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

Cognitive and Linguistic Predictors of Mathematical Word Problems with and without Irrelevant Information

ERIC Educational Resources Information Center

Wang, Amber Y.; Fuchs, Lynn S.; Fuchs, Douglas

2016-01-01

The purpose of this study was to identify cognitive and linguistic predictors of word problems with versus without irrelevant information. The sample was 701 2nd-grade students who received no specialized intervention on word problems. In the fall, they were assessed on initial arithmetic and word-problem skill as well as language ability, working…

Arithmetic learning with the use of graphic organiser

NASA Astrophysics Data System (ADS)

Sai, F. L.; Shahrill, M.; Tan, A.; Han, S. H.

2018-01-01

For this study, Zollman’s four corners-and-a-diamond mathematics graphic organiser embedded with Polya’s Problem Solving Model was used to investigate secondary school students’ performance in arithmetic word problems. This instructional learning tool was used to help students break down the given information into smaller units for better strategic planning. The participants were Year 7 students, comprised of 21 male and 20 female students, aged between 11-13 years old, from a co-ed secondary school in Brunei Darussalam. This study mainly adopted a quantitative approach to investigate the types of differences found in the arithmetic word problem pre- and post-tests results from the use of the learning tool. Although the findings revealed slight improvements in the overall comparisons of the students’ test results, the in-depth analysis of the students’ responses in their activity worksheets shows a different outcome. Some students were able to make good attempts in breaking down the key points into smaller information in order to solve the word problems.

Using the Relational Paradigm: Effects on Pupils' Reasoning in Solving Additive Word Problems

ERIC Educational Resources Information Center

Polotskaia, Elena; Savard, Annie

2018-01-01

Pupils' difficulties in solving word problems continue to attract attention: while researchers highlight the importance of relational reasoning and modelling, school curricula typically use short word problems to develop pupils' knowledge of arithmetic operations and calculation strategies. The Relational Paradigm attributes the leading role in…

Individual differences in solving arithmetic word problems

PubMed Central

2013-01-01

Background With the present functional magnetic resonance imaging (fMRI) study at 3 T, we investigated the neural correlates of visualization and verbalization during arithmetic word problem solving. In the domain of arithmetic, visualization might mean to visualize numbers and (intermediate) results while calculating, and verbalization might mean that numbers and (intermediate) results are verbally repeated during calculation. If the brain areas involved in number processing are domain-specific as assumed, that is, that the left angular gyrus (AG) shows an affinity to the verbal domain, and that the left and right intraparietal sulcus (IPS) shows an affinity to the visual domain, the activation of these areas should show a dependency on an individual’s cognitive style. Methods 36 healthy young adults participated in the fMRI study. The participants habitual use of visualization and verbalization during solving arithmetic word problems was assessed with a short self-report assessment. During the fMRI measurement, arithmetic word problems that had to be solved by the participants were presented in an event-related design. Results We found that visualizers showed greater brain activation in brain areas involved in visual processing, and that verbalizers showed greater brain activation within the left angular gyrus. Conclusions Our results indicate that cognitive styles or preferences play an important role in understanding brain activation. Our results confirm, that strong visualizers use mental imagery more strongly than weak visualizers during calculation. Moreover, our results suggest that the left AG shows a specific affinity to the verbal domain and subserves number processing in a modality-specific way. PMID:23883107

Working Memory and Literacy as Predictors of Performance on Algebraic Word Problems

ERIC Educational Resources Information Center

Lee, Kerry; Ng, Swee-Fong; Ng, Ee-Lynn; Lim, Zee-Ying

2004-01-01

Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient…

Duality of Mathematical Thinking When Making Sense of Simple Word Problems: Theoretical Essay

ERIC Educational Resources Information Center

Polotskaia, Elena; Savard, Annie; Freiman, Viktor

2015-01-01

This essay proposes a reflection on the learning difficulties and teaching approaches associated with arithmetic word problem solving. We question the development of word problem solving skills in the early grades of elementary school. We are trying to revive the discussion because first, the knowledge in question--reversibility of arithmetic…

The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children.

PubMed

Träff, Ulf

2013-10-01

This study examined the relative contributions of general cognitive abilities and number abilities to word problem solving, calculation, and arithmetic fact retrieval in a sample of 134 children aged 10 to 13 years. The following tasks were administered: listening span, visual matrix span, verbal fluency, color naming, Raven's Progressive Matrices, enumeration, number line estimation, and digit comparison. Hierarchical multiple regressions demonstrated that number abilities provided an independent contribution to fact retrieval and word problem solving. General cognitive abilities contributed to problem solving and calculation. All three number tasks accounted for a similar amount of variance in fact retrieval, whereas only the number line estimation task contributed unique variance in word problem solving. Verbal fluency and Raven's matrices accounted for an equal amount of variance in problem solving and calculation. The current findings demonstrate, in accordance with Fuchs and colleagues' developmental model of mathematical learning (Developmental Psychology, 2010, Vol. 46, pp. 1731-1746), that both number abilities and general cognitive abilities underlie 10- to 13-year-olds' proficiency in problem solving, whereas only number abilities underlie arithmetic fact retrieval. Thus, the amount and type of cognitive contribution to arithmetic proficiency varies between the different aspects of arithmetic. Furthermore, how closely linked a specific aspect of arithmetic is to the whole number representation systems is not the only factor determining the amount and type of cognitive contribution in 10- to 13-year-olds. In addition, the mathematical complexity of the task appears to influence the amount and type of cognitive support. Copyright © 2013 Elsevier Inc. All rights reserved.

Error Analysis for Arithmetic Word Problems--A Case Study of Primary Three Students in One Singapore School

ERIC Educational Resources Information Center

Cheng, Lu Pien

2015-01-01

In this study, ways in which 9-year old students from one Singapore school solved 1-step and 2-step word problems based on the three semantic structures were examined. The students' work and diagrams provided insights into the range of errors in word problem solving for 1- step and 2-step word problems. In particular, the errors provided some…

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.

The Impact of Metacognitive Strategies and Self-Regulating Processes of Solving Math Word Problems

ERIC Educational Resources Information Center

Vula, Eda; Avdyli, Rrezarta; Berisha, Valbona; Saqipi, Blerim; Elezi, Shpetim

2017-01-01

This empirical study investigates the impact of metacognitive strategies and self-regulating processes in learners' achievement on solving math word problems. It specifically analyzes the impact of the linguistic factor and the number of steps and arithmetical operations that learners need to apply during the process of solving math word problems.…

Young Filipino Students Making Sense of Arithmetic Word Problems in English

ERIC Educational Resources Information Center

Bautista, Debbie; Mulligan, Joanne; Mitchelmore, Michael

2009-01-01

Young Filipino children are expected to solve mathematical word problems in English, a task which they typically encounter only in schools. In this exploratory study, task-based interviews were conducted with seven Filipino children from a public school. The children were asked to read and solve addition and subtraction word problems in English or…

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.

Middle School Children's Problem-Solving Behavior: A Cognitive Analysis from a Reading Comprehension Perspective

ERIC Educational Resources Information Center

Pape, Stephen J.

2004-01-01

Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem…

Enhancing Arithmetic and Word-Problem Solving Skills Efficiently by Individualized Computer-Assisted Practice

ERIC Educational Resources Information Center

Schoppek, Wolfgang; Tulis, Maria

2010-01-01

The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a…

Air Force Officer Qualifying Test Form T: Initial Item-, Test-, Factor-, and Composite-Level Analyses

DTIC Science & Technology

2016-12-01

five lower-order factors representing verbal, math , spatial, perceptual speed, and aviation knowledge, and a hierarchical general factor showed the...Academic Aptitude Verbal Quant. Verbal Analogies 25 X X X Arithmetic Reasoning 25 X X Word Knowledge 25 X X X Math Knowledge 25 X X...Reasoning (AR) uses word problems to assess the ability to understand arithmetic relations. Math Knowledge (MK) assesses the ability to use

The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

ERIC Educational Resources Information Center

Ng, Swee Fong; Lee, Kerry

2009-01-01

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

Cognitive Benefits and Costs of Bilingualism in Elementary School Students: The Case of Mathematical Word Problems

ERIC Educational Resources Information Center

Kempert, Sebastian; Saalbach, Henrik; Hardy, Ilonca

2011-01-01

Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical…

The Role of Executive Function in Arithmetic Problem-Solving Processes: A Study of Third Graders

ERIC Educational Resources Information Center

Viterbori, Paola; Traverso, Laura; Usai, M. Carmen

2017-01-01

This study investigated the roles of different executive function (EF) components (inhibition, shifting, and working memory) in 2-step arithmetic word problem solving. A sample of 139 children aged 8 years old and regularly attending the 3rd grade of primary school were tested on 6 EF tasks measuring different EF components, a reading task and a…

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

Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension

PubMed Central

Fuchs, Lynn S.; Gilbert, Jennifer K.; Fuchs, Douglas; Seethaler, Pamela M.; Martin, BrittanyLee N.

2018-01-01

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory, and foundational skill (word identification, arithmetic) and (b) year-end WP solving, WP-language processing (understanding WP statements, without calculation demands), and calculations. Multivariate, multilevel path analysis, accounting for classroom and school effects, indicated that TC was a significant and comparably strong predictor of all outcomes. Start-of-year language was a significantly stronger predictor of both year-end WP outcomes than of calculations, whereas start-of-year arithmetic was a significantly stronger predictor of calculations than of either WP measure. Implications are discussed in terms of WP solving as a form of TC and a theoretically coordinated approach, focused on language, for addressing TC and WP-solving instruction. PMID:29643723

Individual differences in children's understanding of inversion and arithmetical skill.

PubMed

Gilmore, Camilla K; Bryant, Peter

2006-06-01

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 their conceptual understanding and arithmetical skills. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6-7 and 8-9 years). Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the 'high ability' and 'low ability' groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem-solving skills.

