA was extracted from the worker honey bees. The quality and quantity of extracted DNA were measured. A set of ten primers were screened with the laboratory populations of honey bees. The number of fragments produced in the different honey bee populations varied from 3 to 10, varying within 150 to 1500 bp. The used ten ISSR primers generated 40 polymorphic fragments, and the average heterozygosity for each primer was 0.266. Maximum numbers of bands were recorded for primer A1. A dendrogram based on the Unweighted Pair Group Method with Arithmetic mean (UPGMA) method generated two sub-clusters. Honey bee populations of Golestan, Mazendaran, Guilan provinces were located in the first group. The second group included honey bee populations of Ardebil, West Azerbaijan, East Azerbaijan provinces, but this group showed a close relationship with other populations. The results showed obviously the ability of the ISSR marker technique to detect the genetic diversity among the honey bee populations.

Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills, and investigating the question of domain-specificity.

PubMed

Morsanyi, Kinga; O'Mahony, Eileen; McCormack, Teresa

2017-12-01

Recent evidence has highlighted the important role that number-ordering skills play in arithmetic abilities, both in children and adults. In the current study, we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was mediated by number-ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor that included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.

Cognitive precursors of arithmetic development in primary school children with cerebral palsy.

PubMed

Van Rooijen, M; Verhoeven, L; Smits, D W; Dallmeijer, A J; Becher, J G; Steenbergen, B

2014-04-01

The aim of this study was to examine the development of arithmetic performance and its cognitive precursors in children with CP from 7 till 9 years of age. Previous research has shown that children with CP are generally delayed in arithmetic performance compared to their typically developing peers. In children with CP, the developmental trajectory of the ability to solve addition- and subtraction tasks has, however, rarely been studied, as well as the cognitive factors affecting this trajectory. Sixty children (M=7.2 years, SD=.23 months at study entry) with CP participated in this study. Standardized tests were administered to assess arithmetic performance, word decoding skills, non-verbal intelligence, and working memory. The results showed that the ability to solve addition- and subtraction tasks increased over a two year period. Word decoding skills were positively related to the initial status of arithmetic performance. In addition, non-verbal intelligence and working memory were associated with the initial status and growth rate of arithmetic performance from 7 till 9 years of age. The current study highlights the importance of non-verbal intelligence and working memory to the development of arithmetic performance of children with CP. Copyright © 2014 Elsevier Ltd. All rights reserved.

Separating stages of arithmetic verification: An ERP study with a novel paradigm.

PubMed

Avancini, Chiara; Soltész, Fruzsina; Szűcs, Dénes

2015-08-01

In studies of arithmetic verification, participants typically encounter two operands and they carry out an operation on these (e.g. adding them). Operands are followed by a proposed answer and participants decide whether this answer is correct or incorrect. However, interpretation of results is difficult because multiple parallel, temporally overlapping numerical and non-numerical processes of the human brain may contribute to task execution. In order to overcome this problem here we used a novel paradigm specifically designed to tease apart the overlapping cognitive processes active during arithmetic verification. Specifically, we aimed to separate effects related to detection of arithmetic correctness, detection of the violation of strategic expectations, detection of physical stimulus properties mismatch and numerical magnitude comparison (numerical distance effects). Arithmetic correctness, physical stimulus properties and magnitude information were not task-relevant properties of the stimuli. We distinguished between a series of temporally highly overlapping cognitive processes which in turn elicited overlapping ERP effects with distinct scalp topographies. We suggest that arithmetic verification relies on two major temporal phases which include parallel running processes. Our paradigm offers a new method for investigating specific arithmetic verification processes in detail. Copyright © 2015 Elsevier Ltd. All rights reserved.

Initialization Method for Grammar-Guided Genetic Programming

NASA Astrophysics Data System (ADS)

García-Arnau, M.; Manrique, D.; Ríos, J.; Rodríguez-Patón, A.

This paper proposes a new tree-generation algorithm for grammarguided genetic programming that includes a parameter to control the maximum size of the trees to be generated. An important feature of this algorithm is that the initial populations generated are adequately distributed in terms of tree size and distribution within the search space. Consequently, genetic programming systems starting from the initial populations generated by the proposed method have a higher convergence speed. Two different problems have been chosen to carry out the experiments: a laboratory test involving searching for arithmetical equalities and the real-world task of breast cancer prognosis. In both problems, comparisons have been made to another five important initialization methods.

Do Children Understand Fraction Addition?

ERIC Educational Resources Information Center

Braithwaite, David W.; Tian, Jing; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

Exponential Arithmetic Based Self-Healing Group Key Distribution Scheme with Backward Secrecy under the Resource-Constrained Wireless Networks

PubMed Central

Guo, Hua; Zheng, Yandong; Zhang, Xiyong; Li, Zhoujun

2016-01-01

In resource-constrained wireless networks, resources such as storage space and communication bandwidth are limited. To guarantee secure communication in resource-constrained wireless networks, group keys should be distributed to users. The self-healing group key distribution (SGKD) scheme is a promising cryptographic tool, which can be used to distribute and update the group key for the secure group communication over unreliable wireless networks. Among all known SGKD schemes, exponential arithmetic based SGKD (E-SGKD) schemes reduce the storage overhead to constant, thus is suitable for the the resource-constrained wireless networks. In this paper, we provide a new mechanism to achieve E-SGKD schemes with backward secrecy. We first propose a basic E-SGKD scheme based on a known polynomial-based SGKD, where it has optimal storage overhead while having no backward secrecy. To obtain the backward secrecy and reduce the communication overhead, we introduce a novel approach for message broadcasting and self-healing. Compared with other E-SGKD schemes, our new E-SGKD scheme has the optimal storage overhead, high communication efficiency and satisfactory security. The simulation results in Zigbee-based networks show that the proposed scheme is suitable for the resource-restrained wireless networks. Finally, we show the application of our proposed scheme. PMID:27136550

Abacus Training Affects Math and Task Switching Abilities and Modulates Their Relationships in Chinese Children

PubMed Central

Yao, Yuan; Weng, Jian; Hu, Yuzheng; Chen, Feiyan

2015-01-01

Our previous work demonstrated that abacus-based mental calculation (AMC), a traditional Chinese calculation method, could help children improve their math abilities (e.g. basic arithmetical ability) and executive function (e.g. working memory). This study further examined the effects of long-term AMC training on math ability in visual-spatial domain and the task switching component of executive function. More importantly, this study investigated whether AMC training modulated the relationship between math abilities and task switching. The participants were seventy 7-year-old children who were randomly assigned into AMC and control groups at primary school entry. Children in AMC group received 2-hour AMC training every week since primary school entry. On the contrary, children in the control group had never received any AMC training. Math and task switching abilities were measured one year and three years respectively after AMC training began. The results showed that AMC children performed better than their peers on math abilities in arithmetical and visual-spatial domains. In addition, AMC group responded faster than control group in the switching task, while no group difference was found in switch cost. Most interestingly, group difference was present in the relationships between math abilities and switch cost. These results implied the effect of AMC training on math abilities as well as its relationship with executive function. PMID:26444689

Abacus Training Affects Math and Task Switching Abilities and Modulates Their Relationships in Chinese Children.

PubMed

Wang, Chunjie; Geng, Fengji; Yao, Yuan; Weng, Jian; Hu, Yuzheng; Chen, Feiyan

2015-01-01

Our previous work demonstrated that abacus-based mental calculation (AMC), a traditional Chinese calculation method, could help children improve their math abilities (e.g. basic arithmetical ability) and executive function (e.g. working memory). This study further examined the effects of long-term AMC training on math ability in visual-spatial domain and the task switching component of executive function. More importantly, this study investigated whether AMC training modulated the relationship between math abilities and task switching. The participants were seventy 7-year-old children who were randomly assigned into AMC and control groups at primary school entry. Children in AMC group received 2-hour AMC training every week since primary school entry. On the contrary, children in the control group had never received any AMC training. Math and task switching abilities were measured one year and three years respectively after AMC training began. The results showed that AMC children performed better than their peers on math abilities in arithmetical and visual-spatial domains. In addition, AMC group responded faster than control group in the switching task, while no group difference was found in switch cost. Most interestingly, group difference was present in the relationships between math abilities and switch cost. These results implied the effect of AMC training on math abilities as well as its relationship with executive function.

Multiple task performance as a predictor of the potential of air traffic controller trainees : a followup study.

DOT National Transportation Integrated Search

1974-11-01

Two hundred and twenty-nine air traffic controller trainees were tested on the CAMI Multiple Task Performance Battery. The battery provides objective measures of monitoring, arithmetical skills, visual discrimination, and group problem solving. The c...

Aztec arithmetic revisited: land-area algorithms and Acolhua congruence arithmetic.

PubMed

Williams, Barbara J; Jorge y Jorge, María del Carmen

2008-04-04

Acolhua-Aztec land records depicting areas and side dimensions of agricultural fields provide insight into Aztec arithmetic. Hypothesizing that recorded areas resulted from indigenous calculation, in a study of sample quadrilateral fields we found that 60% of the area values could be reproduced exactly by computation. In remaining cases, discrepancies between computed and recorded areas were consistently small, suggesting use of an unknown indigenous arithmetic. In revisiting the research, we discovered evidence for the use of congruence principles, based on proportions between the standard linear Acolhua measure and their units of shorter length. This procedure substitutes for computation with fractions and is labeled "Acolhua congruence arithmetic." The findings also clarify variance between Acolhua and Tenochca linear units, long an issue in understanding Aztec metrology.

Reconfigurable pipelined processor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saccardi, R.J.

1989-09-19

This patent describes a reconfigurable pipelined processor for processing data. It comprises: a plurality of memory devices for storing bits of data; a plurality of arithmetic units for performing arithmetic functions with the data; cross bar means for connecting the memory devices with the arithmetic units for transferring data therebetween; at least one counter connected with the cross bar means for providing a source of addresses to the memory devices; at least one variable tick delay device connected with each of the memory devices and arithmetic units; and means for providing control bits to the variable tick delay device formore » variably controlling the input and output operations thereof to selectively delay the memory devices and arithmetic units to align the data for processing in a selected sequence.« less

Algorithmic-Reducibility = Renormalization-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') Replacing CRUTCHES!!!: Gauss Modular/Clock-Arithmetic Congruences = Signal X Noise PRODUCTS..

NASA Astrophysics Data System (ADS)

Siegel, J.; Siegel, Edward Carl-Ludwig

2011-03-01

Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!

Interventions for Primary School Children With Difficulties in Mathematics.

PubMed

Dowker, Ann

2017-01-01

Difficulty with arithmetic is a common problem for children and adults, though there has been some work on the topic for a surprisingly long time. This chapter will review some of the research that has been done over the years on interventions with primary school children. Interventions can be of various levels of intensiveness, ranging from whole-class approaches that take account of individual differences through small-group and limited-time individual interventions to extended-time individual interventions. Interventions discussed here include those involving peer tuition and group collaboration; those involving board and computer games; and those that involve assessing children's strengths and weaknesses in different components of mathematics; and targeting remedial activities to the assessed weaknesses. Most of the interventions discussed in this chapter specifically involve mathematics (usually mainly arithmetic), but there is also some discussion of attempts to improve mathematics by training children in domain-general skills, including Piagetian operations, metacognition, and executive functions. © 2017 Elsevier Inc. All rights reserved.

Contributions of Domain-General Cognitive Resources and Different Forms of Arithmetic Development to Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.

2012-01-01

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n=279; mean age=7.59 yrs) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across grades 2–3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems. PMID:22409764

A natural history of mathematics: George Peacock and the making of English algebra.

PubMed

Lambert, Kevin

2013-06-01

In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's "principle of equivalent forms," which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra.

Neurocognitive predictors of financial capacity in traumatic brain injury.

PubMed

Martin, Roy C; Triebel, Kristen; Dreer, Laura E; Novack, Thomas A; Turner, Crystal; Marson, Daniel C

2012-01-01

To develop cognitive models of financial capacity (FC) in patients with traumatic brain injury (TBI). Longitudinal design. Inpatient brain injury rehabilitation unit. Twenty healthy controls, and 24 adults with moderate-to-severe TBI were assessed at baseline (30 days postinjury) and 6 months postinjury. The FC instrument (FCI) and a neuropsychological test battery. Univariate correlation and multiple regression procedures were employed to develop cognitive models of FCI performance in the TBI group, at baseline and 6-month time follow-up. Three cognitive predictor models of FC were developed. At baseline, measures of mental arithmetic/working memory and immediate verbal memory predicted baseline FCI performance (R = 0.72). At 6-month follow-up, measures of executive function and mental arithmetic/working memory predicted 6-month FCI performance (R = 0.79), and a third model found that these 2 measures at baseline predicted 6-month FCI performance (R = 0.71). Multiple cognitive functions are associated with initial impairment and partial recovery of FC in moderate-to-severe TBI patients. In particular, arithmetic, working memory, and executive function skills appear critical to recovery of FC in TBI. The study results represent an initial step toward developing a neurocognitive model of FC in patients with TBI.

An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1983-01-01

An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.

Conceptual Knowledge of Fraction Arithmetic

ERIC Educational Resources Information Center

Siegler, Robert S.; Lortie-Forgues, Hugues

2015-01-01

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…

Disabilities of Arithmetic and Mathematical Reasoning: Perspectives from Neurology and Neuropsychology.

ERIC Educational Resources Information Center

Rourke, Byron P.; Conway, James A.

1997-01-01

Reviews current research on brain-behavior relationships in disabilities of arithmetic and mathematical reasoning from both a neurological and a neuropsychological perspective. Defines developmental dyscalculia and the developmental importance of right versus left hemisphere integrity for the mediation of arithmetic learning and explores…

Comparative soil CO2 flux measurements and geostatistical estimation methods on Masaya volcano, Nicaragua

USGS Publications Warehouse

Lewicki, Jennifer L.; Bergfeld, Deborah; Cardellini, Carlo; Chiodini, Giovanni; Granieri, Domenico; Varley, Nick; Werner, Cynthia A.

2005-01-01

We present a comparative study of soil CO2 flux (FCO2">FCO2) measured by five groups (Groups 1–5) at the IAVCEI-CCVG Eighth Workshop on Volcanic Gases on Masaya volcano, Nicaragua. Groups 1–5 measured FCO2 using the accumulation chamber method at 5-m spacing within a 900 m2 grid during a morning (AM) period. These measurements were repeated by Groups 1–3 during an afternoon (PM) period. Measured FCO2 ranged from 218 to 14,719 g m−2 day−1. The variability of the five measurements made at each grid point ranged from ±5 to 167%. However, the arithmetic means of fluxes measured over the entire grid and associated total CO2 emission rate estimates varied between groups by only ±22%. All three groups that made PM measurements reported an 8–19% increase in total emissions over the AM results. Based on a comparison of measurements made during AM and PM times, we argue that this change is due in large part to natural temporal variability of gas flow, rather than to measurement error. In order to estimate the mean and associated CO2 emission rate of one data set and to map the spatial FCO2 distribution, we compared six geostatistical methods: arithmetic and minimum variance unbiased estimator means of uninterpolated data, and arithmetic means of data interpolated by the multiquadric radial basis function, ordinary kriging, multi-Gaussian kriging, and sequential Gaussian simulation methods. While the total CO2 emission rates estimated using the different techniques only varied by ±4.4%, the FCO2 maps showed important differences. We suggest that the sequential Gaussian simulation method yields the most realistic representation of the spatial distribution of FCO2, but a variety of geostatistical methods are appropriate to estimate the total CO2 emission rate from a study area, which is a primary goal in volcano monitoring research.

A revision of the subtract-with-borrow random number generators

NASA Astrophysics Data System (ADS)

Sibidanov, Alexei

2017-12-01

The most popular and widely used subtract-with-borrow generator, also known as RANLUX, is reimplemented as a linear congruential generator using large integer arithmetic with the modulus size of 576 bits. Modern computers, as well as the specific structure of the modulus inferred from RANLUX, allow for the development of a fast modular multiplication - the core of the procedure. This was previously believed to be slow and have too high cost in terms of computing resources. Our tests show a significant gain in generation speed which is comparable with other fast, high quality random number generators. An additional feature is the fast skipping of generator states leading to a seeding scheme which guarantees the uniqueness of random number sequences. Licensing provisions: GPLv3 Programming language: C++, C, Assembler

Human Services. Georgia Core Standards for Occupational Clusters.

ERIC Educational Resources Information Center

Georgia Univ., Athens. Dept. of Occupational Studies.

This document lists core standards and occupational knowledge and skills that have been identified and validated by industry as necessary to all Georgia students in secondary-level human services occupations programs. First, foundation skills are grouped as follows: basic skills (reading, writing, arithmetic/mathematics, listening, speaking);…

Technical/Engineering. Georgia Core Standards for Occupational Clusters.

ERIC Educational Resources Information Center

Georgia Univ., Athens. Dept. of Occupational Studies.

This document lists core standards and occupational knowledge and skills that have been identified and validated by industry as necessary to all Georgia students in secondary-level technical/engineering programs. First, foundation skills are grouped as follows: basic skills (reading, writing, arithmetic/mathematics, listening, speaking); thinking…

Health Care. Georgia Core Standards for Occupational Clusters.

ERIC Educational Resources Information Center

Georgia Univ., Athens. Dept. of Occupational Studies.

This document lists core standards and occupational knowledge and skills that have been identified/validated by industry as necessary to all Georgia students in secondary-level health care occupations programs. First, foundation skills are grouped as follows: basic skills (reading, writing, arithmetic/mathematics, listening, speaking); thinking…

The Evaluation of Project SEED, 1989-90.

ERIC Educational Resources Information Center

Webster, William J.; Chadbourn, Russell A.

Project Special Elementary Education for the Disadvantaged (Project SEED) is a nationwide program in which mathematicians and scientists from academia and industry teach abstract, conceptually oriented mathematics to full-sized classes of elementary school students as a supplement to their regular arithmetic classes. A Socratic group-discovery…

Procedural Guide for Designation Surveys of Ocean Dredged Material Disposal Sites. Revision

DTIC Science & Technology

1990-04-01

data standardization." One of the most frequently used clustering strategies is called UPGMA (unweighted pair-group method using arithmetic averages...Sneath and Sokal 1973). Romesburg (1984) 151 evaluated many possible methods and concluded that UPGMA is appropriate for most types of cluster

Assessment of a Problem Posing Task in a Jamaican Grade Four Mathematics Classroom

ERIC Educational Resources Information Center

Munroe, Kayan Lloyd

2016-01-01

This paper analyzes how a teacher of mathematics used problem posing in the assessment of the cognitive development of 26 students at the grade-four level. The students, ages 8 to 10 years, were from a rural elementary school in western Jamaica. Using a picture as a prompt, students were asked to generate three arithmetic problems and to offer…

Children Learn Spurious Associations in Their Math Textbooks: Examples from Fraction Arithmetic

ERIC Educational Resources Information Center

Braithwaite, David W.; Siegler, Robert S.

2018-01-01

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

A Computational Model of Fraction Arithmetic

ERIC Educational Resources Information Center

Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Simulating Network Retrieval of Arithmetic Facts.

ERIC Educational Resources Information Center

Ashcraft, Mark H.

This report describes a simulation of adults' retrieval of arithmetic facts from a network-based memory representation. The goals of the simulation project are to: demonstrate in specific form the nature of a spreading activation model of mental arithmetic; account for three important reaction time effects observed in laboratory investigations;…

Individual Differences in Children's Understanding of Inversion and Arithmetical Skill

ERIC Educational Resources Information Center

Gilmore, Camilla K.; Bryant, Peter

2006-01-01

Background and aims: In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between…

The Practice of Arithmetic in Liberian Schools.

ERIC Educational Resources Information Center

Brenner, Mary E.

1985-01-01

Describes a study of Liberian schools in which students of the Vai tribe are instructed in Western mathematical practices which differ from those of the students' home culture. Reports that the Vai children employed syncretic arithmetic practices, combining two distinct systems of arithmetic in a classroom environment that tacitly facilitated the…

From Arithmetic Sequences to Linear Equations

ERIC Educational Resources Information Center

Matsuura, Ryota; Harless, Patrick

2012-01-01

The first part of the article focuses on deriving the essential properties of arithmetic sequences by appealing to students' sense making and reasoning. The second part describes how to guide students to translate their knowledge of arithmetic sequences into an understanding of linear equations. Ryota Matsuura originally wrote these lessons for…

Baby Arithmetic: One Object Plus One Tone

ERIC Educational Resources Information Center

Kobayashi, Tessei; Hiraki, Kazuo; Mugitani, Ryoko; Hasegawa, Toshikazu

2004-01-01

Recent studies using a violation-of-expectation task suggest that preverbal infants are capable of recognizing basic arithmetical operations involving visual objects. There is still debate, however, over whether their performance is based on any expectation of the arithmetical operations, or on a general perceptual tendency to prefer visually…

Conceptual Knowledge of Decimal Arithmetic

ERIC Educational Resources Information Center

Lortie-Forgues, Hugues; Siegler, Robert S.

2016-01-01

In two studies (N's = 55 and 54), we examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…

IBM system/360 assembly language interval arithmetic software

NASA Technical Reports Server (NTRS)

Phillips, E. J.

1972-01-01

Computer software designed to perform interval arithmetic is described. An interval is defined as the set of all real numbers between two given numbers including or excluding one or both endpoints. Interval arithmetic consists of the various elementary arithmetic operations defined on the set of all intervals, such as interval addition, subtraction, union, etc. One of the main applications of interval arithmetic is in the area of error analysis of computer calculations. For example, it has been used sucessfully to compute bounds on sounding errors in the solution of linear algebraic systems, error bounds in numerical solutions of ordinary differential equations, as well as integral equations and boundary value problems. The described software enables users to implement algorithms of the type described in references efficiently on the IBM 360 system.

Factor structure of the Norwegian version of the WAIS-III in a clinical sample: the arithmetic problem.

PubMed

Egeland, Jens; Bosnes, Ole; Johansen, Hans

2009-09-01

Confirmatory Factor Analyses (CFA) of the Wechsler Adult Intelligence Scale-III (WAIS-III) lend partial support to the four-factor model proposed in the test manual. However, the Arithmetic subtest has been especially difficult to allocate to one factor. Using the new Norwegian WAIS-III version, we tested factor models differing in the number of factors and in the placement of the Arithmetic subtest in a mixed clinical sample (n = 272). Only the four-factor solutions had adequate goodness-of-fit values. Allowing Arithmetic to load on both the Verbal Comprehension and Working Memory factors provided a more parsimonious solution compared to considering the subtest only as a measure of Working Memory. Effects of education were particularly high for both the Verbal Comprehension tests and Arithmetic.

Evaluation of the Triple Code Model of numerical processing-Reviewing past neuroimaging and clinical findings.

PubMed

Siemann, Julia; Petermann, Franz

2018-01-01

This review reconciles past findings on numerical processing with key assumptions of the most predominant model of arithmetic in the literature, the Triple Code Model (TCM). This is implemented by reporting diverse findings in the literature ranging from behavioral studies on basic arithmetic operations over neuroimaging studies on numerical processing to developmental studies concerned with arithmetic acquisition, with a special focus on developmental dyscalculia (DD). We evaluate whether these studies corroborate the model and discuss possible reasons for contradictory findings. A separate section is dedicated to the transfer of TCM to arithmetic development and to alternative accounts focusing on developmental questions of numerical processing. We conclude with recommendations for future directions of arithmetic research, raising questions that require answers in models of healthy as well as abnormal mathematical development. This review assesses the leading model in the field of arithmetic processing (Triple Code Model) by presenting knowledge from interdisciplinary research. It assesses the observed contradictory findings and integrates the resulting opposing viewpoints. The focus is on the development of arithmetic expertise as well as abnormal mathematical development. The original aspect of this article is that it points to a gap in research on these topics and provides possible solutions for future models. Copyright © 2017 Elsevier Ltd. All rights reserved.

If Gravity is Geometry, is Dark Energy just Arithmetic?

NASA Astrophysics Data System (ADS)

Czachor, Marek

2017-04-01

Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, R+4 and (- L/2, L/2)4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms of the corresponding calculus. However, when one switches to the `natural' Diophantine arithmetic and calculus, the Minkowskian character of the space is lost and what one effectively obtains is a Lorentzian manifold. I discuss in more detail the problem of electromagnetic fields produced by a pointlike charge. The solution has the standard form when expressed in terms of the non-Diophantine formalism. When the `natural' formalsm is used, the same solution looks as if the fields were created by a charge located in an expanding universe, with nontrivially accelerating expansion. The effect is clearly visible also in solutions of the Friedman equation with vanishing cosmological constant. All of this suggests that phenomena attributed to dark energy may be a manifestation of a miss-match between the arithmetic employed in mathematical modeling, and the one occurring at the level of natural laws. Arithmetic is as physical as geometry.

Is the SNARC effect related to the level of mathematics? No systematic relationship observed despite more power, more repetitions, and more direct assessment of arithmetic skill.

PubMed

Cipora, Krzysztof; Nuerk, Hans-Christoph

2013-01-01

The SNARC (spatial-numerical association of response codes) described that larger numbers are responded faster with the right hand and smaller numbers with the left hand. It is held in the literature that arithmetically skilled and nonskilled adults differ in the SNARC. However, the respective data are descriptive, and the decisive tests are nonsignificant. Possible reasons for this nonsignificance could be that in previous studies (a) very small samples were used, (b) there were too few repetitions producing too little power and, consequently, reliabilities that were too small to reach conventional significance levels for the descriptive skill differences in the SNARC, and (c) general mathematical ability was assessed by the field of study of students, while individual arithmetic skills were not examined. Therefore we used a much bigger sample, a lot more repetitions, and direct assessment of arithmetic skills to explore relations between the SNARC effect and arithmetic skills. Nevertheless, a difference in SNARC effect between arithmetically skilled and nonskilled participants was not obtained. Bayesian analysis showed positive evidence of a true null effect, not just a power problem. Hence we conclude that the idea that arithmetically skilled and nonskilled participants generally differ in the SNARC effect is not warranted by our data.

Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

NASA Astrophysics Data System (ADS)

Ferrenberg, Alan M.; Xu, Jiahao; Landau, David P.

2018-04-01

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc=0.221 654 626 (5 ) and the critical exponent of the correlation length ν =0.629 912 (86 ) with precision that exceeds all previous Monte Carlo estimates.

A Substituting Meaning for the Equals Sign in Arithmetic Notating Tasks

ERIC Educational Resources Information Center

Jones, Ian; Pratt, Dave

2012-01-01

Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…

Children's Acquisition of Arithmetic Principles: The Role of Experience

ERIC Educational Resources Information Center

Prather, Richard; Alibali, Martha W.

2011-01-01

The current study investigated how young learners' experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children's acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children…

Identifying Simple Numerical Stimuli: Processing Inefficiencies Exhibited by Arithmetic Learning Disabled Children.

ERIC Educational Resources Information Center

Koontz, Kristine L.; Berch, Daniel B.

1996-01-01

Children with arithmetic learning disabilities (n=16) and normally achieving controls (n=16) in grades 3-5 were administered a battery of computerized tasks. Memory spans for both letters and digits were found to be smaller among the arithmetic learning disabled children. Implications for teaching are discussed. (Author/CMS)

Arithmetic Abilities in Children with Developmental Dyslexia: Performance on French ZAREKI-R Test

ERIC Educational Resources Information Center

De Clercq-Quaegebeur, Maryse; Casalis, Séverine; Vilette, Bruno; Lemaitre, Marie-Pierre; Vallée, Louis

2018-01-01

A high comorbidity between reading and arithmetic disabilities has already been reported. The present study aims at identifying more precisely patterns of arithmetic performance in children with developmental dyslexia, defined with severe and specific criteria. By means of a standardized test of achievement in mathematics ("Calculation and…

Binary Arithmetic From Hariot (CA, 1600 A.D.) to the Computer Age.

ERIC Educational Resources Information Center

Glaser, Anton

This history of binary arithmetic begins with details of Thomas Hariot's contribution and includes specific references to Hariot's manuscripts kept at the British Museum. A binary code developed by Sir Francis Bacon is discussed. Briefly mentioned are contributions to binary arithmetic made by Leibniz, Fontenelle, Gauss, Euler, Benzout, Barlow,…

How Is Phonological Processing Related to Individual Differences in Children's Arithmetic Skills?

ERIC Educational Resources Information Center

De Smedt, Bert; Taylor, Jessica; Archibald, Lisa; Ansari, Daniel

2010-01-01

While there is evidence for an association between the development of reading and arithmetic, the precise locus of this relationship remains to be determined. Findings from cognitive neuroscience research that point to shared neural correlates for phonological processing and arithmetic as well as recent behavioral evidence led to the present…

ASIC For Complex Fixed-Point Arithmetic

NASA Technical Reports Server (NTRS)

Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.

1995-01-01

Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.

Cognitive Arithmetic: Evidence for the Development of Automaticity.

ERIC Educational Resources Information Center

LeFevre, Jo-Anne; Bisanz, Jeffrey

To determine whether children's knowledge of arithmetic facts becomes increasingly "automatic" with age, 7-year-olds, 11-year-olds, and adults were given a number-matching task for which mental arithmetic should have been irrelevant. Specifically, students were required to verify the presence of a probe number in a previously presented pair (e.g.,…

Continuity in Representation between Children and Adults: Arithmetic Knowledge Hinders Undergraduates' Algebraic Problem Solving

ERIC Educational Resources Information Center

McNeil, Nicole M.; Rittle-Johnson, Bethany; Hattikudur, Shanta; Petersen, Lori A.