Fundamentals of the Design and the Operation of an Intelligent Tutoring System for the Learning of the Arithmetical and Algebraic Way of Solving Word Problems

ERIC Educational Resources Information Center

Arnau, David; Arevalillo-Herraez, Miguel; Puig, Luis; Gonzalez-Calero, Jose Antonio

2013-01-01

Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…

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.

Number Words in Young Children's Conceptual and Procedural Knowledge of Addition, Subtraction and Inversion

ERIC Educational Resources Information Center

Canobi, Katherine H.; Bethune, Narelle E.

2008-01-01

Three studies addressed children's arithmetic. First, 50 3- to 5-year-olds judged physical demonstrations of addition, subtraction and inversion, with and without number words. Second, 20 3- to 4-year-olds made equivalence judgments of additions and subtractions. Third, 60 4- to 6-year-olds solved addition, subtraction and inversion problems that…

Transition Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2007

2007-01-01

"Transition Mathematics" aims to increase 7th- through 12th-grade students' skills in applied arithmetic, pre-algebra, and pre-geometry. This one-year curriculum also addresses general application to different wordings of problems, types of numbers, and contexts for problems and aims to promote mathematical reading skills. The curriculum…

Performance in Mathematical Problem Solving as a Function of Comprehension and Arithmetic Skills

ERIC Educational Resources Information Center

Voyer, Dominic

2011-01-01

Many factors influence a student's performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils' real-world knowledge, which support the construction of a…

Brain Stretchers Book 4--Advanced.

ERIC Educational Resources Information Center

Anderson, Carolyn

This book provides puzzles, games, and mathematical activities for students in elementary grades. Number concepts and arithmetic are common topics. These classic math, logic, and word-problem activities encourage students to become flexible, creative thinkers while teaching them to draw valid conclusions based on logic and evidence. Each activity…

Consciousness and abilities of dream characters observed during lucid dreaming.

PubMed

Tholey, P

1989-04-01

A description of several phenomenological experiments is given. These were done to investigate of which cognitive accomplishments dream characters are capable in lucid dreams. Nine male experienced lucid dreamers participated as subjects. They were directed to set different tasks to dream characters they met while lucid dreaming. Dream characters were asked to draw or write, to name unknown words, to find rhyme words, to make verses, and to solve arithmetic problems. Part of the dream characters actually agreed to perform the tasks and were successful, although the arithmetic accomplishments were poor. From the phenomenological findings, nothing contradicts the assumption that dream characters have consciousness in a specific sense. Herefrom the conclusion was drawn, that in lucid dream therapy communication with dream characters should be handled as if they were rational beings. Finally, several possibilities of assessing the question, whether dream characters possess consciousness, can be examined with the aid of psychophysiological experiments.

Number word structure in first and second language influences arithmetic skills

PubMed Central

Prior, Anat; Katz, Michal; Mahajna, Islam; Rubinsten, Orly

2015-01-01

Languages differ in how they represent numerical information, and specifically whether the verbal notation of numbers follows the same order as the symbolic notation (in non-inverted languages, e.g., Hebrew, “25, twenty-five”) or whether the two notations diverge (in inverted languages, e.g., Arabic, “25, five-and-twenty”). We examined how the structure of number–words affects how arithmetic operations are processed by bilingual speakers of an inverted and a non-inverted language. We examined Arabic–Hebrew bilinguals’ performance in the first language, L1 (inverted) and in the second language, L2 (non-inverted). Their performance was compared to that of Hebrew L1 speakers, who do not speak an inverted language. Participants judged the accuracy of addition problems presented aurally in L1, aurally in L2 or in visual symbolic notation. Problems were presented such that they matched or did not match the structure of number words in the language. Arabic–Hebrew bilinguals demonstrated both flexibility in processing and adaptation to the language of aural–verbal presentation – they were more accurate for the inverted order of presentation in Arabic, but more accurate for non-inverted order of presentation in Hebrew, thus exhibiting the same pattern found for native Hebrew speakers. In addition, whereas native Hebrew speakers preferred the non-inverted order in visual symbolic presentation as well, the Arabic–Hebrew bilinguals showed enhanced flexibility, without a significant preference for one order over the other, in either speed or accuracy. These findings suggest that arithmetic processing is sensitive to the linguistic representations of number words. Moreover, bilinguals exposed to inverted and non-inverted languages showed influence of both systems, and enhanced flexibility in processing. Thus, the L1 does not seem to have exclusive power in shaping numerical mental representations, but rather the system remains open to influences from a later learned L2. PMID:25852591

Numbers and functional lateralization: A visual half-field and dichotic listening study in proficient bilinguals.

PubMed

Klichowski, Michal; Króliczak, Gregory

2017-06-01

Potential links between language and numbers and the laterality of symbolic number representations in the brain are still debated. Furthermore, reports on bilingual individuals indicate that the language-number interrelationships might be quite complex. Therefore, we carried out a visual half-field (VHF) and dichotic listening (DL) study with action words and different forms of symbolic numbers used as stimuli to test the laterality of word and number processing in single-, dual-language and mixed -task and language- contexts. Experiment 1 (VHF) showed a significant right visual field/left hemispheric advantage in response accuracy for action word, as compared to any form of symbolic number processing. Experiment 2 (DL) revealed a substantially reversed effect - a significant right ear/left hemisphere advantage for arithmetic operations as compared to action word processing, and in response times in single- and dual-language contexts for number vs. action words. All these effects were language independent. Notably, for within-task response accuracy compared across modalities significant differences were found in all studied contexts. Thus, our results go counter to findings showing that action-relevant concepts and words, as well as number words are represented/processed primarily in the left hemisphere. Instead, we found that in the auditory context, following substantial engagement of working memory (here: by arithmetic operations), there is a subsequent functional reorganization of processing single stimuli, whether verbs or numbers. This reorganization - their weakened laterality - at least for response accuracy is not exclusive to processing of numbers, but the number of items to be processed. For response times, except for unpredictable tasks in mixed contexts, the "number problem" is more apparent. These outcomes are highly relevant to difficulties that simultaneous translators encounter when dealing with lengthy auditory material in which single items such as number words (and possibly other types of key words) need to be emphasized. Our results may also shed a new light on the "mathematical savant problem". Copyright © 2017 Elsevier Ltd. 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

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.

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.

Is Word-Problem Solving a Form of Text Comprehension?

PubMed Central

Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.; Hamlett, Carol L.; Wang, Amber Y.

2015-01-01

This study’s hypotheses were that (a) word-problem (WP) solving is a form of text comprehension that involves language comprehension processes, working memory, and reasoning, but (b) WP solving differs from other forms of text comprehension by requiring WP-specific language comprehension as well as general language comprehension. At the start of the 2nd grade, children (n = 206; on average, 7 years, 6 months) were assessed on general language comprehension, working memory, nonlinguistic reasoning, processing speed (a control variable), and foundational skill (arithmetic for WPs; word reading for text comprehension). In spring, they were assessed on WP-specific language comprehension, WPs, and text comprehension. Path analytic mediation analysis indicated that effects of general language comprehension on text comprehension were entirely direct, whereas effects of general language comprehension on WPs were partially mediated by WP-specific language. By contrast, effects of working memory and reasoning operated in parallel ways for both outcomes. PMID:25866461

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.

Brain potentials during mental arithmetic: effects of extensive practice and problem difficulty.

PubMed

Pauli, P; Lutzenberger, W; Rau, H; Birbaumer, N; Rickard, T C; Yaroush, R A; Bourne, L E

1994-07-01

Recent behavioral investigations indicate that the processes underlying mental arithmetic change systematically with practice from deliberate, conscious calculation to automatic, direct retrieval of answers from memory [Bourne, L.E.Jr. and Rickard, T.C., Mental calculation: The development of a cognitive skill, Paper presented at the Interamerican Congress of Psychology, San Jose, Costa Rica, 1991: Psychol. Rev., 95 (1988) 492-527]. Results reviewed by Moscovitch and Winocur [In: The handbook of aging and cognition, Erlbaum, Hillsdale, NJ, 1992, pp. 315-372] suggest that consciously controlled processes are more dependent on frontal lobe function than are automatic processes. It is appropriate, therefore to determine whether transitions in the locus of primary brain activity occur with practice on mental calculation. In this experiment, we examine the relationship between characteristics of event-related brain potentials (ERPs) and mental arithmetic. Single-digit mental multiplication problems varying in difficulty (problem size) were used, and subjects were trained on these problems for four sessions. Problem-size and practice effects were reliably found in behavioral measures (RT). The ERP was characterized by a pronounced late positivity after task presentation followed by a slow wave, and a negativity during response indication. These components responded differentially to the practice and problem-size manipulations. Practice mainly affected topography of the amplitude of positivity and offset latency of slow wave, and problem-size mainly offset latency of slow wave and pre-response negativity. Fronto-central positivity diminished from session to session, and the focus of positivity centered finally at centro-parietal regions.(ABSTRACT TRUNCATED AT 250 WORDS)

The effects of using diagramming as a representational technique on high school students' achievement in solving math word problems

NASA Astrophysics Data System (ADS)

Banerjee, Banmali

Methods and procedures for successfully solving math word problems have been, and continue to be a mystery to many U.S. high school students. Previous studies suggest that the contextual and mathematical understanding of a word problem, along with the development of schemas and their related external representations, positively contribute to students' accomplishments when solving word problems. Some studies have examined the effects of diagramming on students' abilities to solve word problems that only involved basic arithmetic operations. Other studies have investigated how instructional models that used technology influenced students' problem solving achievements. Still other studies have used schema-based instruction involving students with learning disabilities. No study has evaluated regular high school students' achievements in solving standard math word problems using a diagramming technique without technological aid. This study evaluated students' achievement in solving math word problems using a diagramming technique. Using a quasi-experimental experimental pretest-posttest research design, quantitative data were collected from 172 grade 11 Hispanic English language learners (ELLS) and African American learners whose first language is English (EFLLs) in 18 classes at an inner city high school in Northern New Jersey. There were 88 control and 84 experimental students. The pretest and posttest of each participating student and samples of the experimental students' class assignments provided the qualitative data for the study. The data from this study exhibited that the diagramming method of solving math word problems significantly improved student achievement in the experimental group (p<.01) compared to the control group. The study demonstrated that urban, high school, ELLs benefited from instruction that placed emphasis on the mathematical vocabulary and symbols used in word problems and that both ELLs and EFLLs improved their problem solving success through careful attention to the creation and labeling of diagrams to represent the mathematics involved in standard word problems. Although Learnertype (ELL, EFLL), Classtype (Bilingual and Mixed), and Gender (Female, Male) were not significant indicators of student achievement, there was significant interaction between Treatment and Classtype at the level of the Bilingual students ( p<.01) and between Treatment and Learnertype at the level of the ELLs (p<.01).

Memory Updating and Mental Arithmetic

PubMed Central

Han, Cheng-Ching; Yang, Tsung-Han; Lin, Chia-Yuan; Yen, Nai-Shing

2016-01-01

Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM) as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc) could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults. PMID:26869971

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…

Multiple Paths to Mathematics Practice in Al-Kashi's Key to Arithmetic

NASA Astrophysics Data System (ADS)

Taani, Osama

2014-01-01

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his Key to Arithmetic, a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life and his contributions to mathematics and astronomy. Section 2 starts with a brief discussion of the contents and pedagogy of the Key to Arithmetic. Al-Kashi's multiple approaches are discussed through four different examples of his versatility in presenting a topic from multiple perspectives. These examples are multiple definitions, multiple algorithms, multiple formulas, and multiple methods for solving word problems. Section 3 is devoted to some benefits that can be gained by implementing al-Kashi's multiple paths approach in modern curricula. For this discussion, examples from two teaching modules taken from the Key to Arithmetic and implemented in Pre-Calculus and mathematics courses for preservice teachers are discussed. Also, the conclusions are supported by some aspects of these modules. This paper is an attempt to help mathematics educators explore more benefits from reading from original sources.

A 640-MHz 32-megachannel real-time polyphase-FFT spectrum analyzer

NASA Technical Reports Server (NTRS)

Zimmerman, G. A.; Garyantes, M. F.; Grimm, M. J.; Charny, B.

1991-01-01

A polyphase fast Fourier transform (FFT) spectrum analyzer being designed for NASA's Search for Extraterrestrial Intelligence (SETI) Sky Survey at the Jet Propulsion Laboratory is described. By replacing the time domain multiplicative window preprocessing with polyphase filter processing, much of the processing loss of windowed FFTs can be eliminated. Polyphase coefficient memory costs are minimized by effective use of run length compression. Finite word length effects are analyzed, producing a balanced system with 8 bit inputs, 16 bit fixed point polyphase arithmetic, and 24 bit fixed point FFT arithmetic. Fixed point renormalization midway through the computation is seen to be naturally accommodated by the matrix FFT algorithm proposed. Simulation results validate the finite word length arithmetic analysis and the renormalization technique.

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…

Language affects symbolic arithmetic in children: the case of number word inversion.

PubMed

Göbel, Silke M; Moeller, Korbinian; Pixner, Silvia; Kaufmann, Liane; Nuerk, Hans-Christoph

2014-03-01

Specific language influences have been observed in basic numerical tasks such as magnitude comparison, transcoding, and the number line estimation task. However, so far language influences in more complex calculations have not been reported in children. In this translingual study, 7- to 9-year-old German- and Italian-speaking children were tested on a symbolic addition task. Whereas the order of tens and units in Italian number words follows the order of the Arabic notation, the order is inverted in German number words. For both language groups, addition problems were more difficult when a carry operation was needed, that is, when a manipulation within the place-value structure of the Arabic number system was particularly important. Most important, this carry effect was more pronounced in response latencies for children speaking German, a language with inverted verbal mapping of the place-value structure. In addition, independent of language group, the size of the carry effect was significantly related to verbal working memory. The current study indicates that symbolic arithmetic and the carry effect in particular are modulated by language-specific characteristics. Our results underline the fact that the structure of the language of instruction is an important factor in children's mathematical education and needs to be taken into account even for seemingly nonverbal symbolic Arabic tasks. Copyright © 2013 Elsevier Inc. All rights reserved.

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.

A Comparative Analysis of Vocabulary Load of Three Provincially Adopted Primary Arithmetic Series.

ERIC Educational Resources Information Center

Horodezky, Betty; Weinstein, Pauline Smith

1981-01-01

Results indicated considerable difference in total number of running words among series; an increase in different words for grades two-three in each series; repetition of most words in each series between one and nine times; and no high degree of word overlap between series or grades in any given series. (Author/CM)

[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.

Language, procedures, and the non-perceptual origin of number word meanings.

PubMed

Barner, David

2017-05-01

Perceptual representations of objects and approximate magnitudes are often invoked as building blocks that children combine to acquire the positive integers. Systems of numerical perception are either assumed to contain the logical foundations of arithmetic innately, or to supply the basis for their induction. I propose an alternative to this framework, and argue that the integers are not learned from perceptual systems, but arise to explain perception. Using cross-linguistic and developmental data, I show that small (~1-4) and large (~5+) numbers arise both historically and in individual children via distinct mechanisms, constituting independent learning problems, neither of which begins with perceptual building blocks. Children first learn small numbers using the same logic that supports other linguistic number marking (e.g. singular/plural). Years later, they infer the logic of counting from the relations between large number words and their roles in blind counting procedures, only incidentally associating number words with approximate magnitudes.

Memory-driven attentional capture reveals the waxing and waning of working memory activation due to dual-task interference.

PubMed

Sasin, Edyta; Nieuwenstein, Mark

2016-12-01

Previous studies have shown that information held in working memory (WM) actively or as a residue of previous processing can lead to attentional capture by corresponding stimuli in the environment. Here, we compared attentional capture by goal-driven and residual WM activation and examined how these effects are affected by dual-task interference. In two experiments, participants performed an animacy judgment task for a word that they did or did not have to remember for a later recognition test. The word was followed in half of the trials by an arithmetic task that served to disrupt the WM activation of the previously processed word. Subsequently, WM-driven capture was assessed by having participants perform a single-target rapid serial visual presentation task in which a line drawing corresponding to the word was presented shortly before a target. The results showed that the line drawing captured attention irrespective of the presence of the arithmetic task when the word had to be remembered. In comparison, the animacy judgment alone resulted in capture only when the arithmetic task was absent, and this effect was equally strong as the capture effect caused by a to-be-remembered word. Taken together, these findings show that although residual and goal-driven WM activation may be equally potent in guiding attentional selection, these two forms of WM activation differ in that residual activation is overwritten by an attention-demanding task, whereas goal-driven WM activation can lead to the reinstatement of a stimulus after performing such a task.

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)…

[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.

Bit-Wise Arithmetic Coding For Compression Of Data

NASA Technical Reports Server (NTRS)

Kiely, Aaron

1996-01-01

Bit-wise arithmetic coding is data-compression scheme intended especially for use with uniformly quantized data from source with Gaussian, Laplacian, or similar probability distribution function. Code words of fixed length, and bits treated as being independent. Scheme serves as means of progressive transmission or of overcoming buffer-overflow or rate constraint limitations sometimes arising when data compression used.

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.

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 + __),…

Cued Recall from Image and Sentence Memory: A Shift from Episodic to Identical Elements Representation

ERIC Educational Resources Information Center

Rickard, Timothy C.; Bajic, Daniel

2006-01-01

The applicability of the identical elements (IE) model of arithmetic fact retrieval (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994) to cued recall from episodic (image and sentence) memory was explored in 3 transfer experiments. In agreement with results from arithmetic, speedup following even minimal practice recalling a missing word from an…

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.

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

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.

Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

PubMed Central

Geary, David C.

2011-01-01

The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

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

Cognitive Profiles of Mathematical Problem Solving Learning Disability for Different Definitions of Disability

PubMed Central

Tolar, Tammy D.; Fuchs, Lynn; Fletcher, Jack M.; Fuchs, Douglas; Hamlett, Carol L.

2014-01-01

Three cohorts of third-grade students (N = 813) were evaluated on achievement, cognitive abilities, and behavioral attention according to contrasting research traditions in defining math learning disability (LD) status: low achievement versus extremely low achievement and IQ-achievement discrepant versus strictly low-achieving LD. We use methods from these two traditions to form math problem solving LD groups. To evaluate group differences, we used MANOVA-based profile and canonical analyses to control for relations among the outcomes and regression to control for group definition variables. Results suggest that basic arithmetic is the key distinguishing characteristic that separates low-achieving problem solvers (including LD, regardless of definition) from typically achieving students. Word problem solving is the key distinguishing characteristic that separates IQ-achievement-discrepant from strictly low-achieving LD students, favoring the IQ-achievement-discrepant students. PMID:24939971

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…

Navier-Stokes Simulation of Homogeneous Turbulence on the CYBER 205

NASA Technical Reports Server (NTRS)

Wu, C. T.; Ferziger, J. H.; Chapman, D. R.; Rogallo, R. S.

1984-01-01

A computer code which solves the Navier-Stokes equations for three dimensional, time-dependent, homogenous turbulence has been written for the CYBER 205. The code has options for both 64-bit and 32-bit arithmetic. With 32-bit computation, mesh sizes up to 64 (3) are contained within core of a 2 million 64-bit word memory. Computer speed timing runs were made for various vector lengths up to 6144. With this code, speeds a little over 100 Mflops have been achieved on a 2-pipe CYBER 205. Several problems encountered in the coding are discussed.

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).

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.

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.