2010-01-01

This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…

Fostering Formal Commutativity Knowledge with Approximate Arithmetic

PubMed Central

Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert

2015-01-01

How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311

Frontoparietal white matter diffusion properties predict mental arithmetic skills in children

PubMed Central

Tsang, Jessica M.; Dougherty, Robert F.; Deutsch, Gayle K.; Wandell, Brian A.; Ben-Shachar, Michal

2009-01-01

Functional MRI studies of mental arithmetic consistently report blood oxygen level–dependent signals in the parietal and frontal regions. We tested whether white matter pathways connecting these regions are related to mental arithmetic ability by using diffusion tensor imaging (DTI) to measure these pathways in 28 children (age 10–15 years, 14 girls) and assessing their mental arithmetic skills. For each child, we identified anatomically the anterior portion of the superior longitudinal fasciculus (aSLF), a pathway connecting parietal and frontal cortex. We measured fractional anisotropy in a core region centered along the length of the aSLF. Fractional anisotropy in the left aSLF positively correlates with arithmetic approximation skill, as measured by a mental addition task with approximate answer choices. The correlation is stable in adjacent core aSLF regions but lower toward the pathway endpoints. The correlation is not explained by shared variance with other cognitive abilities and did not pass significance in the right aSLF. These measurements used DTI, a structural method, to test a specific functional model of mental arithmetic. PMID:19948963

Naming Speed in Dyslexia and Dyscalculia

ERIC Educational Resources Information Center

Willburger, Edith; Fussenegger, Barbara; Moll, Kristina; Wood, Guilherme; Landerl, Karin

2008-01-01

In four carefully selected samples of 8- to 10-year old children with dyslexia (but age adequate arithmetic skills), dyscalculia (but age adequate reading skills), dyslexia/dyscalculia and controls a domain-general deficit in rapid automatized naming (RAN) was found for both dyslexia groups. Dyscalculic children exhibited a domain-specific deficit…

Environmental and Agricultural Sciences. Georgia Core Standards for Occupational Clusters.

ERIC Educational Resources Information Center

Georgia Univ., Athens. Dept. of Occupational Studies.

This document lists core standards and occupational knowledge amd skills that have been identified/validated by industry as necessary to all Georgia students in secondary-level environmental and agricultural sciences programs. First, foundation skills are grouped as follows: basic skills (reading, writing, arithmetic/mathematics, listening,…

Business, Marketing, and Information Management. Georgia Core Standards for Occupational Clusters.

ERIC Educational Resources Information Center

Georgia Univ., Athens. Dept. of Occupational Studies.

This document lists core standards and occupational knowledge and skills that have been identified and validated by industry as necessary to all Georgia students in business, marketing, and information management programs. First, foundation skills are grouped as follows: basic skills (reading, writing, arithmetic/mathematics, listening, speaking);…

A Comparison of Two Approaches to Beta-Flexible Clustering.

ERIC Educational Resources Information Center

Belbin, Lee; And Others

1992-01-01

A method for hierarchical agglomerative polythetic (multivariate) clustering, based on unweighted pair group using arithmetic averages (UPGMA) is compared with the original beta-flexible technique, a weighted average method. Reasons the flexible UPGMA strategy is recommended are discussed, focusing on the ability to recover cluster structure over…

Arithmetic and Hyperbolic Structures in String Theory

NASA Astrophysics Data System (ADS)

Persson, Daniel

2010-01-01

This monograph is an updated and extended version of the author's PhD thesis. It consists of an introductory text followed by two separate parts which are loosely related but may be read independently of each other. In Part I we analyze certain hyperbolic structures arising when studying gravity in the vicinity of a spacelike singularity (the "BKL-limit"). In this limit, spatial points decouple and the dynamics exhibits ultralocal behaviour which may be described in terms of a (possibly chaotic) hyperbolic billiard. In all supergravities arising as low-energy limits of string theory or M-theory, the billiard dynamics takes place within the fundamental Weyl chambers of certain hyperbolic Kac-Moody algebras, suggesting that these algebras generate hidden infinite-dimensional symmetries of the theory. Part II of the thesis is devoted to a study of how (U-)dualities in string theory provide powerful constraints on perturbative and non-perturbative quantum corrections. These dualities are described by certain arithmetic groups G(Z) which are conjectured to be preserved in the effective action. The exact couplings are given by automorphic forms on the double quotient G(Z)G/K. We discuss in detail various methods of constructing automorphic forms, with particular emphasis on non-holomorphic Eisenstein series. We provide detailed examples for the physically relevant cases of SL(2,Z) and SL(3,Z), for which we construct their respective Eisenstein series and compute their (non-abelian) Fourier expansions. We also show how these techniques can be applied to hypermultiplet moduli spaces in type II Calabi-Yau compactifications, and we provide a detailed analysis for the universal hypermultiplet.

Sources of Group and Individual Differences in Emerging Fraction Skills

PubMed Central

Hecht, Steven A.; Vagi, Kevin J.

2010-01-01

Results from a two year longitudinal study of 181 children from fourth through fifth grade are reported. Levels of growth in children’s computation, word problem, and estimation skills using common fractions were predicted by working memory, attentive classroom behavior, conceptual knowledge about fractions, and simple arithmetic fluency. Comparisons of 55 participants identified as having mathematical difficulties to those without mathematical difficulties revealed that group differences in emerging fraction skills were consistently mediated by attentive classroom behavior and conceptual knowledge about fractions. Neither working memory nor arithmetic fluency mediated group differences in growth in fraction skills. It was also found that the development of basic fraction skills and conceptual knowledge are bidirectional in that conceptual knowledge exerted strong influences on all three types of basic fraction skills, and basic fraction skills exerted a more modest influence on subsequent conceptual knowledge. Results are discussed with reference to how the identification of potentially malleable student characteristics that contribute to the difficulties that some students have with fractions informs interventions and also will contribute to a future theoretical account concerning how domain general and domain specific factors influence the development of basic fraction skills. PMID:21170171

Effect of yoga on cognitive abilities in schoolchildren from a socioeconomically disadvantaged background: a randomized controlled study.

PubMed

Chaya, Mayasandra S; Nagendra, Hongasandra; Selvam, Sumithra; Kurpad, Anura; Srinivasan, Krishnamachari

2012-12-01

The objective of this study was to assess the effect of yoga, compared to physical activity on the cognitive performance in 7-9 year-old schoolchildren from a socioeconomic disadvantaged background. Two hundred (200) schoolchildren from Bangalore, India, after baseline assessment of cognitive functioning were randomly allocated to either a yoga or a physical-activity group. Cognitive functions (attention and concentration, visuo-spatial abilities, verbal ability, and abstract thinking) were assessed using an Indian adaptation of the Wechsler Intelligence Scale for Children at baseline, after 3 months of intervention, and later at a 3-month follow-up. Of the 200 subjects, 193 were assessed at 3 months after the study, and then 180 were assessed at the 3-month follow-up. There were no significant differences in cognitive performance between the two study groups (yoga versus physical activity) at postintervention, after controlling for grade levels. Improvement in the mean scores of cognitive tests following intervention varied from 0.5 (Arithmetic) to 1.4 (Coding) for the yoga group and 0.7 (Arithmetic) to 1.6 (Vocabulary) in the physical-activity group. Yoga was as effective as physical activity in improving cognitive performance in 7-9 year old schoolchildren. Further studies are needed to examine the dose-response relationship between yoga and cognitive performance.

Academic skills in the long term after epilepsy surgery in childhood.

PubMed

Puka, Klajdi; Smith, Mary Lou

2016-09-01

We evaluated the progression of academic skills in a cohort of patients who underwent, or were considered for, epilepsy surgery in childhood, four to eleven years before. The few existing studies that have evaluated cognitive function in the long term after surgery have examined intelligence and memory. Participants were 97 patients with childhood-onset intractable epilepsy; 61 had undergone resective epilepsy surgery. Participants completed standardized tests of reading, spelling, arithmetic, and intelligence at baseline and, on average, 7years after. Surgical patients were additionally assessed one year postsurgery. At baseline and long-term follow-up, 61% and 69% of patients, respectively, scored at least one standard deviation below normative data in at least one academic domain. Evaluation of change over time while controlling for IQ showed that arithmetic scores were lower at long-term follow-up in comparison with those at baseline among all patient groups, whereas reading and spelling scores remained unchanged. Few advantages were associated with seizure control. Multiple regression analyses found that older age at surgery, cessation of antiepileptic medications, improved IQ, and low baseline scores were independently associated with improvement in some academic domains among all patient groups. We found that arithmetic scores were lower at long-term follow-up, suggesting a lack of ongoing development or deterioration in skills. Reading and spelling scores remained stable suggesting that patients made gains in abilities at a rate expected for their increase in age; this finding contrasts with recent short-term outcome studies identifying significantly lower scores over time in these areas. Copyright © 2016 Elsevier Inc. All rights reserved.

Space of symmetry matrices with elements 0, ±1 and complete geometric description; its properties and application.

PubMed

Stróż, Kazimierz

2011-09-01

A fixed set, that is the set of all lattice metrics corresponding to the arithmetic holohedry of a primitive lattice, is a natural tool for keeping track of the symmetry changes that may occur in a deformable lattice [Ericksen (1979). Arch. Rat. Mech. Anal. 72, 1-13; Michel (1995). Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek, W. Florek & S. Walcerz. Singapore: Academic Press; Pitteri & Zanzotto (1996). Acta Cryst. A52, 830-838; and references quoted therein]. For practical applications it is desirable to limit the infinite number of arithmetic holohedries, and simplify their classification and construction of the fixed sets. A space of 480 matrices with cyclic consecutive powers, determinant 1, elements from {0, ±1} and geometric description were analyzed and offered as the framework for dealing with the symmetry of reduced lattices. This matrix space covers all arithmetic holohedries of primitive lattice descriptions related to the three shortest lattice translations in direct or reciprocal spaces, and corresponds to the unique list of 39 fixed points with integer coordinates in six-dimensional space of lattice metrics. Matrices are presented by the introduced dual symbol, which sheds some light on the lattice and its symmetry-related properties, without further digging into matrices. By the orthogonal lattice distortion the lattice group-subgroup relations are easily predicted. It was proven and exemplified that new symbols enable classification of lattice groups on an absolute basis, without metric considerations. In contrast to long established but sophisticated methods for assessing the metric symmetry of a lattice, simple filtering of the symmetry operations from the predefined set is proposed. It is concluded that the space of symmetry matrices with elements from {0, ±1} is the natural environment of lattice symmetries related to the reduced cells and that complete geometric characterization of matrices in the arithmetic holohedry provides a useful tool for solving practical lattice-related problems, especially in the context of lattice deformation. © 2011 International Union of Crystallography

Comparison of neurocognitive results after coronary artery bypass grafting and thoracic aortic surgery using retrograde cerebral perfusion.

PubMed

Miyairi, Takeshi; Takamoto, Shinichi; Kotsuka, Yutaka; Takeuchi, Atsuko; Yamanaka, Katsuo; Sato, Hajime

2005-07-01

Retrograde cerebral perfusion (RCP) is used as an adjunctive method to hypothermic circulatory arrest to enhance cerebral protection in patients undergoing thoracic aortic surgery. It remains unclear whether RCP provides improved neurological and neuropsychological outcome. Forty-six patients undergoing thoracic aortic surgery using RCP, and 28 undergoing coronary artery bypass grafting (CABG; n = 28) with CPB, were enrolled in the study. Patients receiving RCP were subdivided into two groups, those with less than 60 min of RCP (S-RCP; n = 27) and with 60 min or more (L-RCP; n = 19). The patients' neurocognitive state was assessed by the revised Wechsler Adult Intelligence Scale a few days before operation, at 2-3 weeks and 4-6 months after operation. There were no stroke, seizure, and hospital mortality in either group. Significant decline between baseline and early scores were seen in three subtests (digit span, arithmetic, and picture completion) for S-RCP and four (digit span, arithmetic, picture completion, and picture arrangement) for L-RCP. Significant decline between baseline and late scores were seen in one subtest (arithmetic) for S-RCP, four (digit span, arithmetic, picture completion, and picture arrangement) for L-RCP, and one (object assembly) for CABG. The mean change of scores for one late test (digit symbol) was significantly lower in S-RCP than in CABG. The mean change of scores for three early tests (digit span, vocabulary, and picture arrangement) and four late tests (information, digit span, picture completion, and picture arrangement) were significantly lower in L-RCP than in CABG. Stepwise logistic regression analysis disclosed that, after considering the other variables, significant difference in test score changes were observed between CABG and L-RCP for two early tests (picture completion and digit symbol) as well as for three late tests (digit span, similarities, and picture completion). None of test score changes showed significant difference between CABG and S-RCP. The neurocognitive outcome in patients undergoing RCP less than 60 min were comparable with patients undergoing CABG without circulatory arrest. Prolonged RCP of 60 min or more in patients undergoing surgery of the thoracic aorta was associated with postoperative neurocognitive impairment.

Working Memory and Arithmetic Calculation in Children: The Contributory Roles of Processing Speed, Short-Term Memory, and Reading

ERIC Educational Resources Information Center

Berg, Derek H.

2008-01-01

The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing…

Arithmetic Achievement in Children with Cerebral Palsy or Spina Bifida Meningomyelocele

ERIC Educational Resources Information Center

Jenks, Kathleen M.; van Lieshout, Ernest C. D. M.; de Moor, Jan

2009-01-01

The aim of this study was to establish whether children with a physical disability resulting from central nervous system disorders (CNSd) show a level of arithmetic achievement lower than that of non-CNSd children and whether this is related to poor automaticity of number facts or reduced arithmetic instruction time. Twenty-two children with CNSd…

The Association between Arithmetic and Reading Performance in School: A Meta-Analytic Study

ERIC Educational Resources Information Center

Singer, Vivian; Strasser, Kathernie

2017-01-01

Many studies of school achievement find a significant association between reading and arithmetic achievement. The magnitude of the association varies widely across the studies, but the sources of this variation have not been identified. The purpose of this paper is to examine the magnitude and determinants of the relation between arithmetic and…

24 CFR Appendix E to Part 3500 - Arithmetic Steps

Code of Federal Regulations, 2010 CFR

2010-04-01

... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Arithmetic Steps E Appendix E to...—Arithmetic Steps I. Example Illustrating Aggregate Analysis: ASSUMPTIONS: Disbursements: $360 for school... Payment: July 1 Step 1—Initial Trial Balance Aggregate pmt disb bal Jun 0 0 0 Jul 130 500 −370 Aug 130 0...

Computational Fluency and Strategy Choice Predict Individual and Cross-National Differences in Complex Arithmetic

ERIC Educational Resources Information Center

Vasilyeva, Marina; Laski, Elida V.; Shen, Chen

2015-01-01

The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that…

Arithmetic Difficulties in Children with Cerebral Palsy Are Related to Executive Function and Working Memory

ERIC Educational Resources Information Center

Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest C. D. M.

2009-01-01

Background: Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Methods: Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and…

A Cross-Cultural Investigation into the Development of Place-Value Concepts of Children in Taiwan and the United States.

ERIC Educational Resources Information Center

Yang, Ma Tzu-Lin; Cobb, Paul

1995-01-01

Compares mathematics achievement of children in Taiwan and the United States by analyzing the arithmetical learning contexts of each. Interviews with parents and teachers identify cultural beliefs about learning arithmetic; interviews with students identify level of sophistication of arithmetical concepts. Found greater understanding by Chinese…

Comparing the Use of the Interpersonal Computer, Personal Computer and Pen-and-Paper When Solving Arithmetic Exercises

ERIC Educational Resources Information Center

Alcoholado, Cristián; Diaz, Anita; Tagle, Arturo; Nussbaum, Miguel; Infante, Cristián

2016-01-01

This study aims to understand the differences in student learning outcomes and classroom behaviour when using the interpersonal computer, personal computer and pen-and-paper to solve arithmetic exercises. In this multi-session experiment, third grade students working on arithmetic exercises from various curricular units were divided into three…

Chopped molecular beam multiplexing system

NASA Technical Reports Server (NTRS)

Adams, Billy R. (Inventor)

1986-01-01

The integration of a chopped molecular beam mass spectrometer with a time multiplexing system is described. The chopping of the molecular beam is synchronized with the time intervals by a phase detector and a synchronous motor. Arithmetic means are generated for phase shifting the chopper with respect to the multiplexer. A four channel amplifier provides the capacity to independently vary the baseline and amplitude in each channel of the multiplexing system.

A new approach to Catalan numbers using differential equations

NASA Astrophysics Data System (ADS)

Kim, D. S.; Kim, T.

2017-10-01

In this paper, we introduce two differential equations arising from the generating function of the Catalan numbers which are `inverses' to each other in a certain sense. From these differential equations, we obtain some new and explicit identities for Catalan and higher-order Catalan numbers. In addition, by other means than differential equations, we also derive some interesting identities involving Catalan numbers which are of arithmetic and combinatorial nature.

Non-symbolic halving in an Amazonian indigene group

PubMed Central

McCrink, Koleen; Spelke, Elizabeth S.; Dehaene, Stanislas; Pica, Pierre

2014-01-01

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. PMID:23587042

Genetic diversity of popcorn genotypes using molecular analysis.

PubMed

Resh, F S; Scapim, C A; Mangolin, C A; Machado, M F P S; do Amaral, A T; Ramos, H C C; Vivas, M

2015-08-19

In this study, we analyzed dominant molecular markers to estimate the genetic divergence of 26 popcorn genotypes and evaluate whether using various dissimilarity coefficients with these dominant markers influences the results of cluster analysis. Fifteen random amplification of polymorphic DNA primers produced 157 amplified fragments, of which 65 were monomorphic and 92 were polymorphic. To calculate the genetic distances among the 26 genotypes, the complements of the Jaccard, Dice, and Rogers and Tanimoto similarity coefficients were used. A matrix of Dij values (dissimilarity matrix) was constructed, from which the genetic distances among genotypes were represented in a more simplified manner as a dendrogram generated using the unweighted pair-group method with arithmetic average. Clusters determined by molecular analysis generally did not group material from the same parental origin together. The largest genetic distance was between varieties 17 (UNB-2) and 18 (PA-091). In the identification of genotypes with the smallest genetic distance, the 3 coefficients showed no agreement. The 3 dissimilarity coefficients showed no major differences among their grouping patterns because agreement in determining the genotypes with large, medium, and small genetic distances was high. The largest genetic distances were observed for the Rogers and Tanimoto dissimilarity coefficient (0.74), followed by the Jaccard coefficient (0.65) and the Dice coefficient (0.48). The 3 coefficients showed similar estimations for the cophenetic correlation coefficient. Correlations among the matrices generated using the 3 coefficients were positive and had high magnitudes, reflecting strong agreement among the results obtained using the 3 evaluated dissimilarity coefficients.

Changes of brain response induced by simulated weightlessness

NASA Astrophysics Data System (ADS)

Wei, Jinhe; Yan, Gongdong; Guan, Zhiqiang

The characteristics change of brain response was studied during 15° head-down tilt (HDT) comparing with 45° head-up tilt (HUT). The brain responses evaluated included the EEG power spectra change at rest and during mental arithmetic, and the event-related potentials (ERPs) of somatosensory, selective attention and mental arithmetic activities. The prominent feature of brain response change during HDT revealed that the brain function was inhibited to some extent. Such inhibition included that the significant increment of "40Hz" activity during HUT arithmetic almost disappeared during HDT arithmetic, and that the positive-potential effect induced by HDT presented in all kinds of ERPs measured, but the slow negative wave reflecting mental arithmetic and memory process was elongated. These data suggest that the brain function be affected profoundly by the simulated weightlessness, therefore, the brain function change during space flight should be studied systematically.

The relationship between medical impairments and arithmetic development in children with cerebral palsy.

PubMed

Jenks, Kathleen M; van Lieshout, Ernest C D M; de Moor, Jan

2009-05-01

Arithmetic ability was tested in children with cerebral palsy without severe intellectual impairment (verbal IQ >or= 70) attending special (n = 41) or mainstream education (n = 16) as well as control children in mainstream education (n = 16) throughout first and second grade. Children with cerebral palsy in special education did not appear to have fully automatized arithmetic facts by the end of second grade. Their lower accuracy and consistently slower (verbal) response times raise important concerns for their future arithmetic development. Differences in arithmetic performance between children with cerebral palsy in special or mainstream education were not related to localization of cerebral palsy or to gross motor impairment. Rather, lower accuracy and slower verbal responses were related to differences in nonverbal intelligence and the presence of epilepsy. Left-hand impairment was related to slower verbal responses but not to lower accuracy.

Computational fluency and strategy choice predict individual and cross-national differences in complex arithmetic.

PubMed

Vasilyeva, Marina; Laski, Elida V; Shen, Chen

2015-10-01

The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that differed in difficulty: single-, mixed-, and double-digit addition. Children's strategy use varied as a function of problem difficulty, consistent with Siegler's theory of strategy choice. The use of decomposition strategy interacted with computational fluency in predicting the accuracy of double-digit addition. Further, the frequency of decomposition and computational fluency fully mediated cross-national differences in accuracy on these complex arithmetic problems. The results indicate the importance of both fluency with basic number facts and the decomposition strategy for later arithmetic performance. (c) 2015 APA, all rights reserved).

The MasPar MP-1 As a Computer Arithmetic Laboratory

PubMed Central

Anuta, Michael A.; Lozier, Daniel W.; Turner, Peter R.

1996-01-01

This paper is a blueprint for the use of a massively parallel SIMD computer architecture for the simulation of various forms of computer arithmetic. The particular system used is a DEC/MasPar MP-1 with 4096 processors in a square array. This architecture has many advantages for such simulations due largely to the simplicity of the individual processors. Arithmetic operations can be spread across the processor array to simulate a hardware chip. Alternatively they may be performed on individual processors to allow simulation of a massively parallel implementation of the arithmetic. Compromises between these extremes permit speed-area tradeoffs to be examined. The paper includes a description of the architecture and its features. It then summarizes some of the arithmetic systems which have been, or are to be, implemented. The implementation of the level-index and symmetric level-index, LI and SLI, systems is described in some detail. An extensive bibliography is included. PMID:27805123

Symbolic Numerical Magnitude Processing Is as Important to Arithmetic as Phonological Awareness Is to Reading

PubMed Central

Vanbinst, Kiran; Ansari, Daniel; Ghesquière, Pol; De Smedt, Bert

2016-01-01

In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children’s numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties. PMID:26942935

Visuospatial and verbal memory in mental arithmetic.

PubMed

Clearman, Jack; Klinger, Vojtěch; Szűcs, Dénes

2017-09-01

Working memory allows complex information to be remembered and manipulated over short periods of time. Correlations between working memory and mathematics achievement have been shown across the lifespan. However, only a few studies have examined the potentially distinct contributions of domain-specific visuospatial and verbal working memory resources in mental arithmetic computation. Here we aimed to fill this gap in a series of six experiments pairing addition and subtraction tasks with verbal and visuospatial working memory and interference tasks. In general, we found higher levels of interference between mental arithmetic and visuospatial working memory tasks than between mental arithmetic and verbal working memory tasks. Additionally, we found that interference that matched the working memory domain of the task (e.g., verbal task with verbal interference) lowered working memory performance more than mismatched interference (verbal task with visuospatial interference). Findings suggest that mental arithmetic relies on domain-specific working memory resources.

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

One registration multi-atlas-based pseudo-CT generation for attenuation correction in PET/MRI.

PubMed

Arabi, Hossein; Zaidi, Habib

2016-10-01

The outcome of a detailed assessment of various strategies for atlas-based whole-body bone segmentation from magnetic resonance imaging (MRI) was exploited to select the optimal parameters and setting, with the aim of proposing a novel one-registration multi-atlas (ORMA) pseudo-CT generation approach. The proposed approach consists of only one online registration between the target and reference images, regardless of the number of atlas images (N), while for the remaining atlas images, the pre-computed transformation matrices to the reference image are used to align them to the target image. The performance characteristics of the proposed method were evaluated and compared with conventional atlas-based attenuation map generation strategies (direct registration of the entire atlas images followed by voxel-wise weighting (VWW) and arithmetic averaging atlas fusion). To this end, four different positron emission tomography (PET) attenuation maps were generated via arithmetic averaging and VWW scheme using both direct registration and ORMA approaches as well as the 3-class attenuation map obtained from the Philips Ingenuity TF PET/MRI scanner commonly used in the clinical setting. The evaluation was performed based on the accuracy of extracted whole-body bones by the different attenuation maps and by quantitative analysis of resulting PET images compared to CT-based attenuation-corrected PET images serving as reference. The comparison of validation metrics regarding the accuracy of extracted bone using the different techniques demonstrated the superiority of the VWW atlas fusion algorithm achieving a Dice similarity measure of 0.82 ± 0.04 compared to arithmetic averaging atlas fusion (0.60 ± 0.02), which uses conventional direct registration. Application of the ORMA approach modestly compromised the accuracy, yielding a Dice similarity measure of 0.76 ± 0.05 for ORMA-VWW and 0.55 ± 0.03 for ORMA-averaging. The results of quantitative PET analysis followed the same trend with less significant differences in terms of SUV bias, whereas massive improvements were observed compared to PET images corrected for attenuation using the 3-class attenuation map. The maximum absolute bias achieved by VWW and VWW-ORMA methods was 06.4 ± 5.5 in the lung and 07.9 ± 4.8 in the bone, respectively. The proposed algorithm is capable of generating decent attenuation maps. The quantitative analysis revealed a good correlation between PET images corrected for attenuation using the proposed pseudo-CT generation approach and the corresponding CT images. The computational time is reduced by a factor of 1/N at the expense of a modest decrease in quantitative accuracy, thus allowing us to achieve a reasonable compromise between computing time and quantitative performance.

Concentration and distribution of sixty-one elements in coals from DPR Korea

USGS Publications Warehouse

Hu, Jiawen; Zheng, B.; Finkelman, R.B.; Wang, B.; Wang, M.; Li, S.; Wu, D.

2006-01-01

Fifty coal samples (28 anthracite and 22 lignites) were collected from both main and small coal mines in DPR Korea prioritized by resource distribution and coal production. The concentrations of 61 elements in 50 coal samples were determined by several multielement and element-specific techniques, including inductively coupled plasma atomic emission spectrometry (ICP-AES), and inductively coupled plasma mass spectrometry (ICP-MS), ion chromatogram (IC), cold-vapor atomic absorption spectrometry (CV-AAS), and hydride generation atomic absorption spectrometry (HGAAS). The ranges, arithmetic means and geometric means of concentrations of these elements are presented. A comparison with crustal abundances (Clarke values) shows that some potentially hazardous elements in the coals of DPR Korea are highly enriched Li, B, S, Cl, Zn, As, Se, Cd, Sn, Sb, W, Te, Hg, Ag, Pb, and La, Ce, Dy, Tm, Ge, Mo, Cs, Tl, Bi, Th and U are moderately enriched. A comparison of ranges and means of elemental concentrations in DPR Korea, Chinese, and world coals shows the ranges of most elements in DPR Korea coals are very close to the ranges of world coals. Arithmetic means of most elements in DPR Korea coals are close to that of American coals. Most elements arithmetic means are higher in Jurassic and Paleogene coals than coals of other ages. In DPR Korea coals, only seven elements in early Permian coals are higher than other periods: Li, Zn, Se, Cd, Hg, Pb, and Bi. Only five elements B, As, Sr, Mo, W in Neogene coals have arithmetic means higher than others. SiO2 and Al2O 3 in ashes are more than 70% except six samples. The correlation between ash yields and major elements from high to low is in the order of Si>Al>Ti>K>Mg>Fe>Na>Ca>P>S. Most elements have high positive correlation with ash (r>0.5) and show high inorganic affinity. ?? 2005 Elsevier Ltd. All rights reserved.

Intrinsic motivation and learning in a schizophrenia spectrum sample.

PubMed

Choi, Jimmy; Medalia, Alice

2010-05-01

A motivation is a telling hallmark of negative symptomatology in schizophrenia, and it impacts nearly every facet of behavior, including inclination to attempt the difficult cognitive tasks involved in cognitive remediation therapy. Experiences of external reward, reinforcement, and hedonic anticipatory enjoyment are diminished in psychosis, so therapeutics which instead target intrinsic motivation for cognitive tasks may enhance task engagement, and subsequently, remediation outcome. We examined whether outpatients could attain benefits from an intrinsically motivating instructional approach which (a) presents learning materials in a meaningful game-like context, (b) personalizes elements of the learning materials into themes of high interest value, and (c) offers choices so patients can increase their control over the learning process. We directly compared one learning method that incorporated the motivational paradigm into an arithmetic learning program against another method that carefully manipulated out the motivational variables in the same learning program. Fifty-seven subjects with schizophrenia or schizoaffective disorder were randomly assigned to one of the two learning programs for 10 thirty-minute sessions while an intent-to-treat convenience subsample (n=15) was used to account for practice effect. Outcome measures were arithmetic learning, attention, motivation, self competency, and symptom severity. Results showed the motivational group (a) acquired more arithmetic skill, (b) possessed greater intrinsic motivation for the task, (c) reported greater feelings of self competency post-treatment, and (d) demonstrated better post-test attention. Interestingly, baseline perception of self competency was a significant predictor of post-test arithmetic scores. Results demonstrated that incorporating intrinsically motivating instructional techniques into a difficult cognitive task promoted greater learning of the material, higher levels of intrinsic motivation to attempt the demanding task, and greater feelings of self efficacy and achievement to learn. Copyright (c) 2009 Elsevier B.V. All rights reserved.

Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study

PubMed Central

Rodic, Maja; Tikhomirova, Tatiana; Kolienko, Tatiana; Malykh, Sergey; Bogdanova, Olga; Zueva, Dina Y.; Gynku, Elena I.; Wan, Sirui; Zhou, Xinlin; Kovas, Yulia

2015-01-01

Previous research has consistently found an association between spatial and mathematical abilities. We hypothesized that this link may partially explain the consistently observed advantage in mathematics demonstrated by East Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. Seven hundered and twenty one 6–9-year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1) to test whether spatial ability predicts mathematical ability in 7–9 year-old children across the samples; (2) to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age. PMID:25859235

Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study.

PubMed

Rodic, Maja; Tikhomirova, Tatiana; Kolienko, Tatiana; Malykh, Sergey; Bogdanova, Olga; Zueva, Dina Y; Gynku, Elena I; Wan, Sirui; Zhou, Xinlin; Kovas, Yulia

2015-01-01

Previous research has consistently found an association between spatial and mathematical abilities. We hypothesized that this link may partially explain the consistently observed advantage in mathematics demonstrated by East Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. Seven hundered and twenty one 6-9-year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1) to test whether spatial ability predicts mathematical ability in 7-9 year-old children across the samples; (2) to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age.

Design of RISC Processor Using VHDL and Cadence

NASA Astrophysics Data System (ADS)

Moslehpour, Saeid; Puliroju, Chandrasekhar; Abu-Aisheh, Akram

The project deals about development of a basic RISC processor. The processor is designed with basic architecture consisting of internal modules like clock generator, memory, program counter, instruction register, accumulator, arithmetic and logic unit and decoder. This processor is mainly used for simple general purpose like arithmetic operations and which can be further developed for general purpose processor by increasing the size of the instruction register. The processor is designed in VHDL by using Xilinx 8.1i version. The present project also serves as an application of the knowledge gained from past studies of the PSPICE program. The study will show how PSPICE can be used to simplify massive complex circuits designed in VHDL Synthesis. The purpose of the project is to explore the designed RISC model piece by piece, examine and understand the Input/ Output pins, and to show how the VHDL synthesis code can be converted to a simplified PSPICE model. The project will also serve as a collection of various research materials about the pieces of the circuit.

The Arithmetic Project Course for Teachers - 8. Topic: Lower Brackets and Upper Brackets. Supplement: Arithmetic With Frames.

ERIC Educational Resources Information Center

Education Development Center, Inc., Newton, MA.

This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being…

Sex Differences in Mental Arithmetic, Digit Span, and "g" Defined as Working Memory Capacity

ERIC Educational Resources Information Center

Lynn, Richard; Irwing, Paul

2008-01-01

Meta-analyses are presented of sex differences in (1) the (mental) arithmetic subtest of the Wechsler intelligence tests for children and adolescents (the WISC and WPPSI tests), showing that boys obtained a mean advantage of 0.11d; (2) the (mental) arithmetic subtest of the Wechsler intelligence tests for adults (the WAIS tests) showing a mean…

Comparing and Transforming: An Application of Piaget's Morphisms Theory to the Development of Class Inclusion and Arithmetic Problem Solving.

ERIC Educational Resources Information Center

Barrouillet, Pierre; Poirier, Louise

1997-01-01

Outlines Piaget's late ideas on categories and morphisms and the impact of these ideas on the comprehension of the inclusion relationship and the solution of arithmetic problems. Reports a study in which fourth through sixth graders were given arithmetic problems involving two known quantities associated with changes rather than states. Identified…

Working Memory as a Predictor of Written Arithmetical Skills in Children: The Importance of Central Executive Functions

ERIC Educational Resources Information Center

Andersson, Ulf

2008-01-01

Background: The study was conducted in an attempt to further our understanding of how working memory contributes to written arithmetical skills in children. Aim: The aim was to pinpoint the contribution of different central executive functions and to examine the contribution of the two subcomponents of children's written arithmetical skills.…

Contributions of Domain-General Cognitive Resources and Different Forms of Arithmetic Development to Pre-Algebraic Knowledge

ERIC Educational Resources Information Center

Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.

2012-01-01

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems…

Error-correcting codes in computer arithmetic.

NASA Technical Reports Server (NTRS)

Massey, J. L.; Garcia, O. N.

1972-01-01

Summary of the most important results so far obtained in the theory of coding for the correction and detection of errors in computer arithmetic. Attempts to satisfy the stringent reliability demands upon the arithmetic unit are considered, and special attention is given to attempts to incorporate redundancy into the numbers themselves which are being processed so that erroneous results can be detected and corrected.

Limitations to Teaching Children 2 + 2 = 4: Typical Arithmetic Problems Can Hinder Learning of Mathematical Equivalence

ERIC Educational Resources Information Center

McNeil, Nicole M.

2008-01-01

Do typical arithmetic problems hinder learning of mathematical equivalence? Second and third graders (7-9 years old; N= 80) received lessons on mathematical equivalence either with or without typical arithmetic problems (e.g., 15 + 13 = 28 vs. 28 = 28, respectively). Children then solved math equivalence problems (e.g., 3 + 9 + 5 = 6 + __),…

Arithmetic Data Cube as a Data Intensive Benchmark

NASA Technical Reports Server (NTRS)

Frumkin, Michael A.; Shabano, Leonid

2003-01-01

Data movement across computational grids and across memory hierarchy of individual grid machines is known to be a limiting factor for application involving large data sets. In this paper we introduce the Data Cube Operator on an Arithmetic Data Set which we call Arithmetic Data Cube (ADC). We propose to use the ADC to benchmark grid capabilities to handle large distributed data sets. The ADC stresses all levels of grid memory by producing 2d views of an Arithmetic Data Set of d-tuples described by a small number of parameters. We control data intensity of the ADC by controlling the sizes of the views through choice of the tuple parameters.

The Montreal Imaging Stress Task: using functional imaging to investigate the effects of perceiving and processing psychosocial stress in the human brain

PubMed Central

Dedovic, Katarina; Renwick, Robert; Mahani, Najmeh Khalili; Engert, Veronika; Lupien, Sonia J.; Pruessner, Jens C.

2005-01-01

Objective We developed a protocol for inducing moderate psychologic stress in a functional imaging setting and evaluated the effects of stress on physiology and brain activation. Methods The Montreal Imaging Stress Task (MIST), derived from the Trier Mental Challenge Test, consists of a series of computerized mental arithmetic challenges, along with social evaluative threat components that are built into the program or presented by the investigator. To allow the effects of stress and mental arithmetic to be investigated separately, the MIST has 3 test conditions (rest, control and experimental), which can be presented in either a block or an event-related design, for use with functional magnetic resonance imaging (fMRI) or positron emission tomography (PET). In the rest condition, subjects look at a static computer screen on which no tasks are shown. In the control condition, a series of mental arithmetic tasks are displayed on the computer screen, and subjects submit their answers by means of a response interface. In the experimental condition, the difficulty and time limit of the tasks are manipulated to be just beyond the individual's mental capacity. In addition, in this condition the presentation of the mental arithmetic tasks is supplemented by a display of information on individual and average performance, as well as expected performance. Upon completion of each task, the program presents a performance evaluation to further increase the social evaluative threat of the situation. Results In 2 independent studies using PET and a third independent study using fMRI, with a total of 42 subjects, levels of salivary free cortisol for the whole group were significantly increased under the experimental condition, relative to the control and rest conditions. Performing mental arithmetic was linked to activation of motor and visual association cortices, as well as brain structures involved in the performance of these tasks (e.g., the angular gyrus). Conclusions We propose the MIST as a tool for investigating the effects of perceiving and processing psychosocial stress in functional imaging studies. PMID:16151536

Patterns of problem-solving in children's literacy and arithmetic.

PubMed

Farrington-Flint, Lee; Vanuxem-Cotterill, Sophie; Stiller, James

2009-11-01

Patterns of problem-solving among 5-to-7 year-olds' were examined on a range of literacy (reading and spelling) and arithmetic-based (addition and subtraction) problem-solving tasks using verbal self-reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years I and 2 on the arithmetic (addition and subtraction) than literacy-based tasks (reading and spelling). However, across all four tasks, the children showed a tendency to move from less sophisticated procedural-based strategies, which included phonological strategies for reading and spelling and counting-all and finger modellingfor addition and subtraction, to more efficient retrieval methods from Years I to 2. Distinct patterns in children's problem-solving skill were identified on the literacy and arithmetic tasks using two separate cluster analyses. There was a strong association between these two profiles showing that those children with more advanced problem-solving skills on the arithmetic tasks also showed more advanced profiles on the literacy tasks. The results highlight how different-aged children show flexibility in their use of problem-solving strategies across literacy and arithmetical contexts and reinforce the importance of studying variations in children's problem-solving skill across different educational contexts.

Mathematics anxiety in children with developmental dyscalculia.

PubMed

Rubinsten, Orly; Tannock, Rosemary

2010-07-15

Math anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure. Participants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively. Participants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group. These results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety.

Meat supplementation improves growth, cognitive, and behavioral outcomes in Kenyan children.

PubMed

Neumann, Charlotte G; Murphy, Suzanne P; Gewa, Connie; Grillenberger, Monika; Bwibo, Nimrod O

2007-04-01

A randomized, controlled school feeding study was conducted in rural Embu District, Kenya to test for a causal link between animal-source food intake and changes in micronutrient nutrition and growth, cognitive, and behavioral outcomes. Twelve primary schools were randomly assigned to 1 of 4 groups. Children in Standard I classes received the local plant-based dish githeri as a midmorning school snack supplemented with meat, milk, or fat added to equalize energy content in all feedings. The Control children received no feedings but participated in data collection. Main outcome measures assessed at baseline and longitudinally were 24-h food intake recall, anthropometry, cognitive function, physical activity, and behaviors during school free play. For cognitive function, the Meat group showed the steepest rate of increase on Raven's Progressive Matrices scores and in zone-wide school end-term total and arithmetic test scores. The Plain githeri and Meat groups performed better over time than the Milk and Control groups (P < 0.02-0.03) on arithmetic tests. The Meat group showed the greatest increase in percentage time in high levels of physical activity and in initiative and leadership behaviors compared with all other groups. For growth, in the Milk group only younger and stunted children showed a greater rate of gain in height. The Meat group showed near doubling of upper midarm muscle area, and the Milk group a smaller degree of increase. This is the first randomized, controlled feeding study to examine the effect of meat- vs. milk- vs. plant-based snacks on functional outcomes in children.

Genomic Variability of Haemophilus influenzae Isolated from Mexican Children Determined by Using Enterobacterial Repetitive Intergenic Consensus Sequences and PCR

PubMed Central

Gomez-De-Leon, Patricia; Santos, Jose I.; Caballero, Javier; Gomez, Demostenes; Espinosa, Luz E.; Moreno, Isabel; Piñero, Daniel; Cravioto, Alejandro

2000-01-01

Genomic fingerprints from 92 capsulated and noncapsulated strains of Haemophilus influenzae from Mexican children with different diseases and healthy carriers were generated by PCR using the enterobacterial repetitive intergenic consensus (ERIC) sequences. A cluster analysis by the unweighted pair-group method with arithmetic averages based on the overall similarity as estimated from the characteristics of the genomic fingerprints, was conducted to group the strains. A total of 69 fingerprint patterns were detected in the H. influenzae strains. Isolates from patients with different diseases were represented by a variety of patterns, which clustered into two major groups. Of the 37 strains isolated from cases of meningitis, 24 shared patterns and were clustered into five groups within a similarity level of 1.0. One fragment of 1.25 kb was common to all meningitis strains. H. influenzae strains from healthy carriers presented fingerprint patterns different from those found in strains from sick children. Isolates from healthy individuals were more variable and were distributed differently from those from patients. The results show that ERIC-PCR provides a powerful tool for the determination of the distinctive pathogenicity potentials of H. influenzae strains and encourage its use for molecular epidemiology investigations. PMID:10878033

Down-Regulation of Olfactory Receptors in Response to Traumatic Brain Injury Promotes Risk for Alzheimers Disease

DTIC Science & Technology

2015-12-01

group assignment of samples in unsupervised hierarchical clustering by the Unweighted Pair-Group Method using Arithmetic averages ( UPGMA ) based on...log2 transformed MAS5.0 signal values; probe set clustering was performed by the UPGMA method using Cosine correlation as the similarity met- ric. For...differentially-regulated genes identified were subjected to unsupervised hierarchical clustering analysis using the UPGMA algorithm with cosine correlation as

Eastern and Central Kansas Country Schools. Country School Legacy: Humanities on the Frontier.

ERIC Educational Resources Information Center

Judge, Sara E.

Country schools in eastern and central Kansas are explored from six different aspects: country schools as historic sites; teachers (their roles, rules, and restrictions); reading, writing, arithmetic, and recitation (a day in a rural school); country schools and the Americanization of ethnic groups; country schools as community centers; and…

Teacher Candidates' Attitudes towards the Teaching Profession in Turkey

ERIC Educational Resources Information Center

Tok, Turkay Nuri

2012-01-01

This study examined the attitudes of teacher candidates in Turkey towards the teaching profession. Descriptive surveys were used and the research data was obtained from Pamukkale University Classroom Teaching students. During data analysis, the arithmetic means and standard deviations of the groups were calculated and a t-test and One-Way ANOVA…

Modular Arithmetic and Microtonal Music Theory

ERIC Educational Resources Information Center

AsKew, A.; Kennedy, K.; Klima, V.

2018-01-01

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

The influence of cardiorespiratory fitness on strategic, behavioral, and electrophysiological indices of arithmetic cognition in preadolescent children

PubMed Central

Moore, R. Davis; Drollette, Eric S.; Scudder, Mark R.; Bharij, Aashiv; Hillman, Charles H.

2014-01-01

The current study investigated the influence of cardiorespiratory fitness on arithmetic cognition in forty 9–10 year old children. Measures included a standardized mathematics achievement test to assess conceptual and computational knowledge, self-reported strategy selection, and an experimental arithmetic verification task (including small and large addition problems), which afforded the measurement of event-related brain potentials (ERPs). No differences in math achievement were observed as a function of fitness level, but all children performed better on math concepts relative to math computation. Higher fit children reported using retrieval more often to solve large arithmetic problems, relative to lower fit children. During the arithmetic verification task, higher fit children exhibited superior performance for large problems, as evidenced by greater d' scores, while all children exhibited decreased accuracy and longer reaction time for large relative to small problems, and incorrect relative to correct solutions. On the electrophysiological level, modulations of early (P1, N170) and late ERP components (P3, N400) were observed as a function of problem size and solution correctness. Higher fit children exhibited selective modulations for N170, P3, and N400 amplitude relative to lower fit children, suggesting that fitness influences symbolic encoding, attentional resource allocation and semantic processing during arithmetic tasks. The current study contributes to the fitness-cognition literature by demonstrating that the benefits of cardiorespiratory fitness extend to arithmetic cognition, which has important implications for the educational environment and the context of learning. PMID:24829556

Optical computation using residue arithmetic.

PubMed

Huang, A; Tsunoda, Y; Goodman, J W; Ishihara, S

1979-01-15

Using residue arithmetic it is possible to perform additions, subtractions, multiplications, and polynomial evaluation without the necessity for carry operations. Calculations can, therefore, be performed in a fully parallel manner. Several different optical methods for performing residue arithmetic operations are described. A possible combination of such methods to form a matrix vector multiplier is considered. The potential advantages of optics in performing these kinds of operations are discussed.

Second Report of the Multirate Processor (MRP) for Digital Voice Communications.

DTIC Science & Technology

1982-09-30

machine are: * two arithmetic logic units (ALUs)-one for data processing, and the other for address generation, * two memorys -6144 words (70 bits per word...of program memory , and 6094 words (16 bits per word) of data memory , q * input/output through modem and teletype, -15 .9 S-;. KANG AND FRANSEN Table...provides a measure of intelligibility and allows one to evaluate the discriminability of six distinctive features: voicing, nasality, sustention

Numerical predictors of arithmetic success in grades 1-6.

PubMed

Lyons, Ian M; Price, Gavin R; Vaessen, Anniek; Blomert, Leo; Ansari, Daniel

2014-09-01

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1-6. In grades 1-2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing. © 2014 John Wiley & Sons Ltd.

Numbers in action: individual differences and interactivity in mental arithmetic.

PubMed

Guthrie, Lisa G; Vallée-Tourangeau, Frédéric

2018-02-03

Previous research indicates that interactive arithmetic tasks may alleviate the deleterious impact of maths anxiety on arithmetic performance. Our aim here was to further test the impact of interactivity on maths-anxious individuals and those with poorer numeracy skills. In the experiment reported here participants completed sums in two interactivity contexts. In a low-interactivity condition, sums were completed with hands down. In a second, high-interactivity condition, participants used moveable number tokens. As anticipated, accuracy and efficiency were greater in the high compared to the low-interactivity condition. Correlational analyses indicated that maths anxiety, objective numeracy, measures of maths expertise and working memory were stronger predictors of performance in the low- than in the high-interactivity conditions. Interactivity transformed the deployment of arithmetic skills, improved performance, and reduced the gap between high- and low-ability individuals. These findings suggest that traditional psychometric efforts that identify the cognitive capacities and dispositions involved in mental arithmetic should take into account the degree of interactivity afforded by the task environment.

FAST TRACK COMMUNICATION: Reversible arithmetic logic unit for quantum arithmetic

NASA Astrophysics Data System (ADS)

Kirkedal Thomsen, Michael; Glück, Robert; Axelsen, Holger Bock

2010-09-01

This communication presents the complete design of a reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The presented ALU is garbage free and uses reversible updates to combine the standard reversible arithmetic and logical operations in one unit. Combined with a suitable control unit, the ALU permits the construction of an r-Turing complete computing device. The garbage-free ALU developed in this communication requires only 6n elementary reversible gates for five basic arithmetic-logical operations on two n-bit operands and does not use ancillae. This remarkable low resource consumption was achieved by generalizing the V-shape design first introduced for quantum ripple-carry adders and nesting multiple V-shapes in a novel integrated design. This communication shows that the realization of an efficient reversible ALU for a programmable computing device is possible and that the V-shape design is a very versatile approach to the design of quantum networks.

Strategy Choice in Solving Arithmetic Word Problems: Are There Differences between Students with Learning Disabilities, G-V Poor Performance, and Typical Achievement Students?

ERIC Educational Resources Information Center

Gonzalez, Juan E. Jimenez; Espinel, Ana Isabel Garcia

2002-01-01

A study was designed to test whether there are differences between Spanish children (ages 7-9) with arithmetic learning disabilities (n=60), garden-variety (G-V) poor performance (n=44), and typical children (n=44) in strategy choice when solving arithmetic word problems. No significant differences were found between children with dyscalculia and…

Gauss Elimination: Workhorse of Linear Algebra.

DTIC Science & Technology

1995-08-05

linear algebra computation for solving systems, computing determinants and determining the rank of matrix. All of these are discussed in varying contexts. These include different arithmetic or algebraic setting such as integer arithmetic or polynomial rings as well as conventional real (floating-point) arithmetic. These have effects on both accuracy and complexity analyses of the algorithm. These, too, are covered here. The impact of modern parallel computer architecture on GE is also

Comparison of the arithmetic and geometric means in estimating crown diameter and crown cross-sectional area

Treesearch

KaDonna Randolph

2010-01-01

The use of the geometric and arithmetic means for estimating tree crown diameter and crown cross-sectional area were examined for trees with crown width measurements taken at the widest point of the crown and perpendicular to the widest point of the crown. The average difference between the geometric and arithmetic mean crown diameters was less than 0.2 ft in absolute...

Perceiving fingers in single-digit arithmetic problems.

PubMed

Berteletti, Ilaria; Booth, James R

2015-01-01

In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.

A case study of arithmetic facts dyscalculia caused by a hypersensitivity-to-interference in memory.

PubMed

De Visscher, Alice; Noël, Marie-Pascale

2013-01-01

While the heterogeneity of developmental dyscalculia is increasingly recognized, the different profiles have not yet been clearly established. Among the features underpinning types of developmental dyscalculia suggested in the literature, an impairment in arithmetic fact retrieval is particularly prominent. In this paper, we present a case study of an adult woman (DB) with very good cognitive capacities suffering from a specific and developmental arithmetic fact retrieval deficit. We test the main hypotheses about developmental dyscalculia derived from literature. We first explore the influential hypothesis of an approximate number system deficit, through estimation tasks, comparison tasks and a priming comparison task. Secondly, we evaluate whether DB's mathematical deficiencies are caused by a rote verbal memory deficit, using tasks involving completion of expressions, and reciting automatic series such as the alphabet and the months of the year. Alternatively, taking into account the extreme similarity of the arithmetic facts, we propose that a heightened sensitivity to interference could have prevented DB from memorizing the arithmetic facts. The pattern of DB's results on different tasks supports this hypothesis. Our findings identify a new etiology of a specific impairment of arithmetic facts storage, namely a hypersensitivity-to-interference. Copyright © 2012 Elsevier Ltd. All rights reserved.

Perceiving fingers in single-digit arithmetic problems

PubMed Central

Berteletti, Ilaria; Booth, James R.

2015-01-01

In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense. PMID:25852582

Fractionating the neural correlates of individual working memory components underlying arithmetic problem solving skills in children

PubMed Central

Metcalfe, Arron W. S.; Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Menon, Vinod

2013-01-01

Baddeley and Hitch’s multi-component working memory (WM) model has played an enduring and influential role in our understanding of cognitive abilities. Very little is known, however, about the neural basis of this multi-component WM model and the differential role each component plays in mediating arithmetic problem solving abilities in children. Here, we investigate the neural basis of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of WM during a demanding mental arithmetic task in 7–9 year old children (N=74). The VS component was the strongest predictor of math ability in children and was associated with increased arithmetic complexity-related responses in left dorsolateral and right ventrolateral prefrontal cortices as well as bilateral intra-parietal sulcus and supramarginal gyrus in posterior parietal cortex. Critically, VS, CE and PL abilities were associated with largely distinct patterns of brain response. Overlap between VS and CE components was observed in left supramarginal gyrus and no overlap was observed between VS and PL components. Our findings point to a central role of visuo-spatial WM during arithmetic problem-solving in young grade-school children and highlight the usefulness of the multi-component Baddeley and Hitch WM model in fractionating the neural correlates of arithmetic problem solving during development. PMID:24212504

Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex.

PubMed

Rivera, S M; Reiss, A L; Eckert, M A; Menon, V

2005-11-01

Arithmetic reasoning is arguably one of the most important cognitive skills a child must master. Here we examine neurodevelopmental changes in mental arithmetic. Subjects (ages 8-19 years) viewed arithmetic equations and were asked to judge whether the results were correct or incorrect. During two-operand addition or subtraction trials, for which accuracy was comparable across age, older subjects showed greater activation in the left parietal cortex, along the supramarginal gyrus and adjoining anterior intra-parietal sulcus as well as the left lateral occipital temporal cortex. These age-related changes were not associated with alterations in gray matter density, and provide novel evidence for increased functional maturation with age. By contrast, younger subjects showed greater activation in the prefrontal cortex, including the dorsolateral and ventrolateral prefrontal cortex and the anterior cingulate cortex, suggesting that they require comparatively more working memory and attentional resources to achieve similar levels of mental arithmetic performance. Younger subjects also showed greater activation of the hippocampus and dorsal basal ganglia, reflecting the greater demands placed on both declarative and procedural memory systems. Our findings provide evidence for a process of increased functional specialization of the left inferior parietal cortex in mental arithmetic, a process that is accompanied by decreased dependence on memory and attentional resources with development.

The relation between language and arithmetic in bilinguals: insights from different stages of language acquisition

PubMed Central

Van Rinsveld, Amandine; Brunner, Martin; Landerl, Karin; Schiltz, Christine; Ugen, Sonja

2015-01-01

Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g., greater difficulties, error types, etc.) in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German–French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g., unit-ten vs. ten-unit) also induced significant modulations of bilinguals' arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals. PMID:25821442

Specific Learning Disorder: Prevalence and Gender Differences

PubMed Central

Moll, Kristina; Kunze, Sarah; Neuhoff, Nina; Bruder, Jennifer; Schulte-Körne, Gerd

2014-01-01

Comprehensive models of learning disorders have to consider both isolated learning disorders that affect one learning domain only, as well as comorbidity between learning disorders. However, empirical evidence on comorbidity rates including all three learning disorders as defined by DSM-5 (deficits in reading, writing, and mathematics) is scarce. The current study assessed prevalence rates and gender ratios for isolated as well as comorbid learning disorders in a representative sample of 1633 German speaking children in 3rd and 4th Grade. Prevalence rates were analysed for isolated as well as combined learning disorders and for different deficit criteria, including a criterion for normal performance. Comorbid learning disorders occurred as frequently as isolated learning disorders, even when stricter cutoff criteria were applied. The relative proportion of isolated and combined disorders did not change when including a criterion for normal performance. Reading and spelling deficits differed with respect to their association with arithmetic problems: Deficits in arithmetic co-occurred more often with deficits in spelling than with deficits in reading. In addition, comorbidity rates for arithmetic and reading decreased when applying stricter deficit criteria, but stayed high for arithmetic and spelling irrespective of the chosen deficit criterion. These findings suggest that the processes underlying the relationship between arithmetic and reading might differ from those underlying the relationship between arithmetic and spelling. With respect to gender ratios, more boys than girls showed spelling deficits, while more girls were impaired in arithmetic. No gender differences were observed for isolated reading problems and for the combination of all three learning disorders. Implications of these findings for assessment and intervention of learning disorders are discussed. PMID:25072465

Specific learning disorder: prevalence and gender differences.

PubMed

Moll, Kristina; Kunze, Sarah; Neuhoff, Nina; Bruder, Jennifer; Schulte-Körne, Gerd

2014-01-01

Comprehensive models of learning disorders have to consider both isolated learning disorders that affect one learning domain only, as well as comorbidity between learning disorders. However, empirical evidence on comorbidity rates including all three learning disorders as defined by DSM-5 (deficits in reading, writing, and mathematics) is scarce. The current study assessed prevalence rates and gender ratios for isolated as well as comorbid learning disorders in a representative sample of 1633 German speaking children in 3rd and 4th Grade. Prevalence rates were analysed for isolated as well as combined learning disorders and for different deficit criteria, including a criterion for normal performance. Comorbid learning disorders occurred as frequently as isolated learning disorders, even when stricter cutoff criteria were applied. The relative proportion of isolated and combined disorders did not change when including a criterion for normal performance. Reading and spelling deficits differed with respect to their association with arithmetic problems: Deficits in arithmetic co-occurred more often with deficits in spelling than with deficits in reading. In addition, comorbidity rates for arithmetic and reading decreased when applying stricter deficit criteria, but stayed high for arithmetic and spelling irrespective of the chosen deficit criterion. These findings suggest that the processes underlying the relationship between arithmetic and reading might differ from those underlying the relationship between arithmetic and spelling. With respect to gender ratios, more boys than girls showed spelling deficits, while more girls were impaired in arithmetic. No gender differences were observed for isolated reading problems and for the combination of all three learning disorders. Implications of these findings for assessment and intervention of learning disorders are discussed.

Down-Regulation of Olfactory Receptors in Response to Traumatic Brain Injury Promotes Risk for Alzheimer’s Disease

DTIC Science & Technology

2013-10-01

correct group assignment of samples in unsupervised hierarchical clustering by the Unweighted Pair-Group Method using Arithmetic averages ( UPGMA ) based on...centering of log2 transformed MAS5.0 signal values; probe set clustering was performed by the UPGMA method using Cosine correlation as the similarity met...A) The 108 differentially-regulated genes identified were subjected to unsupervised hierarchical clustering analysis using the UPGMA algorithm with

Sequence-related amplified polymorphism (SRAP) marker as a new method for identification of endophytic fungi from Taxus.

PubMed

Ren, Na; Liu, Jiajia; Yang, Dongliang; Chen, Jianhua; Luan, Mingbao; Hong, Juan

2012-01-01

A total of 20 endophytic fungi stains were classified into four groups using traditional morphological identification method, and were studied for genetic diversity by sequence-related amplified polymorphism (SRAP) technique. Genomic DNA (deoxyribonucleic acid) of these strains was extracted with CTAB method. SRAP analysis was done with 24 pairs of primers. All strains could be uniquely distinguished with 584 bands and 446 polymorphism bands which generated 76.4% of polymorphic ratio. Unweighted pair-group method with arithmetical averages cluster analysis enabled construction of a dendrogram for estimating genetic distances between different strains. All strains, which were just divided into four groups by traditional morphology identification, were clustered into four major groups at GS = 0.603 and further separated into eight sub-groups at GS = 0.921. Dendrogram also revealed a large genetic variation in 20 strains; different primer combinations allowed them distinctly distinguished one from others with relatively low genetic similarity. The results show that the SRAP technology is more efficient than traditional morphology identification. It is found that SRAP markers could more really reflect the genetic diversity of endophytic fungi strains from Taxus, and also could be used as a method for identification of endophytic fungi from Taxus. It also suggests that SRAP can be used to establish foundation for further screening of taxol-producing endophytic fungi strains which can produce high levels of paclitaxel.