Specificity and Overlap in Skills Underpinning Reading and Arithmetical Fluency

ERIC Educational Resources Information Center

van Daal, Victor; van der Leij, Aryan; Ader, Herman

2013-01-01

The aim of this study was to examine unique and common causes of problems in reading and arithmetic fluency. 13- to 14-year-old students were placed into one of five groups: reading disabled (RD, n = 16), arithmetic disabled (AD, n = 34), reading and arithmetic disabled (RAD, n = 17), reading, arithmetic, and listening comprehension disabled…

Faster Bit-Parallel Algorithms for Unordered Pseudo-tree Matching and Tree Homeomorphism

NASA Astrophysics Data System (ADS)

Kaneta, Yusaku; Arimura, Hiroki

In this paper, we consider the unordered pseudo-tree matching problem, which is a problem of, given two unordered labeled trees P and T, finding all occurrences of P in T via such many-one embeddings that preserve node labels and parent-child relationship. This problem is closely related to tree pattern matching problem for XPath queries with child axis only. If m > w , we present an efficient algorithm that solves the problem in O(nm log(w)/w) time using O(hm/w + mlog(w)/w) space and O(m log(w)) preprocessing on a unit-cost arithmetic RAM model with addition, where m is the number of nodes in P, n is the number of nodes in T, h is the height of T, and w is the word length. We also discuss a modification of our algorithm for the unordered tree homeomorphism problem, which corresponds to a tree pattern matching problem for XPath queries with descendant axis only.

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…

Weak task-related modulation and stimulus representations during arithmetic problem solving in children with developmental dyscalculia

PubMed Central

Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Tenison, Caitlin; Menon, Vinod

2015-01-01

Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7–9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. While the TD group showed strong modulation of brain responses with increasing arithmetic complexity, children with DD failed to show such modulation. Children with DD showed significantly reduced activation compared to TD children in the intraparietal sulcus, superior parietal lobule, supramarginal gyrus and bilateral dorsolateral prefrontal cortex in relation to arithmetic complexity. Critically, multivariate representational similarity revealed that brain response patterns to complex and simple problems were less differentiated in the DD group in bilateral anterior IPS, independent of overall differences in signal level. Taken together, these results show that children with DD not only under-activate key brain regions implicated in mathematical cognition, but they also fail to generate distinct neural responses and representations for different arithmetic problems. Our findings provide novel insights into the neural basis of DD. PMID:22682904

Weak task-related modulation and stimulus representations during arithmetic problem solving in children with developmental dyscalculia.

PubMed

Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Tenison, Caitlin; Menon, Vinod

2012-02-15

Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7-9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. While the TD group showed strong modulation of brain responses with increasing arithmetic complexity, children with DD failed to show such modulation. Children with DD showed significantly reduced activation compared to TD children in the intraparietal sulcus, superior parietal lobule, supramarginal gyrus and bilateral dorsolateral prefrontal cortex in relation to arithmetic complexity. Critically, multivariate representational similarity revealed that brain response patterns to complex and simple problems were less differentiated in the DD group in bilateral anterior IPS, independent of overall differences in signal level. Taken together, these results show that children with DD not only under-activate key brain regions implicated in mathematical cognition, but they also fail to generate distinct neural responses and representations for different arithmetic problems. Our findings provide novel insights into the neural basis of DD. Copyright © 2011 Elsevier Ltd. All rights reserved.

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

The Feline Josephus Problem

NASA Astrophysics Data System (ADS)

Ruskey, Frank; Williams, Aaron

In the classic Josephus problem, elements 1, 2,...,n are placed in order around a circle and a skip value k is chosen. The problem proceeds in n rounds, where each round consists of traveling around the circle from the current position, and selecting the kth remaining element to be eliminated from the circle. After n rounds, every element is eliminated. Special attention is given to the last surviving element, denote it by j. We generalize this popular problem by introducing a uniform number of lives ℓ, so that elements are not eliminated until they have been selected for the ℓth time. We prove two main results: 1) When n and k are fixed, then j is constant for all values of ℓ larger than the nth Fibonacci number. In other words, the last surviving element stabilizes with respect to increasing the number of lives. 2) When n and j are fixed, then there exists a value of k that allows j to be the last survivor simultaneously for all values of ℓ. In other words, certain skip values ensure that a given position is the last survivor, regardless of the number of lives. For the first result we give an algorithm for determining j (and the entire sequence of selections) that uses O(n 2) arithmetic operations.

[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).

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.

Floating point arithmetic in future supercomputers

NASA Technical Reports Server (NTRS)

Bailey, David H.; Barton, John T.; Simon, Horst D.; Fouts, Martin J.

1989-01-01

Considerations in the floating-point design of a supercomputer are discussed. Particular attention is given to word size, hardware support for extended precision, format, and accuracy characteristics. These issues are discussed from the perspective of the Numerical Aerodynamic Simulation Systems Division at NASA Ames. The features believed to be most important for a future supercomputer floating-point design include: (1) a 64-bit IEEE floating-point format with 11 exponent bits, 52 mantissa bits, and one sign bit and (2) hardware support for reasonably fast double-precision arithmetic.

Equations with Arithmetic Functions of Pell Numbers

DTIC Science & Technology

2014-01-01

Bull. Math. Soc. Sci. Math. Roumanie Tome 57(105) No. 4, 2014, 409–413 Equations with arithmetic functions of Pell numbers by 1Florian Luca...2Pantelimon Stănică Abstract Here, we prove some diophantine results about the Euler function of Pell numbers and their Pell –Lucas companion sequence. For...example, if the Euler function of the nth Pell number Pn or Pell –Lucas companion number Qn is a power of 2, then n ≤ 8. Key Words: Euler function, Pell

The Influence of verbalization on the pattern of cortical activation during mental arithmetic

PubMed Central

2012-01-01

Background The aim of the present functional magnetic resonance imaging (fMRI) study at 3 T was to investigate the influence of the verbal-visual cognitive style on cerebral activation patterns during mental arithmetic. In the domain of arithmetic, a visual style might for example mean to visualize numbers and (intermediate) results, and a verbal style might mean, that numbers and (intermediate) results are verbally repeated. In this study, we investigated, first, whether verbalizers show activations in areas for language processing, and whether visualizers show activations in areas for visual processing during mental arithmetic. Some researchers have proposed that the left and right intraparietal sulcus (IPS), and the left angular gyrus (AG), two areas involved in number processing, show some domain or modality specificity. That is, verbal for the left AG, and visual for the left and right IPS. We investigated, second, whether the activation in these areas implied in number processing depended on an individual's cognitive style. Methods 42 young healthy adults participated in the fMRI study. The study comprised two functional sessions. In the first session, subtraction and multiplication problems were presented in an event-related design, and in the second functional session, multiplications were presented in two formats, as Arabic numerals and as written number words, in an event-related design. The individual's habitual use of visualization and verbalization during mental arithmetic was assessed by a short self-report assessment. Results We observed in both functional sessions that the use of verbalization predicts activation in brain areas associated with language (supramarginal gyrus) and auditory processing (Heschl's gyrus, Rolandic operculum). However, we found no modulation of activation in the left AG as a function of verbalization. Conclusions Our results confirm that strong verbalizers use mental speech as a form of mental imagination more strongly than weak verbalizers. Moreover, our results suggest that the left AG has no specific affinity to the verbal domain and subserves number processing in a modality-general way. PMID:22404872

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

PubMed Central

Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

2014-01-01

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

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.

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

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

Cued recall from image and sentence memory: a shift from episodic to identical elements representation.

PubMed

Rickard, Timothy C; Bajic, Daniel

2006-07-01

The applicability of the identical elements (IE) model of arithmetic fact retrieval (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994) to cued recall from episodic (image and sentence) memory was explored in 3 transfer experiments. In agreement with results from arithmetic, speedup following even minimal practice recalling a missing word from an episodically bound word triplet did not transfer positively to other cued recall items involving the same triplet. The shape of the learning curve further supported a shift from episode-based to IE-based recall, extending some models of skill learning to cued recall practice. In contrast with previous findings, these results indicate that a form of representation that is independent of the original episodic memory underlies cued-recall performance following minimal practice. Copyright 2006 APA, all rights reserved.

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…

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.

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…

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.

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

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.

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

Bit-parallel arithmetic in a massively-parallel associative processor

NASA Technical Reports Server (NTRS)

Scherson, Isaac D.; Kramer, David A.; Alleyne, Brian D.

1992-01-01

A simple but powerful new architecture based on a classical associative processor model is presented. Algorithms for performing the four basic arithmetic operations both for integer and floating point operands are described. For m-bit operands, the proposed architecture makes it possible to execute complex operations in O(m) cycles as opposed to O(m exp 2) for bit-serial machines. A word-parallel, bit-parallel, massively-parallel computing system can be constructed using this architecture with VLSI technology. The operation of this system is demonstrated for the fast Fourier transform and matrix multiplication.

Deaf and Hard of Hearing Students' Problem-Solving Strategies with Signed Arithmetic Story Problems

ERIC Educational Resources Information Center

Pagliaro, Claudia M.; Ansell, Ellen

2011-01-01

The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e.,…

Patterns of Problem-Solving in Children's Literacy and Arithmetic

ERIC Educational Resources Information Center

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

2009-01-01

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 1 and 2 on the…

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 400. A Computer Educational Program.

ERIC Educational Resources Information Center

Firestein, Laurie

"ARITHMETIC 400" is the first of the next generation of educational programs designed to encourage thinking about arithmetic problems. Presented in video game format, performance is a measure of correctness, speed, accuracy, and fortune as well. Play presents a challenge to individuals at various skill levels. The program, run on an Apple…

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

Hold the Pickle!

ERIC Educational Resources Information Center

Lupi, Marsha Mead

1979-01-01

The article illustrates the use of commercial jingles as high interest, low-level reading and language arts materials for primary age mildly retarded students. It is pointed out that jingles can be used in teaching initial consonants, vocabulary words, and arithmetic concepts. (SBH)

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.

A Study of Arithmetical Problem Solving Abilities of Young Children through the Use of Calculators.

ERIC Educational Resources Information Center

McNicol, Shirley; And Others

A study was conducted to: (1) observe through a case study approach the exploratory behavior exhibited by 8-year-old boys and girls when calculators were made available in problem-solving situations; (2) investigate changes that occur in the kinds of arithmetical problems children construct following the introduction of calculators; and (3)…

Neurocognitive Effects of Transcranial Direct Current Stimulation in Arithmetic Learning and Performance: A Simultaneous tDCS-fMRI Study.

PubMed

Hauser, Tobias U; Rütsche, Bruno; Wurmitzer, Karoline; Brem, Silvia; Ruff, Christian C; Grabner, Roland H

A small but increasing number of studies suggest that non-invasive brain stimulation by means of transcranial direct current stimulation (tDCS) can modulate arithmetic processes that are essential for higher-order mathematical skills and that are impaired in dyscalculic individuals. However, little is known about the neural mechanisms underlying such stimulation effects, and whether they are specific to cognitive processes involved in different arithmetic tasks. We addressed these questions by applying tDCS during simultaneous functional magnetic resonance imaging (fMRI) while participants were solving two types of complex subtraction problems: repeated problems, relying on arithmetic fact learning and problem-solving by fact retrieval, and novel problems, requiring calculation procedures. Twenty participants receiving left parietal anodal plus right frontal cathodal stimulation were compared with 20 participants in a sham condition. We found a strong cognitive and neural dissociation between repeated and novel problems. Repeated problems were solved more accurately and elicited increased activity in the bilateral angular gyri and medial plus lateral prefrontal cortices. Solving novel problems, in contrast, was accompanied by stronger activation in the bilateral intraparietal sulci and the dorsomedial prefrontal cortex. Most importantly, tDCS decreased the activation of the right inferior frontal cortex while solving novel (compared to repeated) problems, suggesting that the cathodal stimulation rendered this region unable to respond to the task-specific cognitive demand. The present study revealed that tDCS during arithmetic problem-solving can modulate the neural activity in proximity to the electrodes specifically when the current demands lead to an engagement of this area. Copyright © 2016 Elsevier Inc. All rights reserved.

Preschool predictors of mathematics in first grade children with autism spectrum disorder.

PubMed

Titeca, Daisy; Roeyers, Herbert; Josephy, Haeike; Ceulemans, Annelies; Desoete, Annemie

2014-11-01

Up till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5-6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6-7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Interference and problem size effect in multiplication fact solving: Individual differences in brain activations and arithmetic performance.

PubMed

De Visscher, Alice; Vogel, Stephan E; Reishofer, Gernot; Hassler, Eva; Koschutnig, Karl; De Smedt, Bert; Grabner, Roland H

2018-05-15

In the development of math ability, a large variability of performance in solving simple arithmetic problems is observed and has not found a compelling explanation yet. One robust effect in simple multiplication facts is the problem size effect, indicating better performance for small problems compared to large ones. Recently, behavioral studies brought to light another effect in multiplication facts, the interference effect. That is, high interfering problems (receiving more proactive interference from previously learned problems) are more difficult to retrieve than low interfering problems (in terms of physical feature overlap, namely the digits, De Visscher and Noël, 2014). At the behavioral level, the sensitivity to the interference effect is shown to explain individual differences in the performance of solving multiplications in children as well as in adults. The aim of the present study was to investigate the individual differences in multiplication ability in relation to the neural interference effect and the neural problem size effect. To that end, we used a paradigm developed by De Visscher, Berens, et al. (2015) that contrasts the interference effect and the problem size effect in a multiplication verification task, during functional magnetic resonance imaging (fMRI) acquisition. Forty-two healthy adults, who showed high variability in an arithmetic fluency test, participated in our fMRI study. In order to control for the general reasoning level, the IQ was taken into account in the individual differences analyses. Our findings revealed a neural interference effect linked to individual differences in multiplication in the left inferior frontal gyrus, while controlling for the IQ. This interference effect in the left inferior frontal gyrus showed a negative relation with individual differences in arithmetic fluency, indicating a higher interference effect for low performers compared to high performers. This region is suggested in the literature to be involved in resolution of proactive interference. Besides, no correlation between the neural problem size effect and multiplication performance was found. This study supports the idea that the interference due to similarities/overlap of physical traits (the digits) is crucial in memorizing arithmetic facts and in determining individual differences in arithmetic. Copyright © 2018 Elsevier Inc. All rights reserved.

Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

2017-10-01

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

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

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).

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.

Choice of word length in the design of a specialized hardware for lossless wavelet compression of medical images

NASA Astrophysics Data System (ADS)

Urriza, Isidro; Barragan, Luis A.; Artigas, Jose I.; Garcia, Jose I.; Navarro, Denis

1997-11-01

Image compression plays an important role in the archiving and transmission of medical images. Discrete cosine transform (DCT)-based compression methods are not suitable for medical images because of block-like image artifacts that could mask or be mistaken for pathology. Wavelet transforms (WTs) are used to overcome this problem. When implementing WTs in hardware, finite precision arithmetic introduces quantization errors. However, lossless compression is usually required in the medical image field. Thus, the hardware designer must look for the optimum register length that, while ensuring the lossless accuracy criteria, will also lead to a high-speed implementation with small chip area. In addition, wavelet choice is a critical issue that affects image quality as well as system design. We analyze the filters best suited to image compression that appear in the literature. For them, we obtain the maximum quantization errors produced in the calculation of the WT components. Thus, we deduce the minimum word length required for the reconstructed image to be numerically identical to the original image. The theoretical results are compared with experimental results obtained from algorithm simulations on random test images. These results enable us to compare the hardware implementation cost of the different filter banks. Moreover, to reduce the word length, we have analyzed the case of increasing the integer part of the numbers while maintaining constant the word length when the scale increases.

Development of preschool and academic skills in children born very preterm.

PubMed

Aarnoudse-Moens, Cornelieke Sandrine Hanan; Oosterlaan, Jaap; Duivenvoorden, Hugo Joseph; van Goudoever, Johannes Bernard; Weisglas-Kuperus, Nynke

2011-01-01

To examine performance in preschool and academic skills in very preterm (gestational age ≤ 30 weeks) and term-born comparison children aged 4 to 12 years. Very preterm children (n = 200; mean age, 8.2 ± 2.5 years) born between 1996 and 2004 were compared with 230 term-born children (mean age, 8.3 ± 2.3). The Dutch National Pupil Monitoring System was used to measure preschool numerical reasoning and early linguistics, and primary school simple and complex word reading, reading comprehension, spelling, and mathematics/arithmetic. With univariate analyses of variance, we assessed the effects of preterm birth on performance across grades and on grade retention. In preschool, very preterm children performed comparably with term-born children in early linguistics, but perform more poorly (0.7 standard deviation [SD]) in numerical reasoning skills. In primary school, very preterm children scored 0.3 SD lower in complex word reading and 0.6 SD lower in mathematics/arithmetic, but performed comparably with peers in reading comprehension and spelling. They had a higher grade repeat rate (25.5%), although grade repeat did not improve their academic skills. Very preterm children do well in early linguistics, reading comprehension, and spelling, but have clinically significant deficits in numerical reasoning skills and mathematics/arithmetic, which persist with time. Copyright © 2011 Mosby, Inc. All rights reserved.

Inconsistencies in Numerical Simulations of Dynamical Systems Using Interval Arithmetic

NASA Astrophysics Data System (ADS)

Nepomuceno, Erivelton G.; Peixoto, Márcia L. C.; Martins, Samir A. M.; Rodrigues, Heitor M.; Perc, Matjaž

Over the past few decades, interval arithmetic has been attracting widespread interest from the scientific community. With the expansion of computing power, scientific computing is encountering a noteworthy shift from floating-point arithmetic toward increased use of interval arithmetic. Notwithstanding the significant reliability of interval arithmetic, this paper presents a theoretical inconsistency in a simulation of dynamical systems using a well-known implementation of arithmetic interval. We have observed that two natural interval extensions present an empty intersection during a finite time range, which is contrary to the fundamental theorem of interval analysis. We have proposed a procedure to at least partially overcome this problem, based on the union of the two generated pseudo-orbits. This paper also shows a successful case of interval arithmetic application in the reduction of interval width size on the simulation of discrete map. The implications of our findings on the reliability of scientific computing using interval arithmetic have been properly addressed using two numerical examples.

The Ups and Downs of ASVAB: Fluctuations in Armed Services Vocational Aptitude Battery Scores and Implications for U.S. Army Force Readiness

DTIC Science & Technology

2017-03-30

reflect my own personal views and are not necessarily endorsed by the National Defense University, Joint Forces Staff College, the Department of State, or...thesis and are sincerely appreciated. I also thank Mr. Jeffrey Turner, JAWS Academic Writing Specialist for his tireless r writing assistance, as well... AR ) 28 Word Knowledge (WK) 29 Mechanical Comprehension (MC) 30 2009-2015 31 General Science (GS) 31 Arithmetic Reasoning ( AR ) 32 Word Knowledge (WK) 32

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.

Priming Addition Facts with Semantic Relations

ERIC Educational Resources Information Center

Bassok, Miriam; Pedigo, Samuel F.; Oskarsson, An T.

2008-01-01

Results from 2 relational-priming experiments suggest the existence of an automatic analogical coordination between semantic and arithmetic relations. Word pairs denoting object sets served as primes in a task that elicits "obligatory" activation of addition facts (5 + 3 activates 8; J. LeFevre, J. Bisanz, & L. Mrkonjic, 1988). Semantic relations…

Affected Aspects Regarding Literacy and Numeracy in Children Treated for Brain Tumors.

PubMed

Lönnerblad, Malin; Lovio, Riikka; Berglund, Eva; Van't Hooft, Ingrid

The aim of this study was to investigate the test results of reading speed, reading comprehension, word comprehension, spelling, basic arithmetic skills, and number sense (intuitive understanding of numbers) by children treated for brain tumors. This is a retrospective study based on medical records, including standardized academic tests. In the years of 2010 to 2014, all children in the area of Stockholm between 7 and 18 years (IQ <70) who had no major linguistic or motor difficulties after they had undergone treatment for brain tumors were offered a special education assessment one year after treatment, at school start, or the year before a transition from one stage to another. Our results indicate that children treated for a brain tumor are at risk of having difficulties in spelling, reading speed, and arithmetic and that the test performance may decline over years in arithmetic and spelling. Children diagnosed at age 0 to 6 years may need extra tutoring at school start, especially in basic arithmetic skills. In both reading and mathematics, many children perform better on tests focused on understanding than on tests focused on speed. Continuous special needs assessments including different aspects of literacy and numeracy, are important for understanding each child's specific needs.