Providing Internet Access to High-Resolution Lunar Images

NASA Technical Reports Server (NTRS)

Plesea, Lucian

2008-01-01

The OnMoon server is a computer program that provides Internet access to high-resolution Lunar images, maps, and elevation data, all suitable for use in geographical information system (GIS) software for generating images, maps, and computational models of the Moon. The OnMoon server implements the Open Geospatial Consortium (OGC) Web Map Service (WMS) server protocol and supports Moon-specific extensions. Unlike other Internet map servers that provide Lunar data using an Earth coordinate system, the OnMoon server supports encoding of data in Moon-specific coordinate systems. The OnMoon server offers access to most of the available high-resolution Lunar image and elevation data. This server can generate image and map files in the tagged image file format (TIFF) or the Joint Photographic Experts Group (JPEG), 8- or 16-bit Portable Network Graphics (PNG), or Keyhole Markup Language (KML) format. Image control is provided by use of the OGC Style Layer Descriptor (SLD) protocol. Full-precision spectral arithmetic processing is also available, by use of a custom SLD extension. This server can dynamically add shaded relief based on the Lunar elevation to any image layer. This server also implements tiled WMS protocol and super-overlay KML for high-performance client application programs.

Application of genotypic and phenotypic analyses to commercial probiotic strain identity and relatedness.

PubMed

Yeung, P S M; Kitts, C L; Cano, R; Tong, P S; Sanders, M E

2004-01-01

The objective of this study was to generate strain-specific genomic patterns of a bank of 67 commercial and reference probiotic strains, with a focus on probiotic lactobacilli. Pulsed-field gel electrophoresis (PFGE) was used as the primary method for strain differentiation. This method was compared with carbohydrate fermentation analysis. To supplement visual comparison, PFGE patterns were analysed quantitatively by cluster analysis using unweighted pair group method with arithmetic averages. SmaI, NotI and XbaI were found to effectively generate clear and easy-to-interpret PFGE patterns of a range of probiotic strains. Some probiotic strains from different sources shared highly similar PFGE patterns. Results document the value of genotypic strain identification methods, combined with phenotypic methods, for determining probiotic strain identity and relatedness. No correlation was found between relatedness determined by carbohydrate fermentation profiles alone compared with PFGE analysis alone. Some commercial strains are probably derived from similar sources. This approach is valuable to the probiotic industry to develop commercial strain identification patterns, to provide quality control of strain manufacturing production runs, to track use of protected strains and to determine the relatedness among different research and commercial probiotic strains.

Peers Influence Mathematics Strategy Use in Early Elementary School

ERIC Educational Resources Information Center

Carr, Martha; Barned, Nicole; Otumfuor, Beryl

2016-01-01

This study examined the impact of performance goals on arithmetic strategy use, and how same-sex peer groups contributed to the selection of strategies used by first-graders. It was hypothesized that gender differences in strategy use are a function of performance goals and the influence of same-sex peers. Using a sample of 75 first grade…

Mothers' and Teachers' Attributions of the Academic Functioning of Israeli Second Graders: A Comparison between Social Groups

ERIC Educational Resources Information Center

Korat, Ofra

2004-01-01

Mothers' and teachers' academic attributions of second graders (20 girls; 20 boys) were investigated. Children were recruited equally from high versus low SES schools. Mothers evaluated their own children and teachers evaluated 10 children in each of four classrooms -- compared to classmates -- in six domains: reading, writing, arithmetic, fine…

Sex and Personality Differences in Performance on Number Computation in 11-Year-Old Children.

ERIC Educational Resources Information Center

Riding, R. J.; Borg, M. G.

1987-01-01

Eighty-four 11-year-olds were grouped in three levels of extraversion on the basis of their Junior Eysenck Personality Inventory score. They were then given an arithmetic test consisting of addition, subtraction, division, and multiplication. A significant interaction between extraversion, sex, and type of operation was found. (Author/CH)

Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2014-01-01

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

Psychophysiological differentiation of two types of anxiety and its pharmacological modification by minor tranquillizer and beta-receptor-blocker.

PubMed

Albus, M; Stahl, S; Müller-Spahn, F; Engel, R R

1986-08-01

To evaluate the influence of beta-blockers and/or minor tranquillizers on autonomic reactions during brief stress, 48 healthy subjects were randomised into 4 groups: A = 4 mg Pindolol, B = 1.5 mg Cloxazolam, C = Placebo, D = 4 mg Pindolol + 1.5 mg Cloxazolam. Subjects underwent four stress situations: Counting, noise, mental arithmetic and ergometry, each lasting 4 min with rest periods of 8 min in between. Electromyogram, finger pulse amplitude, heart rate, pulse wave velocity and electrodermal activity were recorded simultaneously on-line. Analysis of variance showed that the two drugs had significant main effects in different systems: Pindolol reduced heart rate, mainly during mental arithmetic and ergometry, Cloxazolam reduced electrodermal activity, mainly during noise. It can be concluded that different structured situations with a varying amount and type of anxiety induce different autonomic reactions; these reactions can be differentially modified by the drugs applied.

Errors in Multi-Digit Arithmetic and Behavioral Inattention in Children With Math Difficulties

PubMed Central

Raghubar, Kimberly; Cirino, Paul; Barnes, Marcia; Ewing-Cobbs, Linda; Fletcher, Jack; Fuchs, Lynn

2009-01-01

Errors in written multi-digit computation were investigated in children with math difficulties. Third-and fourth-grade children (n = 291) with coexisting math and reading difficulties, math difficulties, reading difficulties, or no learning difficulties were compared. A second analysis compared those with severe math learning difficulties, low average achievement in math, and no learning difficulties. Math fact errors were related to the severity of the math difficulties, not to reading status. Contrary to predictions, children with poorer reading, regardless of math achievement, committed more visually based errors. Operation switch errors were not systematically related to group membership. Teacher ratings of behavioral inattention were related to accuracy, math fact errors, and procedural bugs. The findings are discussed with respect to hypotheses about the cognitive origins of arithmetic errors and in relation to current discussions about how to conceptualize math disabilities. PMID:19380494

MRI-based treatment planning with pseudo CT generated through atlas registration.

PubMed

Uh, Jinsoo; Merchant, Thomas E; Li, Yimei; Li, Xingyu; Hua, Chiaho

2014-05-01

To evaluate the feasibility and accuracy of magnetic resonance imaging (MRI)-based treatment planning using pseudo CTs generated through atlas registration. A pseudo CT, providing electron density information for dose calculation, was generated by deforming atlas CT images previously acquired on other patients. The authors tested 4 schemes of synthesizing a pseudo CT from single or multiple deformed atlas images: use of a single arbitrarily selected atlas, arithmetic mean process using 6 atlases, and pattern recognition with Gaussian process (PRGP) using 6 or 12 atlases. The required deformation for atlas CT images was derived from a nonlinear registration of conjugated atlas MR images to that of the patient of interest. The contrasts of atlas MR images were adjusted by histogram matching to reduce the effect of different sets of acquisition parameters. For comparison, the authors also tested a simple scheme assigning the Hounsfield unit of water to the entire patient volume. All pseudo CT generating schemes were applied to 14 patients with common pediatric brain tumors. The image similarity of real patient-specific CT and pseudo CTs constructed by different schemes was compared. Differences in computation times were also calculated. The real CT in the treatment planning system was replaced with the pseudo CT, and the dose distribution was recalculated to determine the difference. The atlas approach generally performed better than assigning a bulk CT number to the entire patient volume. Comparing atlas-based schemes, those using multiple atlases outperformed the single atlas scheme. For multiple atlas schemes, the pseudo CTs were similar to the real CTs (correlation coefficient, 0.787-0.819). The calculated dose distribution was in close agreement with the original dose. Nearly the entire patient volume (98.3%-98.7%) satisfied the criteria of chi-evaluation (<2% maximum dose and 2 mm range). The dose to 95% of the volume and the percentage of volume receiving at least 95% of the prescription dose in the planning target volume differed from the original values by less than 2% of the prescription dose (root-mean-square, RMS < 1%). The PRGP scheme did not perform better than the arithmetic mean process with the same number of atlases. Increasing the number of atlases from 6 to 12 often resulted in improvements, but statistical significance was not always found. MRI-based treatment planning with pseudo CTs generated through atlas registration is feasible for pediatric brain tumor patients. The doses calculated from pseudo CTs agreed well with those from real CTs, showing dosimetric accuracy within 2% for the PTV when multiple atlases were used. The arithmetic mean process may be a reasonable choice over PRGP for the synthesis scheme considering performance and computational costs.

MRI-based treatment planning with pseudo CT generated through atlas registration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Uh, Jinsoo, E-mail: jinsoo.uh@stjude.org; Merchant, Thomas E.; Hua, Chiaho

2014-05-15

Purpose: To evaluate the feasibility and accuracy of magnetic resonance imaging (MRI)-based treatment planning using pseudo CTs generated through atlas registration. Methods: A pseudo CT, providing electron density information for dose calculation, was generated by deforming atlas CT images previously acquired on other patients. The authors tested 4 schemes of synthesizing a pseudo CT from single or multiple deformed atlas images: use of a single arbitrarily selected atlas, arithmetic mean process using 6 atlases, and pattern recognition with Gaussian process (PRGP) using 6 or 12 atlases. The required deformation for atlas CT images was derived from a nonlinear registration ofmore » conjugated atlas MR images to that of the patient of interest. The contrasts of atlas MR images were adjusted by histogram matching to reduce the effect of different sets of acquisition parameters. For comparison, the authors also tested a simple scheme assigning the Hounsfield unit of water to the entire patient volume. All pseudo CT generating schemes were applied to 14 patients with common pediatric brain tumors. The image similarity of real patient-specific CT and pseudo CTs constructed by different schemes was compared. Differences in computation times were also calculated. The real CT in the treatment planning system was replaced with the pseudo CT, and the dose distribution was recalculated to determine the difference. Results: The atlas approach generally performed better than assigning a bulk CT number to the entire patient volume. Comparing atlas-based schemes, those using multiple atlases outperformed the single atlas scheme. For multiple atlas schemes, the pseudo CTs were similar to the real CTs (correlation coefficient, 0.787–0.819). The calculated dose distribution was in close agreement with the original dose. Nearly the entire patient volume (98.3%–98.7%) satisfied the criteria of chi-evaluation (<2% maximum dose and 2 mm range). The dose to 95% of the volume and the percentage of volume receiving at least 95% of the prescription dose in the planning target volume differed from the original values by less than 2% of the prescription dose (root-mean-square, RMS < 1%). The PRGP scheme did not perform better than the arithmetic mean process with the same number of atlases. Increasing the number of atlases from 6 to 12 often resulted in improvements, but statistical significance was not always found. Conclusions: MRI-based treatment planning with pseudo CTs generated through atlas registration is feasible for pediatric brain tumor patients. The doses calculated from pseudo CTs agreed well with those from real CTs, showing dosimetric accuracy within 2% for the PTV when multiple atlases were used. The arithmetic mean process may be a reasonable choice over PRGP for the synthesis scheme considering performance and computational costs.« less

MRI-based treatment planning with pseudo CT generated through atlas registration

PubMed Central

Uh, Jinsoo; Merchant, Thomas E.; Li, Yimei; Li, Xingyu; Hua, Chiaho

2014-01-01

Purpose: To evaluate the feasibility and accuracy of magnetic resonance imaging (MRI)-based treatment planning using pseudo CTs generated through atlas registration. Methods: A pseudo CT, providing electron density information for dose calculation, was generated by deforming atlas CT images previously acquired on other patients. The authors tested 4 schemes of synthesizing a pseudo CT from single or multiple deformed atlas images: use of a single arbitrarily selected atlas, arithmetic mean process using 6 atlases, and pattern recognition with Gaussian process (PRGP) using 6 or 12 atlases. The required deformation for atlas CT images was derived from a nonlinear registration of conjugated atlas MR images to that of the patient of interest. The contrasts of atlas MR images were adjusted by histogram matching to reduce the effect of different sets of acquisition parameters. For comparison, the authors also tested a simple scheme assigning the Hounsfield unit of water to the entire patient volume. All pseudo CT generating schemes were applied to 14 patients with common pediatric brain tumors. The image similarity of real patient-specific CT and pseudo CTs constructed by different schemes was compared. Differences in computation times were also calculated. The real CT in the treatment planning system was replaced with the pseudo CT, and the dose distribution was recalculated to determine the difference. Results: The atlas approach generally performed better than assigning a bulk CT number to the entire patient volume. Comparing atlas-based schemes, those using multiple atlases outperformed the single atlas scheme. For multiple atlas schemes, the pseudo CTs were similar to the real CTs (correlation coefficient, 0.787–0.819). The calculated dose distribution was in close agreement with the original dose. Nearly the entire patient volume (98.3%–98.7%) satisfied the criteria of chi-evaluation (<2% maximum dose and 2 mm range). The dose to 95% of the volume and the percentage of volume receiving at least 95% of the prescription dose in the planning target volume differed from the original values by less than 2% of the prescription dose (root-mean-square, RMS < 1%). The PRGP scheme did not perform better than the arithmetic mean process with the same number of atlases. Increasing the number of atlases from 6 to 12 often resulted in improvements, but statistical significance was not always found. Conclusions: MRI-based treatment planning with pseudo CTs generated through atlas registration is feasible for pediatric brain tumor patients. The doses calculated from pseudo CTs agreed well with those from real CTs, showing dosimetric accuracy within 2% for the PTV when multiple atlases were used. The arithmetic mean process may be a reasonable choice over PRGP for the synthesis scheme considering performance and computational costs. PMID:24784377

AUTOMATED FLOWCHART SYSTEM FROM TEXAS A&M UNIVERSITY

NASA Technical Reports Server (NTRS)

Woodford, W.

1994-01-01

An accurate flowchart is an important part of the documentation for any computer program. The flowchart offers the user an easy to follow overview of program operation and the maintenance programmer an effective debugging tool. The TAMU FLOWCHART System was developed to flowchart any program written in the FORTRAN language. It generates a line printer flowchart which is representative of the program logic. This flowchart provides the user with a detailed representation of the program action taken as each program statement is executed. The TAMU FLOWCHART System should prove to be a valuable aid to groups working with complex FORTRAN programs. Each statement in the program is displayed within a symbol which represents the program action during processing of the enclosed statement. Symbols available include: subroutine, function, and entry statements; arithmetic statements; input and output statements; arithmetical and logical IF statements; subroutine calls with or without argument list returns; computed and assigned GO TO statements; DO statements; STOP and RETURN statements; and CONTINUE and ASSIGN statements. Comment cards within the source program may be suppressed or displayed and associated with a succeeding source statement. Each symbol is annotated with a label (if present in the source code), a block number, and the statement sequence number. Program flow and options within the program are represented by line segments and direction indicators connecting symbols. The TAMU FLOWCHART System should be able to accurately flowchart any working FORTRAN program. This program is written in COBOL for batch execution and has been implemented on an IBM 370 series computer with an OS operating system and with a central memory requirement of approximately 380K of 8 bit bytes. The TAMU FLOWCHART System was developed in 1977.

Language, arithmetic word problems, and deaf students: Linguistic strategies used to solve tasks

NASA Astrophysics Data System (ADS)

Zevenbergen, Robyn; Hyde, Merv; Power, Des

2001-12-01

There has been limited examination of the intersection between language and arithmetic in the performance of deaf students, although some previous research has shown that deaf and hearing-impaired1 students are delayed in both their language acquisition and arithmetic performance. This paper examines the performance of deaf and hearing-impaired students in South-East Queensland, Australia, in solving arithmetic word problems. It was found that the subjects' solutions of word problems confirmed trends for hearing students, but that their performance was delayed in comparison. The results confirm other studies where deaf and hearing-impaired students are delayed in their language acquisition and this impacts on their capacity to successfully undertake the resolution of word problems.

Language and arithmetic--a study using the intracarotid amobarbital procedure.

PubMed

Delazer, Margarete; Karner, Elfriede; Unterberger, Iris; Walser, Gerald; Waldenberger, Peter; Trinka, Eugen; Benke, Thomas

2005-08-22

The intracarotid amobarbital procedure is used as a standard procedure in presurgical evaluation to assess hemispheric lateralization of language and memory, but has not been applied to investigate numerical processing. Patients with medically intractable epilepsy (n=20) were consecutively recruited during a presurgical evaluation programme. All 14 patients with left-lateralized language showed better arithmetic performance with the left hemisphere (intracarotid amobarbital procedure right), while five out of six patients with bilateral or right-hemispheric language representation showed better performance with the right hemisphere (intracarotid amobarbital procedure left). Furthermore, in patients with left-lateralized language, an interaction between intracarotid amobarbital procedure and type of arithmetic operation was found. The study suggests a close association between language lateralization and hemispheric specialization for arithmetic processing.

A mobile application for cognitive screening of dementia.

PubMed

Zorluoglu, Gokhan; Kamasak, Mustafa E; Tavacioglu, Leyla; Ozanar, Pinar O

2015-02-01

Neuropsychological assessment tests have an important role in early detection of dementia. Therefore, we designed and implemented a test battery for mobile devices that can be used for mobile cognitive screening (MCS). This battery consists of 33 questions from 14 type of tests for the assessment of 8 different cognitive functions: Arithmetic, orientation, abstraction, attention, memory, language, visual, and executive functions. This test battery is implemented as an application for mobile devices that operates on Android OS. In order to validate the effectiveness of the neuropsychological test battery, it was applied on a group of 23 elderly persons. Within this group, 9 (of age 81.78±4.77) were healthy and 14 (of age 72.55±9.95) were already diagnosed with dementia. The education level of the control group (healthy) and dementia group were comparable as they spent 13.66±5.07 and 13.71±4.14 years at school respectively. For comparison, a validated paper-and-pencil test (Montreal Cognitive Test - MoCA) was applied along with the proposed MCS battery. The proposed test was able to differentiate the individuals in the control and dementia groups for executive, visual, memory, attention, orientation functions with statistical significance (p<0.05). Results of the remaining functions; language, abstraction, and arithmetic were statistically insignificant (p>0.05). The results of MCS and MoCA were compared, and the scores of individuals from these tests were correlated (r(2)=0.57). Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Realization of a new concept for visible frequency division: phase locking of harmonic and sum frequencies.

PubMed

Telle, H R; Meschede, D; Hänsch, T W

1990-05-15

We explore and demonstrate the feasibility of an optical-frequency-to-radio-frequency division method that is based on visible or near-infrared laser oscillators only. Comparing harmonic and sum frequencies, we generate the arithmetic average of two visible frequencies. Cascading n stages provides difference-frequency division by 2(n). For a demonstration we have phase locked the second harmonic and the sum frequency of two independent diode lasers.

Developmental trajectories of children's symbolic numerical magnitude processing skills and associated cognitive competencies.

PubMed

Vanbinst, Kiran; Ceulemans, Eva; Peters, Lien; Ghesquière, Pol; De Smedt, Bert

2018-02-01

Although symbolic numerical magnitude processing skills are key for learning arithmetic, their developmental trajectories remain unknown. Therefore, we delineated during the first 3years of primary education (5-8years of age) groups with distinguishable developmental trajectories of symbolic numerical magnitude processing skills using a model-based clustering approach. Three clusters were identified and were labeled as inaccurate, accurate but slow, and accurate and fast. The clusters did not differ in age, sex, socioeconomic status, or IQ. We also tested whether these clusters differed in domain-specific (nonsymbolic magnitude processing and digit identification) and domain-general (visuospatial short-term memory, verbal working memory, and processing speed) cognitive competencies that might contribute to children's ability to (efficiently) process the numerical meaning of Arabic numerical symbols. We observed minor differences between clusters in these cognitive competencies except for verbal working memory for which no differences were observed. Follow-up analyses further revealed that the above-mentioned cognitive competencies did not merely account for the cluster differences in children's development of symbolic numerical magnitude processing skills, suggesting that other factors account for these individual differences. On the other hand, the three trajectories of symbolic numerical magnitude processing revealed remarkable and stable differences in children's arithmetic fact retrieval, which stresses the importance of symbolic numerical magnitude processing for learning arithmetic. Copyright © 2017 Elsevier Inc. All rights reserved.

Mathematics anxiety in children with developmental dyscalculia

PubMed Central

2010-01-01

Background Math anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure. Methods Participants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively. Result Participants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group. Conclusion These results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety. PMID:20633269

Physical activity and sedentary time in relation to academic achievement in children.

PubMed

Haapala, Eero A; Väistö, Juuso; Lintu, Niina; Westgate, Kate; Ekelund, Ulf; Poikkeus, Anna-Maija; Brage, Soren; Lakka, Timo A

2017-06-01

To investigate the independent and combined associations of objectively measured moderate-to-vigorous physical activity (MVPA) and sedentary time (ST) with reading and arithmetic skills. Cross-sectional/prospective. Participants were 89 boys and 69 girls aged 6-8 years. MVPA and ST were measured using a combined heart rate and movement sensor and body fat percentage by dual-energy X-ray absorptiometry in Grade 1. Reading fluency, reading comprehension, and arithmetic skills were assessed using standardized tests in Grades 1-3. The data were analyzed using linear regression analyses and analyses of covariance with repeated measures. In boys, MVPA was directly and ST inversely associated with reading fluency in Grades 1-3 and arithmetic skills in Grade 1 (P<0.05). Higher levels of MVPA were also related to better reading comprehension in Grade 1 (P<0.05). Most of the associations of MVPA and ST with reading and arithmetic skills attenuated after mutual adjustment for MVPA or ST. Furthermore, boys with a combination of lower levels of MVPA and higher levels of ST had consistently poorer reading fluency (P=0.002) and reading comprehension (P=0.027) across Grades 1-3 than other boys. In girls, ST was directly associated with arithmetic skills in Grade 2 (P<0.05). However, this relationship of ST with arithmetic skills was no longer significant after adjustment for body fat percentage. Lower levels of MVPA and higher levels of ST and particularly their combination were related to poorer reading skills in boys. In girls, higher levels of ST were related to better arithmetic skills. Copyright © 2016 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.

Algorithm XXX : functions to support the IEEE standard for binary floating-point arithmetic.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cody, W. J.; Mathematics and Computer Science

1993-12-01

This paper describes C programs for the support functions copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x), and isnan(x) recommended in the Appendix to the IEEE Standard for Binary Floating-Point Arithmetic. In the case of logb, the modified definition given in the later IEEE Standard for Radix-Independent Floating-Point Arithmetic is followed. These programs should run without modification on most systems conforming to the binary standard.

Fractionating the neural correlates of individual working memory components underlying arithmetic problem solving skills in children.

PubMed

Metcalfe, Arron W S; Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Menon, Vinod

2013-10-01

Baddeley and Hitch's multi-component working memory (WM) model has played an enduring and influential role in our understanding of cognitive abilities. Very little is known, however, about the neural basis of this multi-component WM model and the differential role each component plays in mediating arithmetic problem solving abilities in children. Here, we investigate the neural basis of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of WM during a demanding mental arithmetic task in 7-9 year old children (N=74). The VS component was the strongest predictor of math ability in children and was associated with increased arithmetic complexity-related responses in left dorsolateral and right ventrolateral prefrontal cortices as well as bilateral intra-parietal sulcus and supramarginal gyrus in posterior parietal cortex. Critically, VS, CE and PL abilities were associated with largely distinct patterns of brain response. Overlap between VS and CE components was observed in left supramarginal gyrus and no overlap was observed between VS and PL components. Our findings point to a central role of visuo-spatial WM during arithmetic problem-solving in young grade-school children and highlight the usefulness of the multi-component Baddeley and Hitch WM model in fractionating the neural correlates of arithmetic problem solving during development. Copyright © 2013 Elsevier Ltd. All rights reserved.

Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.

PubMed

Chen, Yalin; Yanke, Jill; Campbell, Jamie I D

2016-04-01

The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.

Re-assessing acalculia: Distinguishing spatial and purely arithmetical deficits in right-hemisphere damaged patients.

PubMed

Benavides-Varela, S; Piva, D; Burgio, F; Passarini, L; Rolma, G; Meneghello, F; Semenza, C

2017-03-01

Arithmetical deficits in right-hemisphere damaged patients have been traditionally considered secondary to visuo-spatial impairments, although the exact relationship between the two deficits has rarely been assessed. The present study implemented a voxelwise lesion analysis among 30 right-hemisphere damaged patients and a controlled, matched-sample, cross-sectional analysis with 35 cognitively normal controls regressing three composite cognitive measures on standardized numerical measures. The results showed that patients and controls significantly differ in Number comprehension, Transcoding, and Written operations, particularly subtractions and multiplications. The percentage of patients performing below the cutoffs ranged between 27% and 47% across these tasks. Spatial errors were associated with extensive lesions in fronto-temporo-parietal regions -which frequently lead to neglect- whereas pure arithmetical errors appeared related to more confined lesions in the right angular gyrus and its proximity. Stepwise regression models consistently revealed that spatial errors were primarily predicted by composite measures of visuo-spatial attention/neglect and representational abilities. Conversely, specific errors of arithmetic nature linked to representational abilities only. Crucially, the proportion of arithmetical errors (ranging from 65% to 100% across tasks) was higher than that of spatial ones. These findings thus suggest that unilateral right hemisphere lesions can directly affect core numerical/arithmetical processes, and that right-hemisphere acalculia is not only ascribable to visuo-spatial deficits as traditionally thought. Copyright © 2017 Elsevier Ltd. All rights reserved.

When is working memory important for arithmetic? The impact of strategy and age.

PubMed

Cragg, Lucy; Richardson, Sophie; Hubber, Paula J; Keeble, Sarah; Gilmore, Camilla

2017-01-01

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9-11 years, 12-14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition.

Analysis of genetic relationships and identification of lily cultivars based on inter-simple sequence repeat markers.

PubMed

Cui, G F; Wu, L F; Wang, X N; Jia, W J; Duan, Q; Ma, L L; Jiang, Y L; Wang, J H

2014-07-29

Inter-simple sequence repeat (ISSR) markers were used to discriminate 62 lily cultivars of 5 hybrid series. Eight ISSR primers generated 104 bands in total, which all showed 100% polymorphism, and an average of 13 bands were amplified by each primer. Two software packages, POPGENE 1.32 and NTSYSpc 2.1, were used to analyze the data matrix. Our results showed that the observed number of alleles (NA), effective number of alleles (NE), Nei's genetic diversity (H), and Shannon's information index (I) were 1.9630, 1.4179, 0.2606, and 0.4080, respectively. The highest genetic similarity (0.9601) was observed between the Oriental x Trumpet and Oriental lilies, which indicated that the two hybrids had a close genetic relationship. An unweighted pair-group method with arithmetic means dendrogram showed that the 62 lily cultivars clustered into two discrete groups. The first group included the Oriental and OT cultivars, while the Asiatic, LA, and Longiflorum lilies were placed in the second cluster. The distribution of individuals in the principal component analysis was consistent with the clustering of the dendrogram. Fingerprints of all lily cultivars built from 8 primers could be separated completely. This study confirmed the effect and efficiency of ISSR identification in lily cultivars.

Relatedness of Indian flax genotypes (Linum usitatissimum L.): an inter-simple sequence repeat (ISSR) primer assay.

PubMed

Rajwade, Ashwini V; Arora, Ritu S; Kadoo, Narendra Y; Harsulkar, Abhay M; Ghorpade, Prakash B; Gupta, Vidya S

2010-06-01

The objective of this study was to analyze the genetic relationships, using PCR-based ISSR markers, among 70 Indian flax (Linum usitatissimum L.) genotypes actively utilized in flax breeding programs. Twelve ISSR primers were used for the analysis yielding 136 loci, of which 87 were polymorphic. The average number of amplified loci and the average number of polymorphic loci per primer were 11.3 and 7.25, respectively, while the percent loci polymorphism ranged from 11.1 to 81.8 with an average of 63.9 across all the genotypes. The range of polymorphism information content scores was 0.03-0.49, with an average of 0.18. A dendrogram was generated based on the similarity matrix by the Unweighted Pair Group Method with Arithmetic Mean (UPGMA), wherein the flax genotypes were grouped in five clusters. The Jaccard's similarity coefficient among the genotypes ranged from 0.60 to 0.97. When the omega-3 alpha linolenic acid (ALA) contents of the individual genotypes were correlated with the clusters in the dendrogram, the high ALA containing genotypes were grouped in two clusters. This study identified SLS 50, Ayogi, and Sheetal to be the most diverse genotypes and suggested their use in breeding programs and for developing mapping populations.

A cognitive stressor for event-related potential studies: the Portland arithmetic stress task.

PubMed

Atchley, Rachel; Ellingson, Roger; Klee, Daniel; Memmott, Tabatha; Oken, Barry

2017-05-01

In this experiment, we developed and evaluated the Portland Arithmetic Stress Task (PAST) as a cognitive stressor to evaluate acute and sustained stress reactivity for event-related potential (ERP) studies. The PAST is a titrated arithmetic task adapted from the Montreal Imaging Stress Task (MIST), with added experimental control over presentation parameters, improved and synchronized acoustic feedback and generation of timing markers needed for physiological analyzes of real-time brain activity. Thirty-one older adults (M = 60 years) completed the PAST. EEG was recorded to assess feedback-related negativity (FRN) and the magnitude of the stress response through autonomic nervous system activity and salivary cortisol. Physiological measures other than EEG included heart rate, respiration rate, heart rate variability, blood pressure and salivary cortisol. These measures were collected at several time points throughout the task. Feedback-related negativity evoked-potential responses were elicited and they significantly differed depending on whether positive or negative feedback was received. The PAST also increased systolic blood pressure, heart rate variability and respiration rates compared to a control condition attentional task. These preliminary results suggest that the PAST is an effective cognitive stressor. Successful measurement of the feedback-related negativity suggests that the PAST is conducive to EEG and time-sensitive ERP experiments. Moreover, the physiological findings support the PAST as a potent method for inducing stress in older adult participants. Further research is needed to confirm these results, but the PAST shows promise as a tool for cognitive stress induction for time-locked event-related potential experiments.