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.

Language, Procedures, and the Non-Perceptual Origin of Number Word Meanings

ERIC Educational Resources Information Center

Barner, David

2017-01-01

Perceptual representations of objects and approximate magnitudes are often invoked as building blocks that children combine to acquire the positive integers. Systems of numerical perception are either assumed to contain the logical foundations of arithmetic innately, or to supply the basis for their induction. I propose an alternative to this…

The computationalist reformulation of the mind-body problem.

PubMed

Marchal, Bruno

2013-09-01

Computationalism, or digital mechanism, or simply mechanism, is a hypothesis in the cognitive science according to which we can be emulated by a computer without changing our private subjective feeling. We provide a weaker form of that hypothesis, weaker than the one commonly referred to in the (vast) literature and show how to recast the mind-body problem in that setting. We show that such a mechanist hypothesis does not solve the mind-body problem per se, but does help to reduce partially the mind-body problem into another problem which admits a formulation in pure arithmetic. We will explain that once we adopt the computationalist hypothesis, which is a form of mechanist assumption, we have to derive from it how our belief in the physical laws can emerge from *only* arithmetic and classical computer science. In that sense we reduce the mind-body problem to a body problem appearance in computer science, or in arithmetic. The general shape of the possible solution of that subproblem, if it exists, is shown to be closer to "Platonist or neoplatonist theology" than to the "Aristotelian theology". In Plato's theology, the physical or observable reality is only the shadow of a vaster hidden nonphysical and nonobservable, perhaps mathematical, reality. The main point is that the derivation is constructive, and it provides the technical means to derive physics from arithmetic, and this will make the computationalist hypothesis empirically testable, and thus scientific in the Popperian analysis of science. In case computationalism is wrong, the derivation leads to a procedure for measuring "our local degree of noncomputationalism". Copyright © 2013 Elsevier Ltd. All rights reserved.

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.

Presentation format effects in working memory: the role of attention.

PubMed

Foos, Paul W; Goolkasian, Paula

2005-04-01

Four experiments are reported in which participants attempted to remember three or six concrete nouns, presented as pictures, spoken words, or printed words, while also verifying the accuracy of sentences. Hypotheses meant to explain the higher recall of pictures and spoken words over printed words were tested. Increasing the difficulty and changing the type of processing task from arithmetic to a visual/spatial reasoning task did not influence recall. An examination of long-term modality effects showed that those effects were not sufficient to explain the superior performance with spoken words and pictures. Only when we manipulated the allocation of attention to the items in the storage task by requiring the participants to articulate the items and by presenting the stimulus items under a degraded condition were we able to reduce or remove the effect of presentation format. The findings suggest that the better recall of pictures and spoken words over printed words result from the fact that under normal presentation conditions, printed words receive less processing attention than pictures and spoken words do.

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.

Students’ Relational Thinking of Impulsive and Reflective in Solving Mathematical Problem

NASA Astrophysics Data System (ADS)

Satriawan, M. A.; Budiarto, M. T.; Siswono, T. Y. E.

2018-01-01

This is a descriptive research which qualitatively investigates students’ relational thinking of impulsive and reflective cognitive style in solving mathematical problem. The method used in this research are test and interview. The data analyzed by reducing, presenting and concluding the data. The results of research show that the students’ reflective cognitive style can possibly help to find out important elements in understanding a problem. Reading more than one is useful to identify what is being questioned and write the information which is known, building relation in every element and connecting information with arithmetic operation, connecting between what is being questioned with known information, making equation model to find out the value by using substitution, and building a connection on re-checking, re-reading, and re-counting. The impulsive students’ cognitive style supports important elements in understanding problems, building a connection in every element, connecting information with arithmetic operation, building a relation about a problem comprehensively by connecting between what is being questioned with known information, finding out the unknown value by using arithmetic operation without making any equation model. The result of re-checking problem solving, impulsive student was only reading at glance without re-counting the result of problem solving.

Adults' strategies for simple addition and multiplication: verbal self-reports and the operand recognition paradigm.

PubMed

Metcalfe, Arron W S; Campbell, Jamie I D

2011-05-01

Accurate measurement of cognitive strategies is important in diverse areas of psychological research. Strategy self-reports are a common measure, but C. Thevenot, M. Fanget, and M. Fayol (2007) proposed a more objective method to distinguish different strategies in the context of mental arithmetic. In their operand recognition paradigm, speed of recognition memory for problem operands after solving a problem indexes strategy (e.g., direct memory retrieval vs. a procedural strategy). Here, in 2 experiments, operand recognition time was the same following simple addition or multiplication, but, consistent with a wide variety of previous research, strategy reports indicated much greater use of procedures (e.g., counting) for addition than multiplication. Operation, problem size (e.g., 2 + 3 vs. 8 + 9), and operand format (digits vs. words) had interactive effects on reported procedure use that were not reflected in recognition performance. Regression analyses suggested that recognition time was influenced at least as much by the relative difficulty of the preceding problem as by the strategy used. The findings indicate that the operand recognition paradigm is not a reliable substitute for strategy reports and highlight the potential impact of difficulty-related carryover effects in sequential cognitive tasks.

Influence of the large-small split effect on strategy choice in complex subtraction.

PubMed

Xiang, Yan Hui; Wu, Hao; Shang, Rui Hong; Chao, Xiaomei; Ren, Ting Ting; Zheng, Li Ling; Mo, Lei

2018-04-01

Two main theories have been used to explain the arithmetic split effect: decision-making process theory and strategy choice theory. Using the inequality paradigm, previous studies have confirmed that individuals tend to adopt a plausibility-checking strategy and a whole-calculation strategy to solve large and small split problems in complex addition arithmetic, respectively. This supports strategy choice theory, but it is unknown whether this theory also explains performance in solving different split problems in complex subtraction arithmetic. This study used small, intermediate and large split sizes, with each split condition being further divided into problems requiring and not requiring borrowing. The reaction times (RTs) for large and intermediate splits were significantly shorter than those for small splits, while accuracy was significantly higher for large and middle splits than for small splits, reflecting no speed-accuracy trade-off. Further, RTs and accuracy differed significantly between the borrow and no-borrow conditions only for small splits. This study indicates that strategy choice theory is suitable to explain the split effect in complex subtraction arithmetic. That is, individuals tend to choose the plausibility-checking strategy or the whole-calculation strategy according to the split size. © 2016 International Union of Psychological Science.

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.

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…

Metacognition for strategy selection during arithmetic problem-solving in young and older adults.

PubMed

Geurten, Marie; Lemaire, Patrick

2018-04-19

We examined participants' strategy choices and metacognitive judgments during arithmetic problem-solving. Metacognitive judgments were collected either prospectively or retrospectively. We tested whether metacognitive judgments are related to strategy choices on the current problems and on the immediately following problems, and age-related differences in relations between metacognition and strategy choices. Data showed that both young and older adults were able to make accurate retrospective, but not prospective, judgments. Moreover, the accuracy of retrospective judgments was comparable in young and older adults when participants had to select and execute the better strategy. Metacognitive accuracy was even higher in older adults when participants had to only select the better strategy. Finally, low-confidence judgments on current items were more frequently followed by better strategy selection on immediately succeeding items than high-confidence judgments in both young and older adults. Implications of these findings to further our understanding of age-related differences and similarities in adults' metacognitive monitoring and metacognitive regulation for strategy selection in the context of arithmetic problem solving are discussed.

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

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.

Developing "Algebraic Thinking": Two Key Ways to Establish Some Early Algebraic Ideas in Primary Classrooms

ERIC Educational Resources Information Center

Ormond, Christine

2012-01-01

Primary teachers play a key role in their students' future mathematical success in the early secondary years. While the word "algebra" may make some primary teachers feel uncomfortable or worried, the basic arithmetic ideas underlying algebra are vitally important for older primary students as they are increasingly required to use "algebraic…

Programma srednej skoly. Nacal'nye klassy (Primary School Draft Program).

ERIC Educational Resources Information Center

Academy of Pedagogical Sciences of the USSR, Moscow.

This document is an English-language abstract (approximately 1,500 words) of the draft of new elementary school programs in Russian language, arithmetic, and natural history. Elementary Russian courses are regarded as an organic part of the entire course at the eight-year school. Such courses as phonetics and morphology figure in the draft program…

Program of arithmetic improvement by means of cognitive enhancement: an intervention in children with special educational needs.

PubMed

Deaño, Manuel Deaño; Alfonso, Sonia; Das, Jagannath Prasad

2015-03-01

This study reports the cognitive and arithmetic improvement of a mathematical model based on the program PASS Remedial Program (PREP), which aims to improve specific cognitive processes underlying academic skills such as arithmetic. For this purpose, a group of 20 students from the last four grades of Primary Education was divided into two groups. One group (n=10) received training in the program and the other served as control. Students were assessed at pre and post intervention in the PASS cognitive processes (planning, attention, simultaneous and successive processing), general level of intelligence, and arithmetic performance in calculus and solving problems. Performance of children from the experimental group was significantly higher than that of the control group in cognitive process and arithmetic. This joint enhancement of cognitive and arithmetic processes was a result of the operationalization of training that promotes the encoding task, attention and planning, and learning by induction, mediation and verbalization. The implications of this are discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.

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.

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,…

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…

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.

Age-related differences in strategic monitoring during arithmetic problem solving.