Using EEG To Detect and Monitor Mental Fatigue

NASA Technical Reports Server (NTRS)

Montgomery, Leslie; Luna, Bernadette; Trejo, Leonard J.; Montgomery, Richard

2001-01-01

This project aims to develop EEG-based methods for detecting and monitoring mental fatigue. Mental fatigue poses a serious risk, even when performance is not apparently degraded. When such fatigue is associated with sustained performance of a single type of cognitive task it may be related to the metabolic energy required for sustained activation of cortical areas specialized for that task. The objective of this study was to adapt EEG to monitor cortical energy over a long period of performance of a cognitive task. Multielectrode event related potentials (ERPs) were collected every 15 minutes in nine subjects who performed a mental arithmetic task (algebraic sum of four randomly generated negative or positive digits). A new problem was presented on a computer screen 0.5 seconds after each response; some subjects endured for as long as three hours. ERPs were transformed to a quantitative measure of scalp electrical field energy. The average energy level at electrode P3 (near the left angular gyrus), 100-300 msec latency, was compared over the series of ERPs. For most subjects, scalp energy density at P3 gradually fell over the period of task performance and dramatically increased just before the subject was unable to continue the task. This neural response can be simulated for individual subjects using, a differential equation model in which it is assumed that the mental arithmetic task requires a commitment of metabolic energy that would otherwise be used for brain activities that are temporarily neglected. Their cumulative neglect eventually requires a reallocation of energy away from the mental arithmetic task.

Cross-cultural investigation into cognitive underpinnings of individual differences in early arithmetic.

PubMed

Rodic, Maja; Zhou, Xinlin; Tikhomirova, Tatiana; Wei, Wei; Malykh, Sergei; Ismatulina, Victoria; Sabirova, Elena; Davidova, Yulia; Tosto, Maria Grazia; Lemelin, Jean-Pascal; Kovas, Yulia

2015-01-01

The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic - operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were small, 13% of the variance in arithmetic skills could be explained by the sample, replicating the pattern, previously found with older children in PISA. Furthermore, the same cognitive skills were related to early arithmetic in these diverse populations. Only understanding of symbolic number explained variation in mathematical performance in all samples. We discuss the results in terms of potential influences of socio-demographic, linguistic and genetic factors on individual differences in mathematics. © 2014 John Wiley & Sons Ltd.

Genetic analysis of floating Enteromorpha prolifera in the Yellow Sea with AFLP marker

NASA Astrophysics Data System (ADS)

Liu, Cui; Zhang, Jing; Sun, Xiaoyu; Li, Jian; Zhang, Xi; Liu, Tao

2011-09-01

Extremely large accumulation of green algae Enteromorpha prolifera floated along China' coastal region of the Yellow Sea ever since the summer of 2008. Amplified Fragment Length Polymorphism (AFLP) analysis was applied to assess the genetic diversity and relationships among E. prolifera samples collected from 9 affected areas of the Yellow Sea. Two hundred reproducible fragments were generated with 8 AFLP primer combinations, of which 194 (97%) were polymorphic. The average Nei's genetic diversity, the coefficiency of genetic differentiation (Gst), and the average gene flow estimated from Gst in the 9 populations were 0.4018, 0.6404 and 0.2807 respectively. Cluster analysis based on the unweighed pair group method with arithmetic averages (UPGMA) showed that the genetic relationships within one population or among different populations were all related to their collecting locations and sampling time. Large genetic differentiation was detected among the populations. The E. prolifera originated from different areas and were undergoing a course of mixing.

Aberrant Functional Activation in School Age Children At-Risk for Mathematical Disability: A Functional Imaging Study of Simple Arithmetic Skill

ERIC Educational Resources Information Center

Davis, Nicole; Cannistraci, Christopher J.; Rogers, Baxter P.; Gatenby, J. Christopher; Fuchs, Lynn S.; Anderson, Adam W.; Gore, John C.

2009-01-01

We used functional magnetic resonance imaging (fMRI) to explore the patterns of brain activation associated with different levels of performance in exact and approximate calculation tasks in well-defined cohorts of children with mathematical calculation difficulties (MD) and typically developing controls. Both groups of children activated the same…

Compositional Verification with Abstraction, Learning, and SAT Solving

DTIC Science & Technology

2015-05-01

arithmetic, and bit-vectors (currently, via bit-blasting). The front-end is based on an existing tool called UFO [8] which converts C programs to the Horn...supports propositional logic, linear arithmetic, and bit-vectors (via bit-blasting). The front-end is based on the tool UFO [8]. It encodes safety of...tool UFO [8]. The encoding in Horn-SMT only uses the theory of Linear Rational Arithmetic. All experiments were carried out on an Intel R© CoreTM2 Quad

FINANCIAL CAPACITY OF OLDER AFRICAN AMERICANS WITH AMNESTIC MILD COGNITIVE IMPAIRMENT

PubMed Central

Triebel, Kristen L.; Okonkwo, Ozioma C.; Martin, Roy; Griffith, H. Randall; Crowther, Martha; Marson, Daniel C.

2010-01-01

This study investigated financial abilities of 154 patients with mild cognitive impairment (MCI) (116 Caucasian, 38 African American) using the Financial Capacity Instrument (FCI). In a series of linear regression models, we examined the effect of race on FCI performance and identified preliminary predictor variables that mediated observed racial differences on the FCI. Prior/premorbid abilities were identified. Predictor variables examined in the models included race and other demographic factors (age, education, gender), performance on global cognitive measures (MMSE, DRS-2 Total Score), history of cardiovascular disease (hypertension, diabetes, hypercholesterolemia), and a measure of educational achievement (WRAT-3 Arithmetic). African American patients with MCI performed below Caucasian patients with MCI on six of the seven FCI domains examined and on the FCI total score. WRAT-3 Arithmetic emerged as a partial mediator of group differences on the FCI, accounting for 54% of variance. In contrast, performance on global cognitive measures and history of cardiovascular disease only accounted for 14% and 2%, respectively, of the variance. Racial disparities in financial capacity appear to exist among patients with amnestic MCI. Basic academic math skills related to educational opportunity and quality of education account for a substantial proportion of the group difference in financial performance. PMID:20625268

Financial capacity of older African Americans with amnestic mild cognitive impairment.

PubMed

Triebel, Kristen L; Okonkwo, Ozioma C; Martin, Roy; Griffith, Henry Randall; Crowther, Martha; Marson, Daniel C

2010-01-01

This study investigated financial abilities of 154 patients with mild cognitive impairment (MCI) (116 white, 38 African American) using the Financial Capacity Instrument (FCI). In a series of linear regression models, we examined the effect of race on FCI performance and identified preliminary predictor variables that mediated observed racial differences on the FCI. Prior/premorbid abilities were identified. Predictor variables examined in the models included race and other demographic factors (age, education, sex), performance on global cognitive measures (MMSE, DRS-2 Total Score), history of cardiovascular disease (hypertension, diabetes, hypercholesterolemia), and a measure of educational achievement (WRAT-3 Arithmetic). African American patients with MCI performed below white patients with MCI on 6 of the 7 FCI domains examined and on the FCI total score. WRAT-3 Arithmetic emerged as a partial mediator of group differences on the FCI, accounting for 54% of variance. In contrast, performance on global cognitive measures and history of cardiovascular disease only accounted for 14% and 2%, respectively, of the variance. Racial disparities in financial capacity seem to exist among patients with amnestic MCI. Basic academic math skills related to educational opportunity and quality of education account for a substantial proportion of the group difference in financial performance.

Effects of First-Grade Number Knowledge Tutoring With Contrasting Forms of Practice.

PubMed

Fuchs, Lynn S; Geary, David C; Compton, Donald L; Fuchs, Douglas; Schatschneider, Christopher; Hamlett, Carol L; Deselms, Jacqueline; Seethaler, Pamela M; Wilson, Julie; Craddock, Caitlin F; Bryant, Joan D; Luther, Kurstin; Changas, Paul

2013-01-01

The purpose of this study was to investigate the effects of 1st-grade number knowledge tutoring with contrasting forms of practice. Tutoring occurred 3 times per week for 16 weeks. In each 30-min session, the major emphasis (25 min) was number knowledge; the other 5 min provided practice in 1 of 2 forms. Nonspeeded practice reinforced relations and principles addressed in number knowledge tutoring. Speeded practice promoted quick responding and use of efficient counting procedures to generate many correct responses. At-risk students were randomly assigned to number knowledge tutoring with speeded practice ( n = 195), number knowledge tutoring with nonspeeded practice ( n = 190), and control (no tutoring, n = 206). Each tutoring condition produced stronger learning than control on all 4 mathematics outcomes. Speeded practice produced stronger learning than nonspeeded practice on arithmetic and 2-digit calculations, but effects were comparable on number knowledge and word problems. Effects of both practice conditions on arithmetic were partially mediated by increased reliance on retrieval, but only speeded practice helped at-risk children compensate for weak reasoning ability.

Cognitive Analysis of Educational Games: The Number Game.

PubMed

van der Maas, Han L J; Nyamsuren, Enkhbold

2017-04-01

We analyze the cognitive strategies underlying performance in the Number task, a Math game that requires both arithmetic fluency and mathematical creativity. In this game all elements in a set of numbers (for instance, 2, 5, 9) have to be used precisely once to create a target number (for instance, 27) with basic arithmetic operations (solution: [5-2] × 9). We argue that some instances of this game are NP complete, by showing its relation to the well-known Partition problem. We propose heuristics based on the distinction in forward and backward reasoning. The Number Game is part of Math Garden, a popular online educational platform for practicing and monitoring math skills using innovations in computerized adaptive testing. These educational games generate enormous amounts of rich data on children's cognitive development. We found converging evidence for the use of forward proximity heuristics in the data of Math Garden, consisting of more than 20 million answers to 1,700 items. Item difficulties and the structure of correct answers were analyzed. Copyright © 2016 Cognitive Science Society, Inc.

Minimization of color shift generated in RGBW quad structure.

NASA Astrophysics Data System (ADS)

Kim, Hong Chul; Yun, Jae Kyeong; Baek, Heume-Il; Kim, Ki Duk; Oh, Eui Yeol; Chung, In Jae

2005-03-01

The purpose of RGBW Quad Structure Technology is to realize higher brightness than that of normal panel (RGB stripe structure) by adding white sub-pixel to existing RGB stripe structure. However, there is side effect called 'color shift' resulted from increasing brightness. This side effect degrades general color characteristics due to change of 'Hue', 'Brightness' and 'Saturation' as compared with existing RGB stripe structure. Especially, skin-tone colors show a tendency to get darker in contrast to normal panel. We"ve tried to minimize 'color shift' through use of LUT (Look Up Table) for linear arithmetic processing of input data, data bit expansion to 12-bit for minimizing arithmetic tolerance and brightness weight of white sub-pixel on each R, G, B pixel. The objective of this study is to minimize and keep Δu'v' value (we commonly use to represent a color difference), quantitative basis of color difference between RGB stripe structure and RGBW quad structure, below 0.01 level (existing 0.02 or higher) using Macbeth colorchecker that is general reference of color characteristics.

Effects of First-Grade Number Knowledge Tutoring With Contrasting Forms of Practice

PubMed Central

Fuchs, Lynn S.; Geary, David C.; Compton, Donald L.; Fuchs, Douglas; Schatschneider, Christopher; Hamlett, Carol L.; DeSelms, Jacqueline; Seethaler, Pamela M.; Wilson, Julie; Craddock, Caitlin F.; Bryant, Joan D.; Luther, Kurstin; Changas, Paul

2013-01-01

The purpose of this study was to investigate the effects of 1st-grade number knowledge tutoring with contrasting forms of practice. Tutoring occurred 3 times per week for 16 weeks. In each 30-min session, the major emphasis (25 min) was number knowledge; the other 5 min provided practice in 1 of 2 forms. Nonspeeded practice reinforced relations and principles addressed in number knowledge tutoring. Speeded practice promoted quick responding and use of efficient counting procedures to generate many correct responses. At-risk students were randomly assigned to number knowledge tutoring with speeded practice (n = 195), number knowledge tutoring with nonspeeded practice (n = 190), and control (no tutoring, n = 206). Each tutoring condition produced stronger learning than control on all 4 mathematics outcomes. Speeded practice produced stronger learning than nonspeeded practice on arithmetic and 2-digit calculations, but effects were comparable on number knowledge and word problems. Effects of both practice conditions on arithmetic were partially mediated by increased reliance on retrieval, but only speeded practice helped at-risk children compensate for weak reasoning ability. PMID:24065865

Genetic diversity in natural populations of mangaba in Sergipe, the largest producer State in Brazil.

PubMed

Soares, A N R; Vitória, M F; Nascimento, A L S; Ledo, A S; Rabbani, A R C; Silva, A V C

2016-08-19

Mangaba (Hancornia speciosa Gomes) is found in areas of coastal tablelands in the Brazilian Northeast and Cerrado regions. This species has been subjected to habitat fragmentation that is mainly due to human activity, and requires conservation strategies. The aim of this study was to analyze the structure and inter- and intrapopulation genetic diversity of natural populations of H. speciosa Gomes using inter-simple sequence repeat (ISSR) molecular markers. A total of 155 individuals were sampled in 10 natural populations (ITA, PAC, IND, EST, BC, PIR, JAP, BG, NEO, and SANT) in the State of Sergipe, Brazil. Fifteen primers were used to generate 162 fragments with 100% polymorphism. Genetic analysis showed that the variability between populations (77%) was higher than within populations (23%). It was possible to identify five different groups by the unweighted pair group method with arithmetic mean and principal coordinate analysis, and only one individual (E10) remained isolated. Using ISSR markers it was possible to obtain a molecular profile of the populations evaluated, showing that these markers were effective and exhibited sufficient polymorphism to estimate the genetic variability of natural populations of H. speciosa Gomes.

Implementation details of the coupled QMR algorithm

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1992-01-01

The original quasi-minimal residual method (QMR) relies on the three-term look-ahead Lanczos process, to generate basis vectors for the underlying Krylov subspaces. However, empirical observations indicate that, in finite precision arithmetic, three-term vector recurrences are less robust than mathematically equivalent coupled two-term recurrences. Therefore, we recently proposed a new implementation of the QMR method based on a coupled two-term look-ahead Lanczos procedure. In this paper, we describe implementation details of this coupled QMR algorithm, and we present results of numerical experiments.

The Implications of 3D Thermal Structure on 1D Atmospheric Retrieval

NASA Astrophysics Data System (ADS)

Blecic, Jasmina; Dobbs-Dixon, Ian; Greene, Thomas

2017-10-01

Using the atmospheric structure from a 3D global radiation-hydrodynamic simulation of HD 189733b and the open-source Bayesian Atmospheric Radiative Transfer (BART) code, we investigate the difference between the secondary-eclipse temperature structure produced with a 3D simulation and the best-fit 1D retrieved model. Synthetic data are generated by integrating the 3D models over the Spitzer, the Hubble Space Telescope (HST), and the James Web Space Telescope (JWST) bandpasses, covering the wavelength range between 1 and 11 μm where most spectroscopically active species have pronounced features. Using the data from different observing instruments, we present detailed comparisons between the temperature-pressure profiles recovered by BART and those from the 3D simulations. We calculate several averages of the 3D thermal structure and explore which particular thermal profile matches the retrieved temperature structure. We implement two temperature parameterizations that are commonly used in retrieval to investigate different thermal profile shapes. To assess which part of the thermal structure is best constrained by the data, we generate contribution functions for our theoretical model and each of our retrieved models. Our conclusions are strongly affected by the spectral resolution of the instruments included, their wavelength coverage, and the number of data points combined. We also see some limitations in each of the temperature parametrizations, as they are not able to fully match the complex curvatures that are usually produced in hydrodynamic simulations. The results show that our 1D retrieval is recovering a temperature and pressure profile that most closely matches the arithmetic average of the 3D thermal structure. When we use a higher resolution, more data points, and a parametrized temperature profile that allows more flexibility in the middle part of the atmosphere, we find a better match between the retrieved temperature and pressure profile and the arithmetic average. The Spitzer and HST simulated observations sample deep parts of the planetary atmosphere and provide fewer constraints on the temperature and pressure profile, while the JWST observations sample the middle part of the atmosphere, providing a good match with the middle and most complex part of the arithmetic average of the 3D temperature structure.

40 CFR 60.58b - Compliance and performance testing.

Code of Federal Regulations, 2010 CFR

2010-07-01

... demonstrated municipal waste combustor unit load shall be the highest 4-hour arithmetic average load achieved... shall be the highest 4-hour arithmetic average temperature achieved at the particulate matter control...

Optimized 4-bit Quantum Reversible Arithmetic Logic Unit

NASA Astrophysics Data System (ADS)

Ayyoub, Slimani; Achour, Benslama

2017-08-01

Reversible logic has received a great attention in the recent years due to its ability to reduce the power dissipation. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. The arithmetic logic unit (ALU) is an important part of central processing unit (CPU) as the execution unit. This paper presents a complete design of a new reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The proposed ALU based on a reversible low power control unit and small performance parameters full adder named double Peres gates. The presented ALU can produce the largest number (28) of arithmetic and logic functions and have the smallest number of quantum cost and delay compared with existing designs.

Does attentional training improve numerical processing in developmental dyscalculia?

PubMed

Ashkenazi, Sarit; Henik, Avishai

2012-01-01

Recently, a deficit in attention was found in those with pure developmental dyscalculia (DD). Accordingly, the present study aimed to examine the influence of attentional training on attention abilities, basic numerical abilities, and arithmetic in participants who were diagnosed as having DD. Nine university students diagnosed as having DD (IQ and reading abilities in the normal range and no indication of attention-deficit hyperactivity disorder) and nine matched controls participated in attentional training (i.e., video game training). First, training modulated the orienting system; after training, the size of the validity effect (i.e., effect of valid vs. invalid) decreased. This effect was comparable in the two groups. Training modulated abnormalities in the attention systems of those with DD, that is, it reduced their enlarged congruity effect (i.e., faster responding when flanking arrows pointed to the same location as a center arrow). Second, in relation to the enumeration task, training reduced the reaction time of the DD group in the subitizing range but did not change their smaller-than-normal subitizing range. Finally, training improved performance in addition problems in both the DD and control groups. These results imply that attentional training does improve most of the attentional deficits of those with DD. In contrast, training did not improve the abnormalities of the DD group in arithmetic or basic numerical processing. Thus, in contrast to the domain-general hypothesis, the deficits in attention among those with DD and the deficits in numerical processing appear to originate from different sources.

Understanding words, understanding numbers: an exploration of the mathematical profiles of poor comprehenders.

PubMed

Pimperton, Hannah; Nation, Kate

2010-06-01

Poor comprehenders are children who show significant deficits in their reading comprehension performance, despite average, or above-average word reading ability. To date, there have been no in-depth studies of the mathematical performance profiles of such children. This study aimed to explore the mathematical profiles of poor comprehenders. Given that language impairment is associated with difficulties with mathematics, and that poor comprehenders tend to have oral language weaknesses, we hypothesized that poor comprehenders would show relative weaknesses in aspects of mathematical performance. From a sample of 109 children aged 7-8 years, we selected 14 poor comprehenders and 14 controls with age-appropriate reading comprehension ability. The groups were matched on non-verbal ability, multiple measures of reading accuracy, and chronological age. We compared the performance of the group of poor comprehenders with that of the matched controls on two standardized measures of mathematical ability, one measuring procedural arithmetic prowess and the other tapping higher-level mathematical reasoning. Although there were no group differences in performance on the arithmetic measure, the poor comprehenders showed significantly lower scores than the controls on the mathematical reasoning task. The poor comprehenders exhibited impaired verbal ability relative to controls, with these differences in verbal ability associated with the group differences found on the test of mathematical reasoning. Poor comprehenders' deficits are not limited to the domain of literacy; their underlying profile of impairments also seems to selectively impact on certain components of mathematical ability.

Representation of natural numbers in quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benioff, Paul

2001-03-01

This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This paper is limited to k-ary representations of length L and to the axioms for arithmetic modulo k{sup L}. A model of the axioms is described based on an abstract L-fold tensor product Hilbert space H{sup arith}. Unitary maps of this space onto a physicalmore » parameter based product space H{sup phy} are then described. Each of these maps makes states in H{sup phy}, and the induced operators, a model of the axioms. Consequences of the existence of many of these maps are discussed along with the dependence of Grover's and Shor's algorithms on these maps. The importance of the main physical requirement, that the basic arithmetic operations are efficiently implementable, is discussed. This condition states that there exist physically realizable Hamiltonians that can implement the basic arithmetic operations and that the space-time and thermodynamic resources required are polynomial in L.« less

Simple arithmetic: not so simple for highly math anxious individuals.

PubMed

Chang, Hyesang; Sprute, Lisa; Maloney, Erin A; Beilock, Sian L; Berman, Marc G

2017-12-01

Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low-compared to high-math anxious individuals perform better when they activate this network less-a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently. © The Author (2017). Published by Oxford University Press.

When is working memory important for arithmetic? The impact of strategy and age

PubMed Central

Richardson, Sophie; Hubber, Paula J.; Keeble, Sarah; Gilmore, Camilla

2017-01-01

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9–11 years, 12–14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition. PMID:29228008

Simple arithmetic: not so simple for highly math anxious individuals

PubMed Central

Sprute, Lisa; Maloney, Erin A; Beilock, Sian L; Berman, Marc G

2017-01-01

Abstract Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low—compared to high—math anxious individuals perform better when they activate this network less—a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently. PMID:29140499

Marijuana Primes, Marijuana Expectancies, and Arithmetic Efficiency*

PubMed Central

Hicks, Joshua A.; Pedersen, Sarah L.; McCarthy, Denis M.; Friedman, Ronald S.

2009-01-01

Objective: Previous research has shown that primes associated with alcohol influence behavior consistent with specific alcohol expectancies. The present study examined whether exposure to marijuana-related primes and marijuana expectancies interact to produce similar effects. Specifically, the present study examined whether marijuana primes and marijuana expectancies regarding cognitive and behavioral impairment interact to influence performance on an arithmetic task. Method: Two independent samples (N = 260) of undergraduate students (both marijuana users and nonusers) first completed measures of marijuana-outcome expectancies associated with cognitive and behavioral impairment and with general negative effects (Sample 2). Later in the semester, participants were exposed to marijuana-related (or neutral) primes and then completed an arithmetic task. Results: Results from Sample 1 indicated that participants who were exposed to marijuana-themed magazine covers performed more poorly on the arithmetic task if they expected that marijuana would lead to cognitive and behavioral impairment. Results from Sample 2 indicated that, for marijuana users, cognitive and behavioral impairment expectancies, but not expectancies regarding general negative effects, similarly moderated arithmetic performance for participants exposed to marijuana-related words. Conclusions: Results support the hypothesis that the implicit activation of specific marijuana-outcome expectancies can influence cognitive processes. Implications for research on marijuana are discussed. PMID:19371490

The analysis of EEG coherence reflects middle childhood differences in mathematical achievement.

PubMed

González-Garrido, Andrés A; Gómez-Velázquez, Fabiola R; Salido-Ruiz, Ricardo A; Espinoza-Valdez, Aurora; Vélez-Pérez, Hugo; Romo-Vazquez, Rebeca; Gallardo-Moreno, Geisa B; Ruiz-Stovel, Vanessa D; Martínez-Ramos, Alicia; Berumen, Gustavo

2018-07-01

Symbolic numerical magnitude processing is crucial to arithmetic development, and it is thought to be supported by the functional activation of several brain-interconnected structures. In this context, EEG beta oscillations have been recently associated with attention and working memory processing that underlie math achievement. Due to that EEG coherence represents a useful measure of brain functional connectivity, we aimed to contrast the EEG coherence in forty 8-to-9-year-old children with different math skill levels (High: HA, and Low achievement: LA) according to their arithmetic scores in the Fourth Edition of the Wide Range Achievement Test (WRAT-4) while performing a symbolic magnitude comparison task (i.e. determining which of two numbers is numerically larger). The analysis showed significantly greater coherence over the right hemisphere in the two groups, but with a distinctive connectivity pattern. Whereas functional connectivity in the HA group was predominant in parietal areas, especially involving beta frequencies, the LA group showed more extensive frontoparietal relationships, with higher participation of delta, theta and alpha band frequencies, along with a distinct time-frequency domain expression. The results seem to reflect that lower math achievements in children mainly associate with cognitive processing steps beyond stimulus encoding, along with the need of further attentional resources and cognitive control than their peers, suggesting a lower degree of numerical processing automation. Copyright © 2018 Elsevier Inc. All rights reserved.

Impaired reading comprehension and mathematical abilities in male adolescents with average or above general intellectual abilities are associated with comorbid and future psychopathology.

PubMed

Weiser, Mark; Reichenberg, Abraham; Rabinowitz, Jonathan; Nahon, Daniella; Kravitz, Efrat; Lubin, Gad; Knobler, Haim Y; Davidson, Michael; Noy, Shlomo

2007-11-01

Research indicates that persons with learning disorders often suffer from psychopathology. We assessed current and future psychopathology in male adolescents with discrete impairments in reading comprehension (IRC) or arithmetic abilities (IAA) but with average or above-average general intellectual abilities. Subjects were a population-based cohort of 174,994 male adolescents screened by the Israeli Draft Board with average or above-average intellectual abilities but with low scores (8.6th and 10th lowest percentile respectively) on reading or arithmetic tests. They were compared with adolescents who scored in the 10th percentile and above on these tests (comparison group). Relative to the comparison group, male adolescents with IRC, IAA, or IRC and IAA (0.69%), had poorer scores on most behavioral assessments and higher prevalence of current psychopathology: 4.2% (comparison group), 8.0% (IRC), 7.0% (IAA), and 9.8% (IRC and IAA). Adolescents with IRC were also at increased risk for later hospitalization for schizophrenia (hazard ratios = 1.8, 95% confidence interval: 1.3-2.6). Male adolescents with average and above-average general intellectual abilities but with IRC or IAA are more likely to have current and future psychopathology. Impairments in intellectual functioning and abnormal behaviors leading to mental illnesses may share common neurobiological substrates. The results support screening male adolescents with learning disorders for psychopathology.

Exploring Hill Ciphers with Graphing Calculators.

ERIC Educational Resources Information Center

St. John, Dennis

1998-01-01

Explains how to code and decode messages using Hill ciphers which combine matrix multiplication and modular arithmetic. Discusses how a graphing calculator can facilitate the matrix and modular arithmetic used in the coding and decoding procedures. (ASK)

Redundant binary number representation for an inherently parallel arithmetic on optical computers.

PubMed

De Biase, G A; Massini, A

1993-02-10

A simple redundant binary number representation suitable for digital-optical computers is presented. By means of this representation it is possible to build an arithmetic with carry-free parallel algebraic sums carried out in constant time and parallel multiplication in log N time. This redundant number representation naturally fits the 2's complement binary number system and permits the construction of inherently parallel arithmetic units that are used in various optical technologies. Some properties of this number representation and several examples of computation are presented.

Trinary signed-digit arithmetic using an efficient encoding scheme

NASA Astrophysics Data System (ADS)

Salim, W. Y.; Alam, M. S.; Fyath, R. S.; Ali, S. A.

2000-09-01

The trinary signed-digit (TSD) number system is of interest for ultrafast optoelectronic computing systems since it permits parallel carry-free addition and borrow-free subtraction of two arbitrary length numbers in constant time. In this paper, a simple coding scheme is proposed to encode the decimal number directly into the TSD form. The coding scheme enables one to perform parallel one-step TSD arithmetic operation. The proposed coding scheme uses only a 5-combination coding table instead of the 625-combination table reported recently for recoded TSD arithmetic technique.

One-step trinary signed-digit arithmetic using an efficient encoding scheme

NASA Astrophysics Data System (ADS)

Salim, W. Y.; Fyath, R. S.; Ali, S. A.; Alam, Mohammad S.

2000-11-01

The trinary signed-digit (TSD) number system is of interest for ultra fast optoelectronic computing systems since it permits parallel carry-free addition and borrow-free subtraction of two arbitrary length numbers in constant time. In this paper, a simple coding scheme is proposed to encode the decimal number directly into the TSD form. The coding scheme enables one to perform parallel one-step TSD arithmetic operation. The proposed coding scheme uses only a 5-combination coding table instead of the 625-combination table reported recently for recoded TSD arithmetic technique.

Bit-wise arithmetic coding for data compression

NASA Technical Reports Server (NTRS)

Kiely, A. B.

1994-01-01

This article examines the problem of compressing a uniformly quantized independent and identically distributed (IID) source. We present a new compression technique, bit-wise arithmetic coding, that assigns fixed-length codewords to the quantizer output and uses arithmetic coding to compress the codewords, treating the codeword bits as independent. We examine the performance of this method and evaluate the overhead required when used block-adaptively. Simulation results are presented for Gaussian and Laplacian sources. This new technique could be used as the entropy coder in a transform or subband coding system.

Basic mathematical function libraries for scientific computation

NASA Technical Reports Server (NTRS)

Galant, David C.

1989-01-01

Ada packages implementing selected mathematical functions for the support of scientific and engineering applications were written. The packages provide the Ada programmer with the mathematical function support found in the languages Pascal and FORTRAN as well as an extended precision arithmetic and a complete complex arithmetic. The algorithms used are fully described and analyzed. Implementation assumes that the Ada type FLOAT objects fully conform to the IEEE 754-1985 standard for single binary floating-point arithmetic, and that INTEGER objects are 32-bit entities. Codes for the Ada packages are included as appendixes.