PubMed

Geurten, Marie; Lemaire, Patrick

2017-10-01

We examined the role of metacognitive monitoring in strategic behavior during arithmetic problem solving, a process that is expected to shed light on age-related differences in strategy selection. Young and older adults accomplished better strategy-judgment, better strategy-selection, and strategy-execution tasks. Data showed that participants made better strategy judgments when problems were problems with homogeneous unit digits (i.e., problems with both unit digits smaller or larger than 5; 31×62) relative to problems with heterogeneous unit digits (i.e., problems with one unit digit smaller or larger than 5; 31×67) and when the better strategy was cued on rounding-up problems (e.g., 68×23) compared to rounding-down problems (e.g., 36×53). Results also indicated higher rates of better strategy judgment in young than in older adults. These aging effects differed across problem types. Older adults made more accurate judgments on rounding-up problems than on rounding-down problems when the cued strategy was rounding-up, while young adults did not show such problem-related differences. Moreover, strategy selection correlated with strategy judgment, and even more so in older adults than in young adults. To discuss the implications of these findings, we propose a theoretical framework of how strategy judgments occur in young and older adults and discuss how this framework enables to understand relationships between metacognitive monitoring and strategic behaviors when participants solve arithmetic problems. Copyright © 2017 Elsevier B.V. All rights reserved.

Schema Knowledge Structures for Representing and Understanding Arithmetic Story Problems.

DTIC Science & Technology

1987-03-01

do so on a common unit of measure. Implicit in the CP relation is the concept of one-to- one matching of one element in the problem with the other. As...engages in one-to-one matching , removing one member from each set and setting them apart as a matched pair. The smaller of the two sets is the one...to be critical. As we pointed out earlier, some of the semantic * relations can be present in situations that demand any of * the four arithmetic

Contextualizing symbol, symbolizing context

NASA Astrophysics Data System (ADS)

Maudy, Septiani Yugni; Suryadi, Didi; Mulyana, Endang

2017-08-01

When students learn algebra for the first time, inevitably they are experiencing transition from arithmetic to algebraic thinking. Once students could apprehend this essential mathematical knowledge, they are cultivating their ability in solving daily life problems by applying algebra. However, as we dig into this transitional stage, we identified possible students' learning obstacles to be dealt with seriously in order to forestall subsequent hindrance in studying more advance algebra. We come to realize this recurring problem as we undertook the processes of re-personalization and re-contextualization in which we scrutinize the very basic questions: 1) what is variable, linear equation with one variable and their relationship with the arithmetic-algebraic thinking? 2) Why student should learn such concepts? 3) How to teach those concepts to students? By positioning ourselves as a seventh grade student, we address the possibility of children to think arithmetically when confronted with the problems of linear equation with one variable. To help them thinking algebraically, Bruner's modes of representation developed contextually from concrete to abstract were delivered to enhance their interpretation toward the idea of variables. Hence, from the outset we designed the context for student to think symbolically initiated by exploring various symbols that could be contextualized in order to bridge student traversing the arithmetic-algebraic fruitfully.

Development of common neural representations for distinct numerical problems

PubMed Central

Chang, Ting-Ting; Rosenberg-Lee, Miriam; Metcalfe, Arron W. S.; Chen, Tianwen; Menon, Vinod

2015-01-01

How the brain develops representations for abstract cognitive problems is a major unaddressed question in neuroscience. Here we tackle this fundamental question using arithmetic problem solving, a cognitive domain important for the development of mathematical reasoning. We first examined whether adults demonstrate common neural representations for addition and subtraction problems, two complementary arithmetic operations that manipulate the same quantities. We then examined how the common neural representations for the two problem types change with development. Whole-brain multivoxel representational similarity (MRS) analysis was conducted to examine common coding of addition and subtraction problems in children and adults. We found that adults exhibited significant levels of MRS between the two problem types, not only in the intra-parietal sulcus (IPS) region of the posterior parietal cortex (PPC), but also in ventral temporal-occipital, anterior temporal and dorsolateral prefrontal cortices. Relative to adults, children showed significantly reduced levels of MRS in these same regions. In contrast, no brain areas showed significantly greater MRS between problem types in children. Our findings provide novel evidence that the emergence of arithmetic problem solving skills from childhood to adulthood is characterized by maturation of common neural representations between distinct numerical operations, and involve distributed brain regions important for representing and manipulating numerical quantity. More broadly, our findings demonstrate that representational analysis provides a powerful approach for uncovering fundamental mechanisms by which children develop proficiencies that are a hallmark of human cognition. PMID:26160287

Arithmetic learning in advanced age.

PubMed

Zamarian, Laura; Scherfler, Christoph; Kremser, Christian; Pertl, Marie-Theres; Gizewski, Elke; Benke, Thomas; Delazer, Margarete

2018-01-01

Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger participants, while learning in older people might be more widespread. Overall, our study indicates that arithmetic learning depends on the training intensity as well as on person-related factors including individual age, arithmetic competence before training, memory, and executive functions. In conclusion, we suggest that major progress can be also achieved by older participants, but that interventions have to take into account individual variables in order to provide maximal benefit.

Arithmetic learning in advanced age

PubMed Central

Kremser, Christian; Pertl, Marie-Theres; Gizewski, Elke; Benke, Thomas; Delazer, Margarete

2018-01-01

Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger participants, while learning in older people might be more widespread. Overall, our study indicates that arithmetic learning depends on the training intensity as well as on person-related factors including individual age, arithmetic competence before training, memory, and executive functions. In conclusion, we suggest that major progress can be also achieved by older participants, but that interventions have to take into account individual variables in order to provide maximal benefit. PMID:29489905

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.

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.

Deaf and hard of hearing students' problem-solving strategies with signed arithmetic story problems.

PubMed

Pagliaro, Claudia M; Ansell, Ellen

2012-01-01

The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e., modeling, counting, and fact-based strategies), they showed an overwhelming use of counting strategies for all types of problems and at all ages. This difference may have its roots in language or instruction (or in both), and calls attention to the need for conceptual rather than procedural mathematics instruction for deaf and hard of hearing students.

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…

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…

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…

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…

Neural correlates of mathematical problem solving.

PubMed

Lin, Chun-Ling; Jung, Melody; Wu, Ying Choon; She, Hsiao-Ching; Jung, Tzyy-Ping

2015-03-01

This study explores electroencephalography (EEG) brain dynamics associated with mathematical problem solving. EEG and solution latencies (SLs) were recorded as 11 neurologically healthy volunteers worked on intellectually challenging math puzzles that involved combining four single-digit numbers through basic arithmetic operators (addition, subtraction, division, multiplication) to create an arithmetic expression equaling 24. Estimates of EEG spectral power were computed in three frequency bands - θ (4-7 Hz), α (8-13 Hz) and β (14-30 Hz) - over a widely distributed montage of scalp electrode sites. The magnitude of power estimates was found to change in a linear fashion with SLs - that is, relative to a base of power spectrum, theta power increased with longer SLs, while alpha and beta power tended to decrease. Further, the topographic distribution of spectral fluctuations was characterized by more pronounced asymmetries along the left-right and anterior-posterior axes for solutions that involved a longer search phase. These findings reveal for the first time the topography and dynamics of EEG spectral activities important for sustained solution search during arithmetical problem solving.

One-Hundred Years of pH

ERIC Educational Resources Information Center

Myers, Rollie J.

2010-01-01

The idea of expressing the hydrogen-ion concentration on a log arithmetic scale was presented by S. P. L. Sorensen in 1909. The symbol that he used was the letter p and a smaller H appearing almost as a subscript. Typographical convenience led journals to adopt the current symbol. It has been common to assume that the p represented a word such as…

How Does the Representational Status of To-Be-Counted Objects Affect Children's Understanding of Cardinality?

ERIC Educational Resources Information Center

Petersen, Lori A.

2013-01-01

When counting, the final word used to tag the final item in a set represents the cardinality, or total number, of the set. Understanding of this concept serves as a foundation for children's basic mathematical skills, such as arithmetic. However, little is known about how variations in the early learning environment affect children's understanding…

Structural mapping in statistical word problems: A relational reasoning approach to Bayesian inference.

PubMed

Johnson, Eric D; Tubau, Elisabet

2017-06-01

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations.

Moving along the number line: operational momentum in nonsymbolic arithmetic.

PubMed

McCrink, Koleen; Dehaene, Stanislas; Dehaene-Lambertz, Ghislaine

2007-11-01

Can human adults perform arithmetic operations with large approximate numbers, and what effect, if any, does an internal spatial-numerical representation of numerical magnitude have on their responses? We conducted a psychophysical study in which subjects viewed several hundred short videos of sets of objects being added or subtracted from one another and judged whether the final numerosity was correct or incorrect. Over a wide range of possible outcomes, the subjects' responses peaked at the approximate location of the true numerical outcome and gradually tapered off as a function of the ratio of the true and proposed outcomes (Weber's law). Furthermore, an operational momentum effect was observed, whereby addition problems were overestimated and subtraction problems were underestimated. The results show that approximate arithmetic operates according to precise quantitative rules, perhaps analogous to those characterizing movement on an internal continuum.

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

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.

The Ability of Conceptual Monitoring and the Quality of Working Memory at Children With Calculation Difficulties

ERIC Educational Resources Information Center

Arsic, Sladjana; Eminovic, Fadilj; Stankovic, Ivona

2011-01-01

Calculia is considered to be the ability of performing arithmetic operations, the preconditions for the development of mathematical skills in the complex functioning of psychological functions represented in neuro-anatomical systems, as well in the interaction with the environment. Problems in acquiring arithmetic skills can be described as…

On r-circulant matrices with Fibonacci and Lucas numbers having arithmetic indices

NASA Astrophysics Data System (ADS)

Bueno, Aldous Cesar F.

2017-11-01

We investigate r-circulant matrices whose entries are Fibonacci and Lucas numbers having arithmetic indices. We then solve for the eigenvalues, determinant, Euclidean norm and the bounds for the spectral norm of the matrices. We also present some special cases and some results on identities and divisibility. Lastly, we present an open problem.