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (22nd, Stellenbosch, South Africa, July 12-17, 1998). Volume 2.

ERIC Educational Resources Information Center

Olivier, Alwyn, Ed.; Newstead, Karen, Ed.

The second volume of this proceedings contains the first portion of the research reports. Papers include: (1) "Learning Algebraic Strategies Using a Computerized Balance Model" (James Aczel); (2) "Children's Perception of Multiplicative Structure in Diagrams" (Bjornar Alseth); (3) "A Discussion of Different Approaches to Arithmetic Teaching"…

The Duality Principle in Teaching Arithmetic and Geometric Series

ERIC Educational Resources Information Center

Yeshurun, Shraga

1978-01-01

The author discusses the use of the duality principle in combination with the hierarchy of algebraic operations in helping students to retain and use definitions and rules for arithmetic and geometric sequences and series. (MN)

Modified-Signed-Digit Optical Computing Using Fan-Out

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang; Zhou, Shaomin; Yeh, Pochi

1996-01-01

Experimental optical computing system containing optical fan-out elements implements modified signed-digit (MSD) arithmetic and logic. In comparison with previous optical implementations of MSD arithmetic, this one characterized by larger throughput, greater flexibility, and simpler optics.

The association between arithmetic and reading performance in school: A meta-analytic study.

PubMed

Singer, Vivian; Strasser, Kathernie

2017-12-01

Many studies of school achievement find a significant association between reading and arithmetic achievement. The magnitude of the association varies widely across the studies, but the sources of this variation have not been identified. The purpose of this paper is to examine the magnitude and determinants of the relation between arithmetic and reading performance during elementary and middle school years. We meta-analyzed 210 correlations between math and reading measures, coming from 68 independent samples (the overall sample size was 58923 participants). The meta-analysis yielded an average correlation of 0.55 between math and reading measures. Among the moderators tested, only transparency of orthography and use of timed or untimed tests were significant in explaining the size of the correlation, with the largest correlations observed between timed measures of arithmetic and reading and between math and reading in opaque orthographies. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Adults' Arithmetic Builds on Fast and Automatic Processing of Arabic Digits: Evidence from an Audiovisual Matching Paradigm

PubMed Central

Sasanguie, Delphine; Reynvoet, Bert

2014-01-01

Several studies have shown that performance on symbolic number tasks is related to individual differences in arithmetic. However, it is not clear which process is responsible for this association, i.e. fast, automatic processing of symbols per se or access to the underlying non-symbolic representation of the symbols. To dissociate between both options, adult participants performed an audiovisual matching paradigm. Auditory presented number words needed to be matched with either Arabic digits or dot patterns. The results revealed that a distance effect was present in the dots-number word matching task and absent in the digit-number word matching task. Crucially, only performance in the digit task contributed to the variance in arithmetical abilities. This led us to conclude that adults' arithmetic builds on the ability to quickly and automatically process Arabic digits, without the underlying non-symbolic magnitude representation being activated. PMID:24505308

The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds.

PubMed

Durand, Marianne; Hulme, Charles; Larkin, Rebecca; Snowling, Margaret

2005-06-01

A range of possible predictors of arithmetic and reading were assessed in a large sample (N=162) of children between ages 7 years 5 months and 10 years 4 months. A confirmatory factor analysis of the predictors revealed a good fit to a model consisting of four latent variables (verbal ability, nonverbal ability, search speed, and phonological memory) and two manifest variables (digit comparison and phoneme deletion). A path analysis showed that digit comparison and verbal ability were unique predictors of variations in arithmetic skills, whereas phoneme deletion and verbal ability were unique predictors of variations in reading skills. These results confirm earlier findings that phoneme deletion ability appears to be a critical foundation for learning to read (decode). In addition, variations in the speed of accessing numerical quantity information appear to be a critical foundation for the development of arithmetic skills.

Changes in running pattern due to fatigue and cognitive load in orienteering.

PubMed

Millet, Guillaume Y; Divert, Caroline; Banizette, Marion; Morin, Jean-Benoit

2010-01-01

The aim of this study was to examine the influence of fatigue on running biomechanics in normal running, in normal running with a cognitive task, and in running while map reading. Nineteen international and less experienced orienteers performed a fatiguing running exercise of duration and intensity similar to a classic distance orienteering race on an instrumented treadmill while performing mental arithmetic, an orienteering simulation, and control running at regular intervals. Two-way repeated-measures analysis of variance did not reveal any significant difference between mental arithmetic and control running for any of the kinematic and kinetic parameters analysed eight times over the fatiguing protocol. However, these parameters were systematically different between the orienteering simulation and the other two conditions (mental arithmetic and control running). The adaptations in orienteering simulation running were significantly more pronounced in the elite group when step frequency, peak vertical ground reaction force, vertical stiffness, and maximal downward displacement of the centre of mass during contact were considered. The effects of fatigue on running biomechanics depended on whether the orienteers read their map or ran normally. It is concluded that adding a cognitive load does not modify running patterns. Therefore, all changes in running pattern observed during the orienteering simulation, particularly in elite orienteers, are the result of adaptations to enable efficient map reading and/or potentially prevent injuries. Finally, running patterns are not affected to the same extent by fatigue when a map reading task is added.

Dual tasking and balance in those with central and peripheral vision loss.

PubMed

Kotecha, Aachal; Chopra, Reena; Fahy, Rachel T A; Rubin, Gary S

2013-08-09

To investigate the effects of a secondary task on standing balance in patients with glaucoma or AMD compared with age-similar control subjects. Twelve AMD, 12 glaucoma, and 12 control participants underwent posturography under two standing conditions (eyes open on a firm or foam-rubber surface) and two tasks: quiet standing and undertaking a mental arithmetic task. Center of foot-pressure average displacement (root mean square [RMS]; in millimeters) was calculated. The mean (SD) age of the participants in each group was as follows: controls 66.2 (6.4) years, glaucoma 69.2 (4.3) years, and AMD 72.2 (5.3) years. There were significant differences in RMS between controls and AMD patients when undertaking the mental arithmetic task standing on the firm surface (mean difference [SE]: 2.8 [0.8] mm, P = 0.005). There were significant differences between controls and AMD patients when undertaking the mental arithmetic task on the foam surface, with the difference between controls and glaucoma patients approaching significance (mean difference [SE]: control versus AMD = 3.1 [0.9] mm, P = 0.005; control versus glaucoma = 2.2 [0.9] mm, P = 0.06). Postural instability increases with the addition of a secondary task in older persons, which may put them at greater risk of falls. Patients with central losses exhibit greater instability with the addition of a secondary task, particularly during somatosensory perturbations. The negative effects of secondary tasks on balance control in those with peripheral visual losses become more apparent under somatosensory perturbations.

The relative importance of two different mathematical abilities to mathematical achievement.

PubMed

Nunes, Terezinha; Bryant, Peter; Barros, Rossana; Sylva, Kathy

2012-03-01

Two distinct abilities, mathematical reasoning and arithmetic skill, might make separate and specific contributions to mathematical achievement. However, there is little evidence to inform theory and educational practice on this matter. The aims of this study were (1) to assess whether mathematical reasoning and arithmetic make independent contributions to the longitudinal prediction of mathematical achievement over 5 years and (2) to test the specificity of this prediction. Data from Avon Longitudinal Study of Parents and Children (ALSPAC) were available on 2,579 participants for analyses of KS2 achievement and on 1,680 for the analyses of KS3 achievement. Hierarchical regression analyses were used to assess the independence and specificity of the contribution of mathematical reasoning and arithmetic skill to the prediction of achievement in KS2 and KS3 mathematics, science, and English. Age, intelligence, and working memory (WM) were controls in these analyses. Mathematical reasoning and arithmetic did make independent contributions to the prediction of mathematical achievement; mathematical reasoning was by far the stronger predictor of the two. These predictions were specific in so far as these measures were more strongly related to mathematics than to science or English. Intelligence and WM were non-specific predictors; intelligence contributed more to the prediction of science than of maths, and WM predicted maths and English equally well. There is clear justification for making a distinction between mathematical reasoning and arithmetic skills. The implication is that schools must plan explicitly to improve mathematical reasoning as well as arithmetic skills. ©2011 The British Psychological Society.

Network-Physics(NP) Bec DIGITAL(#)-VULNERABILITY Versus Fault-Tolerant Analog

NASA Astrophysics Data System (ADS)

Alexander, G. K.; Hathaway, M.; Schmidt, H. E.; Siegel, E.

2011-03-01

Siegel[AMS Joint Mtg.(2002)-Abs.973-60-124] digits logarithmic-(Newcomb(1881)-Weyl(1914; 1916)-Benford(1938)-"NeWBe"/"OLDbe")-law algebraic-inversion to ONLY BEQS BEC:Quanta/Bosons= digits: Synthesis reveals EMP-like SEVERE VULNERABILITY of ONLY DIGITAL-networks(VS. FAULT-TOLERANT ANALOG INvulnerability) via Barabasi "Network-Physics" relative-``statics''(VS.dynamics-[Willinger-Alderson-Doyle(Not.AMS(5/09)]-]critique); (so called)"Quantum-computing is simple-arithmetic(sans division/ factorization); algorithmic-complexities: INtractibility/ UNdecidability/ INefficiency/NONcomputability / HARDNESS(so MIScalled) "noise"-induced-phase-transitions(NITS) ACCELERATION: Cook-Levin theorem Reducibility is Renormalization-(Semi)-Group fixed-points; number-Randomness DEFINITION via WHAT? Query(VS. Goldreich[Not.AMS(02)] How? mea culpa)can ONLY be MBCS "hot-plasma" versus digit-clumping NON-random BEC; Modular-arithmetic Congruences= Signal X Noise PRODUCTS = clock-model; NON-Shor[Physica A,341,586(04)] BEC logarithmic-law inversion factorization:Watkins number-thy. U stat.-phys.); P=/=NP TRIVIAL Proof: Euclid!!! [(So Miscalled) computational-complexity J-O obviation via geometry.

The impact of finger counting habits on arithmetic in adults and children.

PubMed

Newman, Sharlene D; Soylu, Firat

2014-07-01

Here, we explored the impact of finger counting habits on arithmetic in both adults and children. Two groups of participants were examined, those that begin counting with their left hand (left-starters) and those that begin counting with their right hand (right-starters). For the adults, performance on an addition task in which participants added 2 two-digit numbers was compared. The results revealed that left-starters were slower than right-starters when adding and they had lower forward and backward digit-span scores. The children (aged 5-12) showed similar results on a single-digit timed addition task-right-starters outperformed left-starters. However, the children did not reveal differences in working memory or verbal and non-verbal intelligence as a function of finger counting habit. We argue that the motor act of finger counting influences how number is represented and suggest that left-starters may have a more bilateral representation that accounts for the slower processing.

Activities for Students: Averaging Rates--Deciding when to Use the Harmonic or Arithmetic Mean

ERIC Educational Resources Information Center

Brown, S. L.; Rizzardi, M. A.

2005-01-01

The article describes the harmonic mean and explores situations for using it. Activities that involve hands-on practice for students are provided. Students learn to recognize which mean, harmonic or arithmetic, is appropriate.

Plotting equation for gaussian percentiles and a spreadsheet program for generating probability plots

USGS Publications Warehouse

Balsillie, J.H.; Donoghue, J.F.; Butler, K.M.; Koch, J.L.

2002-01-01

Two-dimensional plotting tools can be of invaluable assistance in analytical scientific pursuits, and have been widely used in the analysis and interpretation of sedimentologic data. We consider, in this work, the use of arithmetic probability paper (APP). Most statistical computer applications do not allow for the generation of APP plots, because of apparent intractable nonlinearity of the percentile (or probability) axis of the plot. We have solved this problem by identifying an equation(s) for determining plotting positions of Gaussian percentiles (or probabilities), so that APP plots can easily be computer generated. An EXCEL example is presented, and a programmed, simple-to-use EXCEL application template is hereby made publicly available, whereby a complete granulometric analysis including data listing, moment measure calculations, and frequency and cumulative APP plots, is automatically produced.

Probability Quantization for Multiplication-Free Binary Arithmetic Coding

NASA Technical Reports Server (NTRS)

Cheung, K. -M.

1995-01-01

A method has been developed to improve on Witten's binary arithmetic coding procedure of tracking a high value and a low value. The new method approximates the probability of the less probable symbol, which improves the worst-case coding efficiency.

Competing Biases in Mental Arithmetic: When Division Is More and Multiplication Is Less.

PubMed

Shaki, Samuel; Fischer, Martin H

2017-01-01

Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such "operational momentum" (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic.

On the structure of arithmetic sums of Cantor sets with constant ratios of dissection

NASA Astrophysics Data System (ADS)

Anisca, Razvan; Chlebovec, Christopher

2009-09-01

We investigate conditions which imply that the topological structure of the arithmetic sum of two Cantor sets with constant ratios of dissection at each step is either: a Cantor set, a finite union of closed intervals, or three mixed models (L, R and M-Cantorval). We obtain general results that apply in particular for the case of homogeneous Cantor sets, thus generalizing the results of Mendes and Oliveira. The method used here is new in this context. We also produce results regarding the arithmetic sum of two affine Cantor sets of a special kind.

Fast reversible wavelet image compressor

NASA Astrophysics Data System (ADS)

Kim, HyungJun; Li, Ching-Chung

1996-10-01

We present a unified image compressor with spline biorthogonal wavelets and dyadic rational filter coefficients which gives high computational speed and excellent compression performance. Convolutions with these filters can be preformed by using only arithmetic shifting and addition operations. Wavelet coefficients can be encoded with an arithmetic coder which also uses arithmetic shifting and addition operations. Therefore, from the beginning to the end, the while encoding/decoding process can be done within a short period of time. The proposed method naturally extends form the lossless compression to the lossy but high compression range and can be easily adapted to the progressive reconstruction.

Fault tolerant computing: A preamble for assuring viability of large computer systems

NASA Technical Reports Server (NTRS)

Lim, R. S.

1977-01-01

The need for fault-tolerant computing is addressed from the viewpoints of (1) why it is needed, (2) how to apply it in the current state of technology, and (3) what it means in the context of the Phoenix computer system and other related systems. To this end, the value of concurrent error detection and correction is described. User protection, program retry, and repair are among the factors considered. The technology of algebraic codes to protect memory systems and arithmetic codes to protect memory systems and arithmetic codes to protect arithmetic operations is discussed.

The Differential Role of Verbal and Spatial Working Memory in the Neural Basis of Arithmetic

PubMed Central

Demir, Özlem Ece; Prado, Jérôme; Booth, James R.

2014-01-01

We examine the relations of verbal and spatial WM ability to the neural bases of arithmetic in school-age children. We independently localize brain regions subserving verbal versus spatial representations. For multiplication, higher verbal WM ability is associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. For multiplication and subtraction, higher spatial WM ability is associated with greater recruitment of right parietal cortex, identified by the spatial localizer. Depending on their WM ability, children engage different neural systems that manipulate different representations to solve arithmetic problems. PMID:25144257

An Input Routine Using Arithmetic Statements for the IBM 704 Digital Computer

NASA Technical Reports Server (NTRS)

Turner, Don N.; Huff, Vearl N.

1961-01-01

An input routine has been designed for use with FORTRAN or SAP coded programs which are to be executed on an IBM 704 digital computer. All input to be processed by the routine is punched on IBM cards as declarative statements of the arithmetic type resembling the FORTRAN language. The routine is 850 words in length. It is capable of loading fixed- or floating-point numbers, octal numbers, and alphabetic words, and of performing simple arithmetic as indicated on input cards. Provisions have been made for rapid loading of arrays of numbers in consecutive memory locations.

Group Work is Not Cooperative Learning: An Evaluation of PowerTeaching in Middle Schools. A Report from the Investing in Innovation (i3) Evaluation

ERIC Educational Resources Information Center

Rappaport, Shelley; Grossman, Jean; Garcia, Ivonne; Zhu, Pei; Avila, Osvaldo; Granito, Kelly

2017-01-01

To succeed in today's economy, students need both proficiency in the "three Rs" (reading, writing and arithmetic) and strong applied skills. Communication skills, team work, and critical thinking have long been at the top of employers' lists of applied skills they seek in employees. States are responding to employers' needs by putting in…

An Assessment of the Condition of Coral Reefs off the Former Navy Bombing Ranges at Isla De Culebra and Isla De Vieques, Puerto Rico

DTIC Science & Technology

2005-04-01

Bray-Curtis distance measure with an Unweighted Pair Group Method with Arithmetic Averages ( UPGMA ) linkage method to perform a cluster analysis of the...59 35 Comparison of reef condition indicators clustering by UPGMA analysis...Polyvinyl Chloride RBD Red-band Disease SACEX Supporting Arms Coordination Exercise SAV Submerged Aquatic Vegetation SD Standard Deviation UPGMA

Personalized Medicine in Veterans with Traumatic Brain Injuries

DTIC Science & Technology

2013-05-01

Pair-Group Method using Arithmetic averages ( UPGMA ) based on cosine correlation of row mean centered log2 signal values; this was the top 50%-tile...cluster- ing was performed by the UPGMA method using Cosine correlation as the similarity metric. For comparative purposes, clustered heat maps included...non-mTBI cases were subjected to unsupervised hierarchical clustering analysis using the UPGMA algorithm with cosine correlation as the similarity

Personalized Medicine in Veterans with Traumatic Brain Injuries

DTIC Science & Technology

2014-07-01

9 control cases are subjected to unsupervised hierarchical clustering analysis using the UPGMA algorithm with cosine correlation as the similarity...in unsu- pervised hierarchical clustering by the Un- weighted Pair-Group Method using Arithmetic averages ( UPGMA ) based on cosine correlation of row...of log2 trans- formed MAS5.0 signal values; probe set cluster- ing was performed by the UPGMA method using Cosine correlation as the similarity

Superior analgesic effect of an active distraction versus pleasant unfamiliar sounds and music: the influence of emotion and cognitive style.

PubMed

Villarreal, Eduardo A Garza; Brattico, Elvira; Vase, Lene; Østergaard, Leif; Vuust, Peter

2012-01-01

Listening to music has been found to reduce acute and chronic pain. The underlying mechanisms are poorly understood; however, emotion and cognitive mechanisms have been suggested to influence the analgesic effect of music. In this study we investigated the influence of familiarity, emotional and cognitive features, and cognitive style on music-induced analgesia. Forty-eight healthy participants were divided into three groups (empathizers, systemizers and balanced) and received acute pain induced by heat while listening to different sounds. Participants listened to unfamiliar Mozart music rated with high valence and low arousal, unfamiliar environmental sounds with similar valence and arousal as the music, an active distraction task (mental arithmetic) and a control, and rated the pain. Data showed that the active distraction led to significantly less pain than did the music or sounds. Both unfamiliar music and sounds reduced pain significantly when compared to the control condition; however, music was no more effective than sound to reduce pain. Furthermore, we found correlations between pain and emotion ratings. Finally, systemizers reported less pain during the mental arithmetic compared with the other two groups. These findings suggest that familiarity may be key in the influence of the cognitive and emotional mechanisms of music-induced analgesia, and that cognitive styles may influence pain perception.

Post-error response inhibition in high math-anxious individuals: Evidence from a multi-digit addition task.

PubMed

Núñez-Peña, M Isabel; Tubau, Elisabet; Suárez-Pellicioni, Macarena

2017-06-01

The aim of the study was to investigate how high math-anxious (HMA) individuals react to errors in an arithmetic task. Twenty HMA and 19 low math-anxious (LMA) individuals were presented with a multi-digit addition verification task and were given response feedback. Post-error adjustment measures (response time and accuracy) were analyzed in order to study differences between groups when faced with errors in an arithmetical task. Results showed that both HMA and LMA individuals were slower to respond following an error than following a correct answer. However, post-error accuracy effects emerged only for the HMA group, showing that they were also less accurate after having committed an error than after giving the right answer. Importantly, these differences were observed only when individuals needed to repeat the same response given in the previous trial. These results suggest that, for HMA individuals, errors caused reactive inhibition of the erroneous response, facilitating performance if the next problem required the alternative response but hampering it if the response was the same. This stronger reaction to errors could be a factor contributing to the difficulties that HMA individuals experience in learning math and doing math tasks. Copyright © 2017 Elsevier B.V. All rights reserved.

Visual-spatial abilities relate to mathematics achievement in children with heavy prenatal alcohol exposure

PubMed Central

Crocker, N.; Riley, E.P.; Mattson, S.N.

2014-01-01

Objective The current study examined the relationship between mathematics and attention, working memory, and visual memory in children with heavy prenatal alcohol exposure and controls. Method Fifty-six children (29 AE, 27 CON) were administered measures of global mathematics achievement (WRAT-3 Arithmetic & WISC-III Written Arithmetic), attention, (WISC-III Digit Span forward and Spatial Span forward), working memory (WISC-III Digit Span backward and Spatial Span backward), and visual memory (CANTAB Spatial Recognition Memory and Pattern Recognition Memory). The contribution of cognitive domains to mathematics achievement was analyzed using linear regression techniques. Attention, working memory and visual memory data were entered together on step 1 followed by group on step 2, and the interaction terms on step 3. Results Model 1 accounted for a significant amount of variance in both mathematics achievement measures, however, model fit improved with the addition of group on step 2. Significant predictors of mathematics achievement were Spatial Span forward and backward and Spatial Recognition Memory. Conclusions These findings suggest that deficits in spatial processing may be related to math impairments seen in FASD. In addition, prenatal alcohol exposure was associated with deficits in mathematics achievement, above and beyond the contribution of general cognitive abilities. PMID:25000323

Visual-spatial abilities relate to mathematics achievement in children with heavy prenatal alcohol exposure.

PubMed

Crocker, Nicole; Riley, Edward P; Mattson, Sarah N

2015-01-01

The current study examined the relationship between mathematics and attention, working memory, and visual memory in children with heavy prenatal alcohol exposure and controls. Subjects were 56 children (29 AE, 27 CON) who were administered measures of global mathematics achievement (WRAT-3 Arithmetic & WISC-III Written Arithmetic), attention, (WISC-III Digit Span forward and Spatial Span forward), working memory (WISC-III Digit Span backward and Spatial Span backward), and visual memory (CANTAB Spatial Recognition Memory and Pattern Recognition Memory). The contribution of cognitive domains to mathematics achievement was analyzed using linear regression techniques. Attention, working memory, and visual memory data were entered together on Step 1 followed by group on Step 2, and the interaction terms on Step 3. Model 1 accounted for a significant amount of variance in both mathematics achievement measures; however, model fit improved with the addition of group on Step 2. Significant predictors of mathematics achievement were Spatial Span forward and backward and Spatial Recognition Memory. These findings suggest that deficits in spatial processing may be related to math impairments seen in FASD. In addition, prenatal alcohol exposure was associated with deficits in mathematics achievement, above and beyond the contribution of general cognitive abilities. PsycINFO Database Record (c) 2015 APA, all rights reserved.

Redesigning Arithmetic for Student Success: Supporting Faculty to Teach in New Ways

ERIC Educational Resources Information Center

Bickerstaff, Susan; Lontz, Barbara; Cormier, Maria Scott; Xu, Di

2014-01-01

This chapter describes a promising new approach to teaching developmental arithmetic and prealgebra, and presents research findings that demonstrate how a faculty support network helped instructors adopt new teaching strategies and gain confidence in teaching the reformed course.

Versatile analog pulse height computer performs real-time arithmetic operations

NASA Technical Reports Server (NTRS)

Brenner, R.; Strauss, M. G.

1967-01-01

Multipurpose analog pulse height computer performs real-time arithmetic operations on relatively fast pulses. This computer can be used for identification of charged particles, pulse shape discrimination, division of signals from position sensitive detectors, and other on-line data reduction techniques.

Pre-schoolers Learn at Home.

ERIC Educational Resources Information Center

Smith, Penny

1985-01-01

Reviews: "ArithMagic (Counting, Addition, Subtraction)" which uses graphics to illustrate/review basic arithmetic concepts; "The Sweet Shop" which uses graphics (and a character called Mr. Jellybean) to teach arithmetic concepts; and "Math Magic," a monster-filled arcade game that teaches addition and subtraction.…

What difference does a year of schooling make?: Maturation of brain response and connectivity between 2nd and 3rd grades during arithmetic problem solving

PubMed Central

Rosenberg-Lee, Miriam; Barth, Maria; Menon, Vinod

2011-01-01

Early elementary schooling in 2nd and 3rd grades (ages 7-9) is an important period for the acquisition and mastery of basic mathematical skills. Yet, we know very little about neurodevelopmental changes that might occur over a year of schooling. Here we examine behavioral and neurodevelopmental changes underlying arithmetic problem solving in a well-matched group of 2nd (n = 45) and 3rd (n = 45) grade children. Although 2nd and 3rd graders did not differ on IQ or grade- and age-normed measures of math, reading and working memory, 3rd graders had higher raw math scores (effect sizes = 1.46-1.49) and were more accurate than 2nd graders in an fMRI task involving verification of simple and complex two-operand addition problems (effect size = 0.43). In both 2nd and 3rd graders, arithmetic complexity was associated with increased responses in right inferior frontal sulcus and anterior insula, regions implicated in domain-general cognitive control, and in left intraparietal sulcus (IPS) and superior parietal lobule (SPL) regions important for numerical and arithmetic processing. Compared to 2nd graders, 3rd graders showed greater activity in dorsal stream parietal areas right SPL, IPS and angular gyrus (AG) as well as ventral visual stream areas bilateral lingual gyrus (LG), right lateral occipital cortex (LOC) and right parahippocampal gyrus (PHG). Significant differences were also observed in the prefrontal cortex (PFC), with 3rd graders showing greater activation in left dorsal lateral PFC (dlPFC) and greater deactivation in the ventral medial PFC (vmPFC). Third graders also showed greater functional connectivity between the left dlPFC and multiple posterior brain areas, with larger differences in dorsal stream parietal areas SPL and AG, compared to ventral stream visual areas LG, LOC and PHG. No such between-grade differences were observed in functional connectivity between the vmPFC and posterior brain regions. These results suggest that even the narrow one-year interval spanning grades 2 and 3 is characterized by significant arithmetic task-related changes in brain response and connectivity, and argue that pooling data across wide age ranges and grades can miss important neurodevelopmental changes. Our findings have important implications for understanding brain mechanisms mediating early maturation of mathematical skills and, more generally, for educational neuroscience. PMID:21620984

Learning, Realizability and Games in Classical Arithmetic

NASA Astrophysics Data System (ADS)

Aschieri, Federico

2010-12-01

In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel modified realizability to a classical fragment of first order Arithmetic, Heyting Arithmetic plus EM1 (Excluded middle axiom restricted to Sigma^0_1 formulas). We introduce a new realizability semantics we call "Interactive Learning-Based Realizability". Our realizers are self-correcting programs, which learn from their errors and evolve through time. Secondly, we extend the class of learning based realizers to a classical version PCFclass of PCF and, then, compare the resulting notion of realizability with Coquand game semantics and prove a full soundness and completeness result. In particular, we show there is a one-to-one correspondence between realizers and recursive winning strategies in the 1-Backtracking version of Tarski games. Third, we provide a complete and fully detailed constructive analysis of learning as it arises in learning based realizability for HA+EM1, Avigad's update procedures and epsilon substitution method for Peano Arithmetic PA. We present new constructive techniques to bound the length of learning processes and we apply them to reprove - by means of our theory - the classic result of Godel that provably total functions of PA can be represented in Godel's system T. Last, we give an axiomatization of the kind of learning that is needed to computationally interpret Predicative classical second order Arithmetic. Our work is an extension of Avigad's and generalizes the concept of update procedure to the transfinite case. Transfinite update procedures have to learn values of transfinite sequences of non computable functions in order to extract witnesses from classical proofs.

Floating-point geometry: toward guaranteed geometric computations with approximate arithmetics

NASA Astrophysics Data System (ADS)

Bajard, Jean-Claude; Langlois, Philippe; Michelucci, Dominique; Morin, Géraldine; Revol, Nathalie

2008-08-01

Geometric computations can fail because of inconsistencies due to floating-point inaccuracy. For instance, the computed intersection point between two curves does not lie on the curves: it is unavoidable when the intersection point coordinates are non rational, and thus not representable using floating-point arithmetic. A popular heuristic approach tests equalities and nullities up to a tolerance ɛ. But transitivity of equality is lost: we can have A approx B and B approx C, but A not approx C (where A approx B means ||A - B|| < ɛ for A,B two floating-point values). Interval arithmetic is another, self-validated, alternative; the difficulty is to limit the swell of the width of intervals with computations. Unfortunately interval arithmetic cannot decide equality nor nullity, even in cases where it is decidable by other means. A new approach, developed in this paper, consists in modifying the geometric problems and algorithms, to account for the undecidability of the equality test and unavoidable inaccuracy. In particular, all curves come with a non-zero thickness, so two curves (generically) cut in a region with non-zero area, an inner and outer representation of which is computable. This last approach no more assumes that an equality or nullity test is available. The question which arises is: which geometric problems can still be solved with this last approach, and which cannot? This paper begins with the description of some cases where every known arithmetic fails in practice. Then, for each arithmetic, some properties of the problems they can solve are given. We end this work by proposing the bases of a new approach which aims to fulfill the geometric computations requirements.

Is 1/f sound more effective than simple resting in reducing stress response?

PubMed

Oh, Eun-Joo; Cho, Il-Young; Park, Soon-Kwon

2014-01-01

It has been previously demonstrated that listening to 1/f sound effectively reduces stress. However, these findings have been inconsistent and further study on the relationship between 1/f sound and the stress response is consequently necessary. The present study examined whether sound with 1/f properties (1/f sound) affects stress-induced electroencephalogram (EEG) changes. Twenty-six subjects who voluntarily participated in the study were randomly assigned to the experimental or control group. Data from four participants were excluded because of EEG artifacts. A mental arithmetic task was used as a stressor. Participants in the experiment group listened to 1/f sound for 5 minutes and 33 seconds, while participants in the control group sat quietly for the same duration. EEG recordings were obtained at various points throughout the experiment. After the experiment, participants completed a questionnaire on the affective impact of the 1/f sound. The results indicated that the mental arithmetic task effectively induced a stress response measurable by EEG. Relative theta power at all electrode sites was significantly lower than baseline in both the control and experimental group. Relative alpha power was significantly lower, and relative beta power was significantly higher in the T3 and T4 areas. Secondly, 1/f sound and simple resting affected task-associated EEG changes in a similar manner. Finally, participants reported in the questionnaire that they experienced a positive feeling in response to the 1/f sound. Our results suggest that a commercialized 1/f sound product is not more effective than simple resting in alleviating the physiological stress response.

One way Doppler Extractor. Volume 2: Digital VCO technique

NASA Technical Reports Server (NTRS)

Nossen, E. J.; Starner, E. R.

1974-01-01

A feasibility analysis and trade-offs for a one-way Doppler extractor using digital VCO techniques is presented. The method of Doppler measurement involves the use of a digital phase lock loop; once this loop is locked to the incoming signal, the precise frequency and hence the Doppler component can be determined directly from the contents of the digital control register. The only serious error source is due to internally generated noise. Techniques are presented for minimizing this error source and achieving an accuracy of 0.01 Hz in a one second averaging period. A number of digitally controlled oscillators were analyzed from a performance and complexity point of view. The most promising technique uses an arithmetic synthesizer as a digital waveform generator.

System for monitoring an industrial process and determining sensor status

DOEpatents

Gross, K.C.; Hoyer, K.K.; Humenik, K.E.

1995-10-17

A method and system for monitoring an industrial process and a sensor are disclosed. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test. 17 figs.

System for monitoring an industrial process and determining sensor status

DOEpatents

Gross, K.C.; Hoyer, K.K.; Humenik, K.E.

1997-05-13

A method and system are disclosed for monitoring an industrial process and a sensor. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test. 17 figs.

System for monitoring an industrial process and determining sensor status

DOEpatents

Gross, Kenneth C.; Hoyer, Kristin K.; Humenik, Keith E.

1995-01-01

A method and system for monitoring an industrial process and a sensor. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test.

System for monitoring an industrial process and determining sensor status

DOEpatents

Gross, Kenneth C.; Hoyer, Kristin K.; Humenik, Keith E.

1997-01-01

A method and system for monitoring an industrial process and a sensor. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test.

Effect of root planing on surface topography: an in-vivo randomized experimental trial.

PubMed

Rosales-Leal, J I; Flores, A B; Contreras, T; Bravo, M; Cabrerizo-Vílchez, M A; Mesa, F

2015-04-01

The root surface topography exerts a major influence on clinical attachment and bacterial recolonization after root planing. In-vitro topographic studies have yielded variable results, and clinical studies are necessary to compare root surface topography after planing with current ultrasonic devices and with traditional manual instrumentation. The aim of this study was to compare the topography of untreated single-rooted teeth planed in vivo with a curette, a piezoelectric ultrasonic (PU) scraper or a vertically oscillating ultrasonic (VOU) scraper. In a randomized experimental trial of 19 patients, 44 single-rooted teeth were randomly assigned to one of four groups for: no treatment; manual root planing with a curette; root planing with a PU scraper; or root planing with a VOU scraper. Post-treatment, the teeth were extracted and their topography was analyzed in 124 observations with white-light confocal microscopy, measuring the roughness parameters arithmetic average height, root-mean-square roughness, maximum height of peaks, maximum depth of valleys, absolute height, skewness and kurtosis. The roughness values arithmetic average height and root-mean-square roughness were similar after each treatment and lower than after no treatment ( p < 0.05). Absolute height was lower in the VOU group than in the untreated ( p = 0.0026) and PU (p = 0.045) groups. Surface morphology was similar after the three treatments and was less irregular than in the untreated group. Values for the remaining roughness parameters were similar among all treatment groups ( p > 0.05). Both ultrasonic devices reduce the roughness, producing a similar topography to that observed after manual instrumentation with a curette, to which they appear to represent a valid alternative. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Using the Binomial Series to Prove the Arithmetic Mean-Geometric Mean Inequality

ERIC Educational Resources Information Center

Persky, Ronald L.

2003-01-01

In 1968, Leon Gerber compared (1 + x)[superscript a] to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean-geometric mean inequality is presented.

Optoelectronic switch matrix as a look-up table for residue arithmetic.

PubMed

Macdonald, R I

1987-10-01

The use of optoelectronic matrix switches to perform look-up table functions in residue arithmetic processors is proposed. In this application, switchable detector arrays give the advantage of a greatly reduced requirement for optical sources by comparison with previous optoelectronic residue processors.

Instabilities caused by floating-point arithmetic quantization.

NASA Technical Reports Server (NTRS)

Phillips, C. L.

1972-01-01

It is shown that an otherwise stable digital control system can be made unstable by signal quantization when the controller operates on floating-point arithmetic. Sufficient conditions of instability are determined, and an example of loss of stability is treated when only one quantizer is operated.

Babies and Math: A Meta-Analysis of Infants' Simple Arithmetic Competence

ERIC Educational Resources Information Center

Christodoulou, Joan; Lac, Andrew; Moore, David S.

2017-01-01

Wynn's (1992) seminal research reported that infants looked longer at stimuli representing "incorrect" versus "correct" solutions of basic addition and subtraction problems and concluded that infants have innate arithmetical abilities. Since then, infancy researchers have attempted to replicate this effect, yielding mixed…

Phonology and arithmetic in the language-calculation network.

PubMed

Andin, Josefine; Fransson, Peter; Rönnberg, Jerker; Rudner, Mary

2015-04-01

Arithmetic and language processing involve similar neural networks, but the relative engagement remains unclear. In the present study we used fMRI to compare activation for phonological, multiplication and subtraction tasks, keeping the stimulus material constant, within a predefined language-calculation network including left inferior frontal gyrus and angular gyrus (AG) as well as superior parietal lobule and the intraparietal sulcus bilaterally. Results revealed a generally left lateralized activation pattern within the language-calculation network for phonology and a bilateral activation pattern for arithmetic, and suggested regional differences between tasks. In particular, we found a more prominent role for phonology than arithmetic in pars opercularis of the left inferior frontal gyrus but domain generality in pars triangularis. Parietal activation patterns demonstrated greater engagement of the visual and quantity systems for calculation than language. This set of findings supports the notion of a common, but regionally differentiated, language-calculation network. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Temporal Comparison Between NIRS and EEG Signals During a Mental Arithmetic Task Evaluated with Self-Organizing Maps.

PubMed

Oyama, Katsunori; Sakatani, Kaoru

2016-01-01

Simultaneous monitoring of brain activity with near-infrared spectroscopy and electroencephalography allows spatiotemporal reconstruction of the hemodynamic response regarding the concentration changes in oxyhemoglobin and deoxyhemoglobin that are associated with recorded brain activity such as cognitive functions. However, the accuracy of state estimation during mental arithmetic tasks is often different depending on the length of the segment for sampling of NIRS and EEG signals. This study compared the results of a self-organizing map and ANOVA, which were both used to assess the accuracy of state estimation. We conducted an experiment with a mental arithmetic task performed by 10 participants. The lengths of the segment in each time frame for observation of NIRS and EEG signals were compared with the 30-s, 1-min, and 2-min segment lengths. The optimal segment lengths were different for NIRS and EEG signals in the case of classification of feature vectors into the states of performing a mental arithmetic task and being at rest.

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

Arithmetic of five-part of leukocytes based on image process

NASA Astrophysics Data System (ADS)

Li, Yian; Wang, Guoyou; Liu, Jianguo

2007-12-01

This paper apply computer image processing and pattern recognizition methods to solve the problem of auto classification and counting of leukocytes (white blood cell) in peripheral blood. In this paper a new leukocyte arithmetic of five-part based on image process and pattern recognizition is presented, which relized auto classify of leukocyte. The first aim is detect the leukocytes . A major requirement of the whole system is to classify these leukocytes to 5 classes. This arithmetic bases on notability mechanism of eyes, process image by sequence, divides up leukocytes and pick up characters. Using the prior kwonledge of cells and image shape information, this arithmetic divides up the probable shape of Leukocyte first by a new method based on Chamfer and then gets the detail characters. It can reduce the mistake judge rate and the calculation greatly. It also has the learning fuction. This paper also presented a new measurement of karyon's shape which can provide more accurate information. This algorithm has great application value in clinical blood test .

Developing Asbestos Job Exposure Matrix Using Occupation and Industry Specific Exposure Data (1984-2008) in Republic of Korea.

PubMed

Choi, Sangjun; Kang, Dongmug; Park, Donguk; Lee, Hyunhee; Choi, Bongkyoo

2017-03-01

The goal of this study is to develop a general population job-exposure matrix (GPJEM) on asbestos to estimate occupational asbestos exposure levels in the Republic of Korea. Three Korean domestic quantitative exposure datasets collected from 1984 to 2008 were used to build the GPJEM. Exposure groups in collected data were reclassified based on the current Korean Standard Industrial Classification (9 th edition) and the Korean Standard Classification of Occupations code (6 th edition) that is in accordance to international standards. All of the exposure levels were expressed by weighted arithmetic mean (WAM) and minimum and maximum concentrations. Based on the established GPJEM, the 112 exposure groups could be reclassified into 86 industries and 74 occupations. In the 1980s, the highest exposure levels were estimated in "knitting and weaving machine operators" with a WAM concentration of 7.48 fibers/mL (f/mL); in the 1990s, "plastic products production machine operators" with 5.12 f/mL, and in the 2000s "detergents production machine operators" handling talc containing asbestos with 2.45 f/mL. Of the 112 exposure groups, 44 groups had higher WAM concentrations than the Korean occupational exposure limit of 0.1 f/mL. The newly constructed GPJEM which is generated from actual domestic quantitative exposure data could be useful in evaluating historical exposure levels to asbestos and could contribute to improved prediction of asbestos-related diseases among Koreans.

The influence of shyness on children's test performance.

PubMed

Crozier, W Ray; Hostettler, Kirsten

2003-09-01

Research has shown that shy children differ from their peers not only in their use of language in routine social encounters but also in formal assessments of their language development, including psychometric tests of vocabulary. There has been little examination of factors contributing to these individual differences. To investigate cognitive-competence and social anxiety interpretations of differences in children's performance on tests of vocabulary. To examine the performance of shy and less shy children under different conditions of test administration, individually with an examiner or among their peers within the familiar classroom setting. The sample consisted of 240 Year 5 pupils (122 male, 118 female) from 24 primary schools. Shy and less shy children, identified by teacher nomination and checklist ratings, completed vocabulary and mental arithmetic tests in one of three conditions, in a between-subjects design. The conditions varied individual and group administration, and oral and written responses. The conditions of test administration influenced the vocabulary test performance of shy children. They performed significantly more poorly than their peers in the two face-to-face conditions but not in the group test condition. A comparable trend for the arithmetic test was not statistically significant. Across the sample as a whole, shyness correlated significantly with test scores. Shyness does influence children's cognitive test performance and its impact is larger when children are tested face-to-face rather than in a more anonymous group setting. The results are of significance for theories of shyness and have implications for the assessment of schoolchildren.

Stress-evoked opioid release inhibits pain in major depressive disorder.

PubMed

Frew, Ashley K; Drummond, Peter D

2008-10-15

To determine whether stress-evoked release of endogenous opioids might account for hypoalgesia in major depressive disorder (MDD), the mu-opioid antagonist naltrexone (50mg) or placebo was administered double-blind to 24 participants with MDD and to 31 non-depressed controls. Eighty minutes later participants completed a painful foot cold pressor test and, after a 5-min interval, began a 25-min arithmetic task interspersed with painful electric shocks. Ten minutes later participants completed a second cold pressor test. Negative affect was greater in participants with MDD than in non-depressed controls throughout the experiment, and increased significantly in both groups during mental arithmetic. Before the math task, naltrexone unmasked direct linear relationships between severity of depression, negative affect while resting quietly, and cold-induced pain in participants with MDD. In contrast, facilitatory effects of naltrexone on cold- and shock-induced pain were greatest in controls with the lowest depression scores. Naltrexone strengthened the relationship between negative affect and shock-induced pain during the math task, particularly in the depressed group, and heightened anxiety in both groups toward the end of the task. Thus, mu-opioid activity apparently masked a positive association between negative affect and pain in the most distressed participants. These findings suggest that psychological distress inhibits pain via stress-evoked release of opioid peptides in severe cases of MDD. In addition, tonic endogenous opioid neurotransmission could inhibit depressive symptoms and pain in people with low depression scores.

File compression and encryption based on LLS and arithmetic coding

NASA Astrophysics Data System (ADS)

Yu, Changzhi; Li, Hengjian; Wang, Xiyu

2018-03-01

e propose a file compression model based on arithmetic coding. Firstly, the original symbols, to be encoded, are input to the encoder one by one, we produce a set of chaotic sequences by using the Logistic and sine chaos system(LLS), and the values of this chaotic sequences are randomly modified the Upper and lower limits of current symbols probability. In order to achieve the purpose of encryption, we modify the upper and lower limits of all character probabilities when encoding each symbols. Experimental results show that the proposed model can achieve the purpose of data encryption while achieving almost the same compression efficiency as the arithmetic coding.

Developing an effective multimedia in education for special education (MESE): An introduction to arithmetic

NASA Astrophysics Data System (ADS)

Munir, Kusnendar, Jajang; Rahmadhani

2016-02-01

This research aims to develop and test the effectiveness of multimedia in education for special education (MESE) of students with cognitive disabilities in introducing Arithmetic. Students with cognitive disabilities are those who have a level of intelligence under the normal ones. They think concretely and tend to have a very limited memory, switched concentration and forgot easily. The mastery of words is minimal, and also requires a long time to learn. These limitations will interfere in introduction learning to Arithmetic, with the material of numbers 1 to 10. The study resulted that MESE is worth to be used and enhanced the ability of the students.

The ALARM Experiment

ERIC Educational Resources Information Center

Gerhardt, Ira

2015-01-01

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

Updating Working Memory and Arithmetical Attainment in School

ERIC Educational Resources Information Center

Iuculano, Teresa; Moro, Raffaella; Butterworth, Brian

2011-01-01

Here we wished to determine how the sub-components of Working Memory (Phonological-Loop and Central Executive) influence children's arithmetical development. Specifically, we aimed at distinguishing between Working Memory inhibition and updating processes within the Central Executive, and the domain-specificity (words and numbers) of both…

Does Your Graphing Software Real-ly Work?

ERIC Educational Resources Information Center

Marchand, R. J.; McDevitt, T. J.; Bosse, Michael J.; Nandakumar, N. R.

2007-01-01

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…

Attentional bias induced by solving simple and complex addition and subtraction problems.

PubMed

Masson, Nicolas; Pesenti, Mauro

2014-01-01

The processing of numbers has been shown to induce shifts of spatial attention in simple probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. Recently, the investigation of this spatial-numerical association has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems may induce attentional displacements (to the right and to the left, respectively) along a mental number line onto which the magnitude of the numbers would range from left to right, from small to large numbers. Here we investigated such attentional shifts using a target detection task primed by arithmetic problems in healthy participants. The constituents of the addition and subtraction problems (first operand; operator; second operand) were flashed sequentially in the centre of a screen, then followed by a target on the left or the right side of the screen, which the participants had to detect. This paradigm was employed with arithmetic facts (Experiment 1) and with more complex arithmetic problems (Experiment 2) in order to assess the effects of the operation, the magnitude of the operands, the magnitude of the results, and the presence or absence of a requirement for the participants to carry or borrow numbers. The results showed that arithmetic operations induce some spatial shifts of attention, possibly through a semantic link between the operation and space.

Molecular characterization of accessions of Cratylia argentea (Camaratuba) using ISSR markers.

PubMed

Luz, G A; Gomes, S O; Araujo Neto, R B; Nascimento, M S C B; Lima, P S C

2015-11-27

Cratylia argentea (Desv.) Kuntze (Fabaceae) is a drought-tolerant, perennial legume found primarily in Brazil, Bolivia, and Peru. The shrub is well adapted to acid soils and exhibits high productivity and nutritional value, characteristics that would favor its use as a dry season animal forage supplement in semiarid regions. In plant improvement programs, the production of elite hybrids with superior traits is generally achieved by crossing parents that exhibit the highest level of genetic divergence. Therefore, the aim of the present study was to assess genetic diversity among 13 accessions of C. argentea from the same population maintained in the active germplasm bank of Embrapa Meio-Norte using inter-simple sequence repeat (ISSR) markers. Genetic similarities between C. argentea accessions were estimated from Jaccard coefficients, and a dendrogram was constructed using the unweighted pair group method with arithmetic average (UPGMA). The set of 15 primers selected for ISSR analysis generated a total of 313 loci of which 79.23% were polymorphic. The mean number of bands per primer was 20.87, and the amplicons ranged from 280 to 3000 bp in size. Primers UBC834 and UBC827 generated the largest number of polymorphic loci and exhibited 90.91 and 100% polymorphism, respectively. The coefficients of genetic similarity among accessions varied between 0.49 and 0.73. UPGMA cluster analysis allowed the identification of four genotypic groups and demonstrated the existence of considerable variability within the collection. Potential progenitors were selected that would offer good possibilities of obtaining unusual and favorable combinations of genes in a plant breeding program.

Characterization of Aspergillus flavus strains from Brazilian Brazil nuts and cashew by RAPD and ribosomal DNA analysis.

PubMed

Midorikawa, G E O; Pinheiro, M R R; Vidigal, B S; Arruda, M C; Costa, F F; Pappas, G J; Ribeiro, S G; Freire, F; Miller, R N G

2008-07-01

The aim of this study was to determine the genetic variability in Aspergillus flavus populations from Brazil nut and cashew and develop a polymerase chain reaction (PCR) detection method. Chomatography analysis of 48 isolates identified 36 as aflatoxigenic (75%). One hundred and forty-one DNA bands were generated with 11 random amplified polymorphic DNA (RAPD) primers and analysed via unweighted pair group analysis, using arithmetic means (UPGMA). Isolates grouped according to host, with differentiation of those from A. occidentale also according to geographical origin. Aspergillus flavus-specific PCR primers ASPITSF2 and ASPITSR3 were designed from ribosomal DNA internal transcribed spacers (ITS 1 and 2), and an internal amplification control was developed, to prevent false negative results. Specificity to only A. flavus was confirmed against DNA from additional aspergilli and other fungi. RAPD-based characterization differentiated isolates according to plant host. The PCR primer pair developed showed specificity to A. flavus, with a detection limit of 10 fg. Genetic variability observed in A. flavus isolates from two Brazilian agroecosystems suggested reproductive isolation. The PCR detection method developed for A. flavus represents progress towards multiplex PCR detection of aflatoxigenic and nonaflatoxigenic strains in Hazard Analysis Critical Control Point systems.

Isolation and characterization of microsatellite markers for Dendranthema morifolium (Asteraceae) using next-generation sequencing.

PubMed

Yuan, W-J; Ye, S; Du, L-H; Li, S-M; Miao, X; Shang, F-D

2016-10-05

Dendranthema morifolium (Asteraceae) is a perennial herbaceous plant native to China. A long history of artificial crossings may have resulted in complex genetic background and decreased genetic diversity. To protect the genetic diversity of D. morifolium and enabling breeding of new D. morifolium cultivars, we developed a set of molecular markers. We used pyrosequencing of an enriched microsatellite library by Roche 454 FLX+ platform, to isolate D. morifolium simple sequence repeats (SSRs). A total of 32,863 raw reads containing 2251 SSRs were obtained. To test the effectiveness of these SSR markers, we designed primers by randomly selecting 100 novel SSRs, and amplified them across 60 cultivars representing five different petal shape groups. Sixteen SSRs were polymorphic with the number of alleles ranging from 6 to 19, and their expected and observed heterozygosities ranging from 0.477 to 0.848, and 0.250 to 0.804, respectively. The polymorphism information content ranged from 0.459 to 0.854 and the inbreeding coefficient ranged from -0.119 to 0.759. An unweighted pair-group method arithmetic average analysis was performed to survey the phylogenetic relationships of these 60 cultivars and five clusters were identified. These markers can be used for investigating genetic relationships and identifying elite alleles through linkage and association analyses.

Crystallographic interpretation of Galois symmetries for magnetic pentagonal ring

NASA Astrophysics Data System (ADS)

Milewski, J.; Lulek, T.; Łabuz, M.

2017-03-01

Galois symmetry of exact Bethe Ansatz eigenstates for the magnetic pentagonal ring within the XXX model are investigated by a comparison with crystallographic constructions of space groups. It follows that the arithmetic symmetry of Bethe parameters for the interior of the Brillouin zone admits crystallographic interpretation, in terms of the periodic square Z2 ×Z2 , that is the two-dimensional crystal lattice with Born-Karman period two in both directions.

Convergence to equilibrium under a random Hamiltonian.

PubMed

Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek

2012-09-01

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

Convergence to equilibrium under a random Hamiltonian

NASA Astrophysics Data System (ADS)

Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek

2012-09-01

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.

Schema Knowledge for Solving Arithmetic Story Problems: Some Affective Components.

ERIC Educational Resources Information Center

Marshall, Sandra P.

This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…

The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems

ERIC Educational Resources Information Center

Xin, Ziqiang; Lin, Chongde; Zhang, Li; Yan, Rong

2007-01-01

Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate "real-world" knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure…

Counting and RAN: Predictors of Arithmetic Calculation and Reading Fluency

ERIC Educational Resources Information Center

Koponen, Tuire; Salmi, Paula; Eklund, Kenneth; Aro, Tuija

2013-01-01

This study examined whether counting and rapid automatized naming (RAN) could operate as significant predictors of both later arithmetic calculation and reading fluency. The authors also took an important step to clarify the cognitive mechanisms underlying these predictive relationships by controlling for the effect of phonological awareness and…

The Development of Arithmetical Abilities

ERIC Educational Resources Information Center

Butterworth, Brian

2005-01-01

Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…

Arithmetic Facts Storage Deficit: The Hypersensitivity-to-Interference in Memory Hypothesis

ERIC Educational Resources Information Center

De Visscher, Alice; Noël, Marie-Pascale

2014-01-01

Dyscalculia, or mathematics learning disorders, is currently known to be heterogeneous (Wilson & Dehaene, 2007). While various profiles of dyscalculia coexist, a general and persistent hallmark of this math learning disability is the difficulty in memorizing arithmetic facts (Geary, Hoard & Hamson, 1999; Jordan & Montani, 1997; Slade…

Arithmetic Word-Problem-Solving in Huntington's Disease

ERIC Educational Resources Information Center

Allain, P.; Verny, C.; Aubin, G.; Pinon, K.; Bonneau, D.; Dubas, F.; Gall, D.L.

2005-01-01

The purpose of this study was to examine executive functioning in patients with Huntington's disease using an arithmetic word-problem-solving task including eight solvable problems of increasing complexity and four aberrant problems. Ten patients with Huntington's disease and 12 normal control subjects matched by age and education were tested.…

Numerical Processing Efficiency Improved in Experienced Mental Abacus Children

ERIC Educational Resources Information Center

Wang, Yunqi; Geng, Fengji; Hu, Yuzheng; Du, Fenglei; Chen, Feiyan

2013-01-01

Experienced mental abacus (MA) users are able to perform mental arithmetic calculations with unusual speed and accuracy. However, it remains unclear whether their extraordinary gains in mental arithmetic ability are accompanied by an improvement in numerical processing efficiency. To address this question, the present study, using a numerical…

40 CFR 133.101 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... arithmetic mean of pollutant parameter values for samples collected in a period of 7 consecutive days. (b) 30-day average. The arithmetic mean of pollutant parameter values of samples collected in a period of 30... percentile value for the 30-day average effluent quality achieved by a treatment works in a period of at...

Retrieval-Induced Forgetting of Arithmetic Facts

ERIC Educational Resources Information Center

Campbell, Jamie I. D.; Thompson, Valerie A.

2012-01-01

Retrieval-induced forgetting (RIF) is a widely studied phenomenon of human memory, but RIF of arithmetic facts remains relatively unexplored. In 2 experiments, we investigated RIF of simple addition facts (2 + 3 = 5) from practice of their multiplication counterparts (2 x 3 = 6). In both experiments, robust RIF expressed in response times occurred…

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

ERIC Educational Resources Information Center

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

The Codevelopment of Children's Fraction Arithmetic Skill and Fraction Magnitude Understanding

ERIC Educational Resources Information Center

Bailey, Drew H.; Hansen, Nicole; Jordan, Nancy C.

2017-01-01

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

Mathematics: Essential to Marketing. Student's Manual and Teacher's Guide.

ERIC Educational Resources Information Center

Helton, Betty G.; Griffin, Jennie

This document contains both a student's manual and a teacher's guide for high school mathematics essential to marketing. The student's manual contains 34 assignments within the following 11 units: (1) arithmetic fundamentals; (2) application of arithmetic fundamentals; (3) cashiering; (4) inventory procedures; (5) invoices; (6) computing employee…

Basic Mathematics Operations--A Math Practice Booklet.

ERIC Educational Resources Information Center

Herr, Nicholas K.

Intended for use in vocational high schools, the workbook is designed to help the student understand and develop skill in performing the four basic arithmetical operations: addition, subtraction, multiplication, and division. Also stressed is the correct reading and writing of numbers. The booklet consists of explanatory text, arithmetic problems,…

Teacher Actions to Facilitate Early Algebraic Reasoning

ERIC Educational Resources Information Center

Hunter, Jodie

2015-01-01

In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

SMP That Help Foster Algebraic Thinking

ERIC Educational Resources Information Center

Billings, Esther M. H.

2017-01-01

Arithmetic is a major mathematical focus in elementary school curriculum, and researchers such as Mason (2008) claim that "algebraic thinking is required in order to make sense of arithmetic" (p. 58). When adding, subtracting, multiplying, and dividing, learners must rely on a small set of fundamental properties also important for the…

Positive and Negative Consequences in Contingency Contracts: Their Relative Effectiveness on Arithmetic Performance.

ERIC Educational Resources Information Center

Kidd, Teresa A.; Saudargas, Richard A.

1988-01-01

The study with two elementary students who had low levels of completion and accuracy on daily arithmetic assignments found that a negative consequence was not necessary and that use of a positive component alone was sufficient to maintain high levels of completion and accuracy. (Author/DB)

Idempotents a la mod

ERIC Educational Resources Information Center

Sibley, Thomas Q.

2012-01-01

An idempotent satisfies the equation x[superscript 2] = x. In ordinary arithmetic, this is so easy to solve it's boring. We delight the mathematical palette here, topping idempotents off with modular arithmetic and a series of exercises determining for which n there are more than two idempotents (mod n) and exactly how many there are.

Early Numeracy in Cerebral Palsy: Review and Future Research

ERIC Educational Resources Information Center

van Rooijen, Maaike; Verhoeven, Ludo; Steenbergen, Bert

2011-01-01

Children with cerebral palsy (CP) often have problems with arithmetic, but the development of numerical abilities in these children has received only minor attention. In comparison, detailed accounts have been written on the arithmetic abilities of typically developing children, but a theoretical framework is still lacking. A promising perspective…

Remedial Instruction to Enhance Mathematical Ability of Dyscalculics

ERIC Educational Resources Information Center

Kumar, S. Praveen; Raja, B. William Dharma

2012-01-01

The ability to do arithmetic calculations is essential to school-based learning and skill development in an information rich society. Arithmetic is a basic academic skill that is needed for learning which includes the skills such as counting, calculating, reasoning etc. that are used for performing mathematical calculations. Unfortunately, many…

Assessment of genetic diversity in lettuce (Lactuca sativa L.) germplasm using RAPD markers.

PubMed

Sharma, Shubhangi; Kumar, Pankaj; Gambhir, Geetika; Kumar, Ramesh; Srivastava, D K

2018-01-01

The importance of germplasm characterization is an important link between the conservation and utilization of plant genetic resources in various breeding programmes. In the present study, genetic variability and relationships among 25 Lactuca sativa L. genotypes were tested using random amplified polymorphic DNA (RAPD) molecular markers. A total of 45 random decamer oligonucleotide primers were examined to generate RAPD profiles, out of these reproducible patterns were obtained with 22 primers. A total of 87 amplicon were obtained, out of which all were polymorphic and 7 were unique bands. The level of polymorphism across genotypes was 100% as revealed by RAPD. Genetic similarity matrix, based on Jaccard's coefficients ranged from 13.7 to 84.10% indicating a wide genetic base. Dendrogram was constructed by unweighted pair group method with arithmetic averages method. RAPD technology could be useful for identification of different accessions as well as assessing the genetic similarity among different genotypes of lettuce. The study reveals the limited genetic base and the needs to diversify using new sources from the germplasm.

High-order computer-assisted estimates of topological entropy

NASA Astrophysics Data System (ADS)

Grote, Johannes

The concept of Taylor Models is introduced, which offers highly accurate C0-estimates for the enclosures of functional dependencies, combining high-order Taylor polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified interval arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly nonlinear dynamical systems. A method to obtain sharp rigorous enclosures of Poincare maps for certain types of flows and surfaces is developed and numerical examples are presented. Differential algebraic techniques allow the efficient and accurate computation of polynomial approximations for invariant curves of certain planar maps around hyperbolic fixed points. Subsequently we introduce a procedure to extend these polynomial curves to verified Taylor Model enclosures of local invariant manifolds with C0-errors of size 10-10--10 -14, and proceed to generate the global invariant manifold tangle up to comparable accuracy through iteration in Taylor Model arithmetic. Knowledge of the global manifold structure up to finite iterations of the local manifold pieces enables us to find all homoclinic and heteroclinic intersections in the generated manifold tangle. Combined with the mapping properties of the homoclinic points and their ordering we are able to construct a subshift of finite type as a topological factor of the original planar system to obtain rigorous lower bounds for its topological entropy. This construction is fully automatic and yields homoclinic tangles with several hundred homoclinic points. As an example rigorous lower bounds for the topological entropy of the Henon map are computed, which to the best knowledge of the authors yield the largest such estimates published so far.

The Implications of 3D Thermal Structure on 1D Atmospheric Retrieval

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blecic, Jasmina; Dobbs-Dixon, Ian; Greene, Thomas, E-mail: jasmina@nyu.edu

Using the atmospheric structure from a 3D global radiation-hydrodynamic simulation of HD 189733b and the open-source Bayesian Atmospheric Radiative Transfer (BART) code, we investigate the difference between the secondary-eclipse temperature structure produced with a 3D simulation and the best-fit 1D retrieved model. Synthetic data are generated by integrating the 3D models over the Spitzer , the Hubble Space Telescope ( HST ), and the James Web Space Telescope ( JWST ) bandpasses, covering the wavelength range between 1 and 11 μ m where most spectroscopically active species have pronounced features. Using the data from different observing instruments, we present detailedmore » comparisons between the temperature–pressure profiles recovered by BART and those from the 3D simulations. We calculate several averages of the 3D thermal structure and explore which particular thermal profile matches the retrieved temperature structure. We implement two temperature parameterizations that are commonly used in retrieval to investigate different thermal profile shapes. To assess which part of the thermal structure is best constrained by the data, we generate contribution functions for our theoretical model and each of our retrieved models. Our conclusions are strongly affected by the spectral resolution of the instruments included, their wavelength coverage, and the number of data points combined. We also see some limitations in each of the temperature parametrizations, as they are not able to fully match the complex curvatures that are usually produced in hydrodynamic simulations. The results show that our 1D retrieval is recovering a temperature and pressure profile that most closely matches the arithmetic average of the 3D thermal structure. When we use a higher resolution, more data points, and a parametrized temperature profile that allows more flexibility in the middle part of the atmosphere, we find a better match between the retrieved temperature and pressure profile and the arithmetic average. The Spitzer and HST simulated observations sample deep parts of the planetary atmosphere and provide fewer constraints on the temperature and pressure profile, while the JWST observations sample the middle part of the atmosphere, providing a good match with the middle and most complex part of the arithmetic average of the 3D temperature structure.« less

Cardiac Repolarization Instability during Psychological Stress in Patients with Ventricular Arrhythmias

PubMed Central

Abisse, Saddam S.; Lampert, Rachel; Burg, Mattew; Soufer, Robert; Shusterman, Vladimir

2011-01-01

Introduction Changes in the autonomic nervous system activity (ANS) are a major trigger of life-threatening ventricular tachyarrhythmias (VTA). Mental arithmetic, a condition administered in a laboratory setting, can provide insight into the ANS effects on cardiac physiology. We examined the responses of cardiac repolarization to laboratory-induced psychological stressors in patients with implantable cardioverter defibrillators (ICDs) with the objective of identifying the indices that differentiate patients with and without subsequent VTA in follow-up. Methods Continuous ECG signals were recorded using 3 standard bipolar (Holter) leads in 56 patients (age: 63.6±11.9, female: 12%, LVEF: 32.3±11) with ICDs during mental arithmetic. The patients were separated into those with subsequent VTA during 3–4 years of follow-up (Group 1: N=9 pts) and those without VTA (Group 2: N=47 pts). Changes in repolarization (QT-interval, mean T-wave amplitude (Tamp), and T-wave area (Tarea) were analyzed during 5min of baseline, stress and recovery. The temporal instability of Tamp and Tarea was examined using the range (Δ) and variance (σ2) of beat-to-beat variations of the corresponding parameters. Results There were no significant differences in HR between the two groups at baseline (61 vs. 63 bpm, p=0.97), during stress (64 vs. 65 bpm, p=0.40), and recovery (62 vs. 61 bpm, p= 0.88). However, during mental stress and post-stress recovery ΔTamp was almost 2-fold greater in Group 1 compared with Group 2 (111 (57–203)) vs. 68 (44–94) μV p=0.04, respectively). Changes in QT-intervals were also greater in Group 1 compared with Group 2 (p=0.02). Conclusion Among patients with ICDs, changes of T-wave amplitude after psychological stress were greater in those with subsequent arrhythmic events. This might signal proarrhythmic repolarization response and help identify patients who would benefit the most from ICD implantation and proactive management. PMID:21920534

Trinary arithmetic and logic unit (TALU) using savart plate and spatial light modulator (SLM) suitable for optical computation in multivalued logic

NASA Astrophysics Data System (ADS)

Ghosh, Amal K.; Bhattacharya, Animesh; Raul, Moumita; Basuray, Amitabha

2012-07-01

Arithmetic logic unit (ALU) is the most important unit in any computing system. Optical computing is becoming popular day-by-day because of its ultrahigh processing speed and huge data handling capability. Obviously for the fast processing we need the optical TALU compatible with the multivalued logic. In this regard we are communicating the trinary arithmetic and logic unit (TALU) in modified trinary number (MTN) system, which is suitable for the optical computation and other applications in multivalued logic system. Here the savart plate and spatial light modulator (SLM) based optoelectronic circuits have been used to exploit the optical tree architecture (OTA) in optical interconnection network.

Genetic study of kelp ``901'' strain

NASA Astrophysics Data System (ADS)

Xia, Peng; Wang, Xiuliang; Li, Xiaojie; Zhao, Yushan; Yao, Lin; Duan, Delin

2005-06-01

Based on DNA extraction and optimization of random amplified reaction (RAPD) to the gametophytes and sporophytes of Kelp “901” strain, genetic study on variation was conducted to its parents and offsprings of F6, F7, F8, and F9 generation. RAPD results have shown that among 30 selected primers for gametophytes, 297 loci ranging from 200 to 3 000 bp were obtained in the average of 9.9 loci for each primer. This indicated a high polymorphic rate with RAPD detection. UPGMA (unweighted pair-group method arithmetic average) analysis showed that each male and female gametophyte of a generation could be clustered into one pair separately. The genetic distances of the Kelp 901 generation were 0.3212 0.4767, and the maximum was between F7 and F8 (0.4767). Identity analysis showed that F6 generation was more close to the female parent (0.6593), and F7 generation was more close to the male parent (0.578 8). To the sporophytes study in 24 selected primers for RAPD amplification, 191 loci ranging from 230 2800 bp were obtained, in the average to each primer of 8.0 loci. The heterozygosity to six populations were male parent (0.2239), female parent (0.1072), F6 (0.2164), F7(0.2286), F8(0.2296) and F9(0.3172). The nearest genetic distance was 0.083 5(F8, F9). Total heterozygosity (HT) of F6, F7, F8 and F9 generations was 0.3186, the average heterozygosity (HS) for F6, F7, F8 and F9 generations was 0.2480, and deduced coefficient of population differentiation (Gst) was 22.2%. Six sequence characterized amplified regions (SCAR) were preliminary screened through RAPD analysis. It needed to be verified in detail as they are significant for molecular marker assistance in breeding and selecting Laminaria.

Developing an Energy Policy for the United States

ERIC Educational Resources Information Center

Keefe, Pat

2014-01-01

Al Bartlett's video "Arithmetic, Population, and Energy" spells out many of the complex issues related to energy use in our society. Bartlett makes the point that basic arithmetic is the fundamental obstacle preventing us from being able to grasp the relationships between energy consumption, population, and lifestyles. In an earlier…

Computer-Assisted Instruction: Stanford's 1965-66 Arithmetic Program.

ERIC Educational Resources Information Center

Suppes, Patrick; And Others

A review of the possibilities and challenges of computer-assisted instruction (CAI), and a brief history of CAI projects at Stanford serve to give the reader the context of the particular program described and analyzed in this book. The 1965-66 arithmetic drill-and-practice program is described, summarizing the curriculum and project operation. An…

Sex Differences in Arithmetical Performance Scores: Central Tendency and Variability

ERIC Educational Resources Information Center

Martens, R.; Hurks, P. P. M.; Meijs, C.; Wassenberg, R.; Jolles, J.

2011-01-01

The present study aimed to analyze sex differences in arithmetical performance in a large-scale sample of 390 children (193 boys) frequenting grades 1-9. Past research in this field has focused primarily on average performance, implicitly assuming homogeneity of variance, for which support is scarce. This article examined sex differences in…

Language, Arithmetic Word Problems, and Deaf Students: Linguistic Strategies Used To Solve Tasks.

ERIC Educational Resources Information Center

Zevenbergen, Robyn; Hyde, Merv; Power, Des

2001-01-01

Examines the performance of deaf and hearing-impaired students in Queensland, Australia when solving arithmetic word problems. Subjects' solutions of word problems confirmed trends for learning students but their performance was delayed in comparison. Confirms other studies in which deaf and hearing-impaired students are delayed in their language…

Arithmetic Practice Can Be Modified to Promote Understanding of Mathematical Equivalence

ERIC Educational Resources Information Center

McNeil, Nicole M.; Fyfe, Emily R.; Dunwiddie, April E.

2015-01-01

This experiment tested if a modified version of arithmetic practice facilitates understanding of math equivalence. Children within 2nd-grade classrooms (N = 166) were randomly assigned to practice single-digit addition facts using 1 of 2 workbooks. In the control workbook, problems were presented in the traditional "operations = answer"…

Developmental Dissociation in the Neural Responses to Simple Multiplication and Subtraction Problems

ERIC Educational Resources Information Center

Prado, Jérôme; Mutreja, Rachna; Booth, James R.

2014-01-01

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

The Teachers' Views on Soroban Abacus Training

ERIC Educational Resources Information Center

Altiparmak, Kemal

2016-01-01

Soroban abacus training is called as mental arithmetic training in our country. It is known for mental arithmetic to increase the ability of four mode operations. Besides this, how is the situation for the students which are having Soroban abacus training in the terms of problem solving abilities, creativity, development of concepts, attraction…

The Role of the Updating Function in Solving Arithmetic Word Problems

ERIC Educational Resources Information Center

Mori, Kanetaka; Okamoto, Masahiko

2017-01-01

We investigated how the updating function supports the integration process in solving arithmetic word problems. In Experiment 1, we measured reading time, that is, translation and integration times, when undergraduate and graduate students (n = 78) were asked to solve 2 types of problems: those containing only necessary information and those…

Why Is Learning Fraction and Decimal Arithmetic so Difficult?

ERIC Educational Resources Information Center

Lortie-Forgues, Hugues; Tian, Jing; Siegler, Robert S.

2015-01-01

Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…

An Experimental Comparison of an Intrinsically Programed Text and a Narrative Text.

ERIC Educational Resources Information Center

Senter, R. J.; And Others

The study compared three methods of instruction in binary and octal arithmetic, i.e., (1) Norman Crowder's branched programed text, "The Arithmetic of Computers," (2) another version of this text modified so that subjects could not see the instructional material while answering "branching" questions, and (3) a narrative text…

Measuring Middle Grades Teachers' Understanding of Rational Numbers with the Mixture Rasch Model

ERIC Educational Resources Information Center

Izsak, Andrew; Orrill, Chandra Hawley; Cohen, Allan S.; Brown, Rachael Eriksen

2010-01-01

We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to…

Sign Language for K-8 Mathematics by 3D Interactive Animation

ERIC Educational Resources Information Center

Adamo-Villani, Nicoletta; Doublestein, John; Martin, Zachary

2005-01-01

We present a new highly interactive computer animation tool to increase the mathematical skills of deaf children. We aim at increasing the effectiveness of (hearing) parents in teaching arithmetic to their deaf children, and the opportunity of deaf children to learn arithmetic via interactive media. Using state-of-the-art computer animation…

Using Microcomputers To Help Learning Disabled Student with Arithmetic Difficulties.

ERIC Educational Resources Information Center

Brevil, Margarette

The use of microcomputers to help the learning disabled increase their arithmetic skills is examined. The microcomputer should be used to aid the learning disabled student to practice the concepts taught by the teacher. Computer-aided instruction such as drill and practice may help the learning disabled student because it gives immediate feedback…

Advancing Fourth-Grade Students' Understanding of Arithmetic Properties with Instruction That Promotes Mathematical Argumentation

ERIC Educational Resources Information Center

Rumsey, Chepina Witkowski

2012-01-01

The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…

On Arithmetic-Geometric-Mean Polynomials

ERIC Educational Resources Information Center

Griffiths, Martin; MacHale, Des

2017-01-01

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

Arithmetical Strategies of a Student with Down Syndrome

ERIC Educational Resources Information Center

Rumiati, Rumi

2014-01-01

Kayla was a 15 years old girl with Down syndrome attending a special education school in Indonesia. A modification of Wright et al.'s (2006) approach to assessment documented her number knowledge and arithmetical strategies. This paper discusses the assessment process and the results focusing on her ability to solve number problems. Results show…

Individual Differences in Mathematical Competence Modulate Brain Responses to Arithmetic Errors: An fMRI Study

ERIC Educational Resources Information Center

Ansari, Daniel; Grabner, Roland H.; Koschutnig, Karl; Reishofer, Gernot; Ebner, Franz

2011-01-01

Data from both neuropsychological and neuroimaging studies have implicated the left inferior parietal cortex in calculation. Comparatively less attention has been paid to the neural responses associated with the commission of calculation errors and how the processing of arithmetic errors is modulated by individual differences in mathematical…

Effects of Numerical Surface Form in Arithmetic Word Problems

ERIC Educational Resources Information Center

Orrantia, Josetxu; Múñez, David; San Romualdo, Sara; Verschaffel, Lieven

2015-01-01

Adults' simple arithmetic performance is more efficient when operands are presented in Arabic digit (3 + 5) than in number word (three + five) formats. An explanation provided is that visual familiarity with digits is higher respect to number words. However, most studies have been limited to single-digit addition and multiplication problems. In…

Assessing Adult Learner's Numeracy as Related to Gender and Performance in Arithmetic

ERIC Educational Resources Information Center

Awofala, Adeneye O. A.; Anyikwa, Blessing E.

2014-01-01

The study investigated adult learner numeracy as related to gender and performance in arithmetic among 32 Nigerian adult learners from one government accredited adult literacy centre in Lagos State using the quantitative research method within the blueprint of descriptive survey design. Data collected were analysed using the descriptive statistics…

Do Birth Order, Family Size and Gender Affect Arithmetic Achievement in Elementary School?

ERIC Educational Resources Information Center

Desoete, Annemie

2008-01-01

Introduction: For decades birth order and gender differences have attracted research attention. Method: Birth order, family size and gender, and the relationship with arithmetic achievement is studied among 1152 elementary school children (540 girls, 612 boys) in Flanders. Children were matched on socioeconomic status of the parents and…

Hard Lessons: Why Rational Number Arithmetic Is so Difficult for so Many People

ERIC Educational Resources Information Center

Siegler, Robert S.; Lortie-Forgues, Hugues

2017-01-01

Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem, because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of…

Early Integration of Tutorial Support in Beginning Algebra

ERIC Educational Resources Information Center

Copus, Colleen; McKinney, Betsy

2016-01-01

Anecdotal observations reveal that most students with strong arithmetic skills will succeed in the Beginning Algebra course even if they have no previous experience with algebra. In trying to quantify this with an initial teacher-created survey of arithmetic skills, it was observed, for three consecutive semesters, that students who scored in the…

Informal Numeracy Skills: The Structure and Relations among Numbering, Relations, and Arithmetic Operations in Preschool

ERIC Educational Resources Information Center

Purpura, David J.; Lonigan, Christopher J.

2013-01-01

Validating the structure of informal numeracy skills is critical to understanding the developmental trajectories of mathematics skills at early ages; however, little research has been devoted to construct evaluation of the Numbering, Relations, and Arithmetic Operations domains. This study was designed to address this knowledge gap by examining…

Assessment of Psychological Readiness Situation of Students Starting to Primary School

ERIC Educational Resources Information Center

Halmatov, Medera

2018-01-01

There are important responsibilities expected from primary school students. The most important of these are the learning of reading, writing and arithmetic. There is a "psychological readiness" aspect besides reading, writing and arithmetic in order to be ready for the school. In this study, among the first-grade students, those who were…

Secret Codes, Remainder Arithmetic, and Matrices.

ERIC Educational Resources Information Center

Peck, Lyman C.

This pamphlet is designed for use as enrichment material for able junior and senior high school students who are interested in mathematics. No more than a clear understanding of basic arithmetic is expected. Students are introduced to ideas from number theory and modern algebra by learning mathematical ways of coding and decoding secret messages.…

The effects of anxious responding on mental arithmetic and lexical decision task performance.

PubMed

Hopko, Derek R; McNeil, Daniel W; Lejuez, C W; Ashcraft, Mark H; Eifert, Georg H; Riel, Jim

2003-01-01

Anxiety-related responding and skill deficits historically are associated with performance-based problems such as mathematics anxiety, yet the relative contribution of these variables to substandard performance remains poorly understood. Utilizing a 7% carbon dioxide (CO2) gas to induce anxiety, the present study examined the impact of anxious responding on two performance tasks, mental arithmetic and lexical decision. Independent variables included math anxiety group, gender, and gas condition. Dependent variables included task performance and physiological and self-report indices of anxiety. A total of 64 university undergraduate students participated. Physiological and verbal-report measures of anxiety supported the utility of 7% carbon dioxide-enriched air as an anxiety-inducing stimulus. Behavioral disruption on performance tasks, however, did not differ as a function of carbon dioxide inhalation. Performance did differ as a function of math anxiety. High math anxious individuals generally exhibited higher error rates on mathematical tasks, particularly on tasks designed to measure advanced math skill and those requiring working memory resources. These findings are discussed with reference to processing efficiency theory, discordance among anxiety response systems, and the intricacies associated with skill measurement.

Populations of Erythrina velutina Willd. at risk of extinction.

PubMed

Melo, M F V; Gonçalves, L O; Rabbani, A R C; Álvares-Carvalho, S V; Pinheiro, J B; Zucchi, M I; Silva-Mann, R

2015-08-28

The goal of this study was to characterize the structure of two natural populations of the coral tree using RAPD and ISSR markers. The study evaluated all individuals in two different areas in the northeastern region of Brazil: the first was in the riparian area, 10 km x 100 m along the edge of the lower São Francisco River, and the second was in the municipality of Pinhão, in a semiarid region between the municipalities of Neópolis and Santana do São Francisco. We used all the coral trees present in those two areas (37 individuals). The results of the RAPD and ISSR markers were highly congruent, supporting the reliability of the techniques used. Similarity was estimated using the Jaccard arithmetic complement index. A dendrogram was constructed using the unweighted pair group method with arithmetic mean cluster algorithm, and the robustness of the data was bootstrapped with 5000 replicates. A principal coordinate analysis was performed on the basis of Jaccard coefficients. The total genetic variation observed was 21%, corresponding to the variation between the populations, and 79% of the variation was observed within the populations.

Cognitive and numerosity predictors of mathematical skills in middle school.

PubMed

Cirino, Paul T; Tolar, Tammy D; Fuchs, Lynn S; Huston-Warren, Emily

2016-05-01

There is a strong research base on the underlying concomitants of early developing math skills. Fewer studies have focused on later developing skills. Here, we focused on direct and indirect contributions of cognitive measures (e.g., language, spatial skills, working memory) and numerosity measures, as well as arithmetic proficiency, on key outcomes of fraction performance, proportional reasoning, and broad mathematics achievement at sixth grade (N=162) via path analysis. We expected a hierarchy of skill development, with predominantly indirect effects of cognitive factors via number and arithmetic. Results controlling for age showed that the combination of cognitive, number, and arithmetic variables cumulatively accounted for 38% to 44% of the variance in fractions, proportional reasoning, and broad mathematics. There was consistency across outcomes, with more proximal skills providing direct effects and with the effects of cognitive skills being mediated by number and by more proximal skills. Results support a hierarchical progression from domain-general cognitive processes through numerosity and arithmetic skills to proportional reasoning to broad mathematics achievement. Copyright © 2016 Elsevier Inc. All rights reserved.

Developmental dyscalculia.

PubMed

Shalev, Ruth S

2004-10-01

Developmental dyscalculia is a specific learning disability affecting the normal acquisition of arithmetic skills. Genetic, neurobiologic, and epidemiologic evidence indicates that dyscalculia, like other learning disabilities, is a brain-based disorder. However, poor teaching and environmental deprivation have also been implicated in its etiology. Because the neural network of both hemispheres comprises the substrate of normal arithmetic skills, dyscalculia can result from dysfunction of either hemisphere, although the left parietotemporal area is of particular significance. The prevalence of developmental dyscalculia is 5 to 6% in the school-aged population and is as common in girls as in boys. Dyscalculia can occur as a consequence of prematurity and low birthweight and is frequently encountered in a variety of neurologic disorders, such as attention-deficit hyperactivity disorder (ADHD), developmental language disorder, epilepsy, and fragile X syndrome. Developmental dyscalculia has proven to be a persisting learning disability, at least for the short term, in about half of affected preteen pupils. Educational interventions for dyscalculia range from rote learning of arithmetic facts to developing strategies for solving arithmetic exercises. The long-term prognosis of dyscalculia and the role of remediation in its outcome are yet to be determined.

The calculating brain: an fMRI study.

PubMed

Rickard, T C; Romero, S G; Basso, G; Wharton, C; Flitman, S; Grafman, J

2000-01-01

To explore brain areas involved in basic numerical computation, functional magnetic imaging (fMRI) scanning was performed on college students during performance of three tasks; simple arithmetic, numerical magnitude judgment, and a perceptual-motor control task. For the arithmetic relative to the other tasks, results for all eight subjects revealed bilateral activation in Brodmann's area 44, in dorsolateral prefrontal cortex (areas 9 and 10), in inferior and superior parietal areas, and in lingual and fusiform gyri. Activation was stronger on the left for all subjects, but only at Brodmann's area 44 and the parietal cortices. No activation was observed in the arithmetic task in several other areas previously implicated for arithmetic, including the angular and supramarginal gyri and the basal ganglia. In fact, angular and supramarginal gyri were significantly deactivated by the verification task relative to both the magnitude judgment and control tasks for every subject. Areas activated by the magnitude task relative to the control were more variable, but in five subjects included bilateral inferior parietal cortex. These results confirm some existing hypotheses regarding the neural basis of numerical processes, invite revision of others, and suggest productive lines for future investigation.

Comparing Repetition Priming Effects in Words and Arithmetic Equations: Robust Priming Regardless of Color or Response Hand Change.

PubMed

Humphries, Ailsa; Chen, Zhe; Neumann, Ewald

2017-01-01

Previous studies have shown that stimulus repetition can lead to reliable behavioral improvements. Although this repetition priming (RP) effect has been reported in a number of paradigms using a variety of stimuli including words, objects, and faces, only a few studies have investigated mathematical cognition involving arithmetic computation, and no prior research has directly compared RP effects in a linguistic task with an arithmetic task. In two experiments, we used a within-subjects design to investigate and compare the magnitude of RP, and the effects of changing the color or the response hand for repeated, otherwise identical, stimuli in a word and an arithmetic categorization task. The results show that the magnitude of RP was comparable between the two tasks and that changing the color or the response hand had a negligible effect on priming in either task. These results extended previous findings in mathematical cognition. They also indicate that priming does not vary with stimulus domain. The implications of the results were discussed with reference to both facilitation of component processes and episodic memory retrieval of stimulus-response binding.

Finger gnosis predicts a unique but small part of variance in initial arithmetic performance.

PubMed

Wasner, Mirjam; Nuerk, Hans-Christoph; Martignon, Laura; Roesch, Stephanie; Moeller, Korbinian

2016-06-01

Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies. In this study, we aimed at examining whether finger gnosis is also a unique predictor for initial arithmetic competencies at the beginning of first grade-and thus before formal math instruction starts. Therefore, we controlled for influences of domain-specific numerical precursor competencies, domain-general cognitive ability, and natural variables such as gender and age. Results from 321 German first-graders revealed that finger gnosis indeed predicted a unique and relevant but nevertheless only small part of the variance in initial arithmetic performance (∼1%-2%) as compared with influences of general cognitive ability and numerical precursor competencies. Taken together, these results substantiated the notion of a unique association between finger gnosis and arithmetic and further corroborate the theoretical idea of finger-based representations contributing to numerical cognition. However, the only small part of variance explained by finger gnosis seems to limit its relevance for diagnostic purposes. Copyright © 2016. Published by Elsevier Inc.

Symptoms of anxiety and depression are related to cardiovascular responses to active, but not passive, coping tasks.

PubMed

Yuenyongchaiwat, Kornanong; Baker, Ian S; Sheffield, David

2017-01-01

Anxiety and depression have been linked to blunted blood pressure (BP) and heart rate (HR) reactions to mental stress tests; however, most studies have not included indices of underlying hemodynamics nor multiple stress tasks. This study sought to examine the relationships of anxiety and depression with hemodynamic responses to acute active and passive coping tasks. A total of 104 participants completed the Hospital Anxiety and Depression Scales and mental arithmetic, speech, and cold pressor tasks while BP, HR, total peripheral resistance, and cardiac output (CO) were assessed. After adjustment for traditional risk factors and baseline cardiovascular activity, depression scores were negatively associated with systolic BP, HR, and CO responses to the mental arithmetic task, while anxiety scores were inversely related to the systolic BP response to mental arithmetic. High anxiety or depression scores appear to be associated with blunted cardiac reactions to mental arithmetic (an active coping task), but not to the cold pressor test or speech tasks. Future research should further examine potential mechanisms and longitudinal pathways relating depression and anxiety to cardiovascular reactivity. TCTR20160208004.

Failure detection in high-performance clusters and computers using chaotic map computations

DOEpatents

Rao, Nageswara S.

2015-09-01

A programmable media includes a processing unit capable of independent operation in a machine that is capable of executing 10.sup.18 floating point operations per second. The processing unit is in communication with a memory element and an interconnect that couples computing nodes. The programmable media includes a logical unit configured to execute arithmetic functions, comparative functions, and/or logical functions. The processing unit is configured to detect computing component failures, memory element failures and/or interconnect failures by executing programming threads that generate one or more chaotic map trajectories. The central processing unit or graphical processing unit is configured to detect a computing component failure, memory element failure and/or an interconnect failure through an automated comparison of signal trajectories generated by the chaotic maps.

Approaches in highly parameterized inversion: TSPROC, a general time-series processor to assist in model calibration and result summarization

USGS Publications Warehouse

Westenbroek, Stephen M.; Doherty, John; Walker, John F.; Kelson, Victor A.; Hunt, Randall J.; Cera, Timothy B.

2012-01-01

The TSPROC (Time Series PROCessor) computer software uses a simple scripting language to process and analyze time series. It was developed primarily to assist in the calibration of environmental models. The software is designed to perform calculations on time-series data commonly associated with surface-water models, including calculation of flow volumes, transformation by means of basic arithmetic operations, and generation of seasonal and annual statistics and hydrologic indices. TSPROC can also be used to generate some of the key input files required to perform parameter optimization by means of the PEST (Parameter ESTimation) computer software. Through the use of TSPROC, the objective function for use in the model-calibration process can be focused on specific components of a hydrograph.

[Development of opened instrument for generating and measuring physiological signal].

PubMed

Chen, Longcong; Hu, Guohu; Gao, Bin

2004-12-01

An opened instrument with liquid crystal display (LCD) for generating and measuring physiological signal is introduced in this paper. Based on a single-chip microcomputer. the instrument uses the technique of LCD screen to display signal wave and information, and it realizes man-machine interaction by keyboard. This instrument can produce not only defined signal in common use by utilizing important saved data and relevant arithmetic, but also user-defined signal. Therefore, it is open to produce signal. In addition, this instrument has strong extension because of its modularized design as computer, which has much function such as displaying, measuring and saving physiological signal, and many features such as low power consumption, small volume, low cost and portability. Hence this instrument is convenient for experiment teaching, clinic examining, maintaining of medical instrument.

An investigation into the probabilistic combination of quasi-static and random accelerations

NASA Technical Reports Server (NTRS)

Schock, R. W.; Tuell, L. P.

1984-01-01

The development of design load factors for aerospace and aircraft components and experiment support structures, which are subject to a simultaneous vehicle dynamic vibration (quasi-static) and acoustically generated random vibration, require the selection of a combination methodology. Typically, the procedure is to define the quasi-static and the random generated response separately, and arithmetically add or root sum square to get combined accelerations. Since the combination of a probabilistic and a deterministic function yield a probabilistic function, a viable alternate approach would be to determine the characteristics of the combined acceleration probability density function and select an appropriate percentile level for the combined acceleration. The following paper develops this mechanism and provides graphical data to select combined accelerations for most popular percentile levels.