Investigating Children's Understanding of Inversion Using the Missing Number Paradigm

ERIC Educational Resources Information Center

Gilmore, Camilla K.

2006-01-01

The development of conceptual understanding in arithmetic is a gradual process and children may make use of a concept in some situations before others. Previous research has demonstrated that when children are given arithmetic problems with an inverse relationship they can infer that the initial and final quantities are the same. However, we do…

Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

ERIC Educational Resources Information Center

Hickendorff, Marian; Heiser, Willem J.; van Putten, Cornelis M.; Verhelst, Norman D.

2009-01-01

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in…

Spatial Skills as a Predictor of First Grade Girls' Use of Higher Level Arithmetic Strategies

ERIC Educational Resources Information Center

Laski, Elida V.; Casey, Beth M.; Yu, Qingyi; Dulaney, Alana; Heyman, Miriam; Dearing, Eric

2013-01-01

Girls are more likely than boys to use counting strategies rather than higher-level mental strategies to solve arithmetic problems. Prior research suggests that dependence on counting strategies may have negative implications for girls' later math achievement. We investigated the relation between first-grade girls' verbal and spatial skills and…

Functional neuroanatomy of arithmetic and word reading and its relationship to age

PubMed Central

Evans, Tanya M.; Flowers, D. Lynn; Luetje, Megan M.; Napoliello, Eileen; Eden, Guinevere F.

2016-01-01

Arithmetic and written language are uniquely human skills acquired during early schooling and used daily. While prior studies have independently characterized the neural bases for arithmetic and reading, here we examine both skills in a single study to capture their shared and unique cognitive mechanisms, as well as the role of age/experience in modulating their neural representations. We used functional MRI in 7- to 29-year-olds who performed single-digit subtraction, single-digit addition, and single-word reading. Using a factorial design, we examined the main effects of Task (subtraction, addition, reading) and Age (as a continuous variable), and their interactions. A main effect of Task revealed preferential activation for subtraction in bilateral intraparietal sulci and supramarginal gyri, right insula, inferior frontal gyrus, and cingulate. The right middle temporal gyrus and left superior temporal gyrus were preferentially active for both addition and reading, and left fusiform gyrus was preferentially active for reading. A main effect of Age revealed increased activity in older participants in right angular gyrus, superior temporal sulcus, and putamen, and less activity in left supplementary motor area, suggesting a left frontal to right temporo-parietal shift of activity with increasing age/experience across all tasks. Interactions for Task by Age were found in right hippocampus and left middle frontal gyrus, with older age invoking greater activity for addition and at the same time less activity for subtraction and reading. Together, in a study conducted in the same participants using similar task and acquisition parameters, the results reveal the neural substrates of these educationally relevant cognitive skills in typical participants in the context of age/experience. PMID:27566261

Study the Problem.

ERIC Educational Resources Information Center

Choate, Joyce S.

1990-01-01

The initial step of a strategic process for solving mathematical problems, "studying the question," is discussed. A lesson plan for teaching students to identify and revise arithmetic problems is presented, involving directed instruction and supervised practice. (JDD)

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.

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

Sound arithmetic: auditory cues in the rehabilitation of impaired fact retrieval.

PubMed

Domahs, Frank; Zamarian, Laura; Delazer, Margarete

2008-04-01

The present single case study describes the rehabilitation of an acquired impairment of multiplication fact retrieval. In addition to a conventional drill approach, one set of problems was preceded by auditory cues while the other half was not. After extensive repetition, non-specific improvements could be observed for all trained problems (e.g., 3 * 7) as well as for their non-trained complementary problems (e.g., 7 * 3). Beyond this general improvement, specific therapy effects were found for problems trained with auditory cues. These specific effects were attributed to an involvement of implicit memory systems and/or attentional processes during training. Thus, the present results demonstrate that cues in the training of arithmetic facts do not have to be visual to be effective.

How are things adding up? Neural differences between arithmetic operations are due to general problem solving strategies.

PubMed

Tschentscher, Nadja; Hauk, Olaf

2014-05-15

A number of previous studies have interpreted differences in brain activation between arithmetic operation types (e.g. addition and multiplication) as evidence in favor of distinct cortical representations, processes or neural systems. It is still not clear how differences in general task complexity contribute to these neural differences. Here, we used a mental arithmetic paradigm to disentangle brain areas related to general problem solving from those involved in operation type specific processes (addition versus multiplication). We orthogonally varied operation type and complexity. Importantly, complexity was defined not only based on surface criteria (for example number size), but also on the basis of individual participants' strategy ratings, which were validated in a detailed behavioral analysis. We replicated previously reported operation type effects in our analyses based on surface criteria. However, these effects vanished when controlling for individual strategies. Instead, procedural strategies contrasted with memory retrieval reliably activated fronto-parietal and motor regions, while retrieval strategies activated parietal cortices. This challenges views that operation types rely on partially different neural systems, and suggests that previously reported differences between operation types may have emerged due to invalid measures of complexity. We conclude that mental arithmetic is a powerful paradigm to study brain networks of abstract problem solving, as long as individual participants' strategies are taken into account. Copyright © 2014 Elsevier Inc. All rights reserved.

[A case of pure anarithmetia associated with disability in processing of abstract spatial relationship].

PubMed

Hirayama, Kazumi; Taguchi, Yuzuru; Tsukamoto, Tetsuro

2002-10-01

A 35-year-old right handed man developed pure anarithmetia after an left parieto-occipital subcortical hemorrhage. His intelligence, memory, language, and construction ability were all within normal limits. No hemispatial neglect, agraphia, finger agnosia, or right-left disorientation were noted. He showed no impairments in reading numbers aloud, pointing to written numbers, writing numbers to dictation, decomposition of numbers, estimation of numbers of dots, reading and writing of arithmetic signs, comprehension of arithmetic signs, appreciation of number values, appreciation of dots' number, counting aloud, alignment numbers, comprehension of the commulative law and the distributive law, retrieval of the table value (ku-ku), immediate memory for arithmetic problems, and use of electric calculator. He showed, however, remarkable difficulty even in addition and subtraction between one figure digits, and used counting on his fingers or intuitive strategy to solve the problems even when he could solve them. He could not execute multiplication and division, if the problems required other than the table value (ku-ku). Thus, he seemed to have difficulties in both of elemental arithmetic facts and calculating procedures. In addition, his backward digit span and reading of analogue clocks were deteriorated, and he showed logico-grammatical disorder of Luria. Our case supports the notion that there is a neural system which was shared in part between processing of abstract spatial relationship and calculation.

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.

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.

A Single-Boundary Accumulator Model of Response Times in an Addition Verification Task

PubMed Central

Faulkenberry, Thomas J.

2017-01-01

Current theories of mathematical cognition offer competing accounts of the interplay between encoding and calculation in mental arithmetic. Additive models propose that manipulations of problem format do not interact with the cognitive processes used in calculation. Alternatively, interactive models suppose that format manipulations have a direct effect on calculation processes. In the present study, we tested these competing models by fitting participants' RT distributions in an arithmetic verification task with a single-boundary accumulator model (the shifted Wald distribution). We found that in addition to providing a more complete description of RT distributions, the accumulator model afforded a potentially more sensitive test of format effects. Specifically, we found that format affected drift rate, which implies that problem format has a direct impact on calculation processes. These data give further support for an interactive model of mental arithmetic. PMID:28769853

Frontal and Parietal Cortices Show Different Spatiotemporal Dynamics across Problem-solving Stages.

PubMed

Tschentscher, Nadja; Hauk, Olaf

2016-08-01

Arithmetic problem-solving can be conceptualized as a multistage process ranging from task encoding over rule and strategy selection to step-wise task execution. Previous fMRI research suggested a frontal-parietal network involved in the execution of complex numerical and nonnumerical tasks, but evidence is lacking on the particular contributions of frontal and parietal cortices across time. In an arithmetic task paradigm, we evaluated individual participants' "retrieval" and "multistep procedural" strategies on a trial-by-trial basis and contrasted those in time-resolved analyses using combined EEG and MEG. Retrieval strategies relied on direct retrieval of arithmetic facts (e.g., 2 + 3 = 5). Procedural strategies required multiple solution steps (e.g., 12 + 23 = 12 + 20 + 3 or 23 + 10 + 2). Evoked source analyses revealed independent activation dynamics within the first second of problem-solving in brain areas previously described as one network, such as the frontal-parietal cognitive control network: The right frontal cortex showed earliest effects of strategy selection for multistep procedural strategies around 300 msec, before parietal cortex activated around 700 msec. In time-frequency source power analyses, memory retrieval and multistep procedural strategies were differentially reflected in theta, alpha, and beta frequencies: Stronger beta and alpha desynchronizations emerged for procedural strategies in right frontal, parietal, and temporal regions as function of executive demands. Arithmetic fact retrieval was reflected in right prefrontal increases in theta power. Our results demonstrate differential brain dynamics within frontal-parietal networks across the time course of a problem-solving process, and analyses of different frequency bands allowed us to disentangle cortical regions supporting the underlying memory and executive functions.

Arithmetical Computation: Competence after Three Years of Learning under Differing Instructional Programs.

ERIC Educational Resources Information Center

Brownell, William A.; And Others

Reported are the results and conclusions of an arithmetic investigation made in the schools of Scotland in the spring and fall of 1966. The first problem in this investigation was to ascertain which, if either, of two unlike programs of instruction was more effective in developing skill in computation. The second was to determine the value of an…

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…

Children's patterns of reasoning about reading and addition concepts.

PubMed

Farrington-Flint, Lee; Canobi, Katherine H; Wood, Clare; Faulkner, Dorothy

2010-06-01

Children's reasoning was examined within two educational contexts (word reading and addition) so as to understand the factors that contribute to relational reasoning in the two domains. Sixty-seven 5- to 7-year-olds were given a series of related words to read or single-digit addition items to solve (interspersed with unrelated items). The frequency, accuracy, and response times of children's self-reports on the conceptually related items provided a measure of relational reasoning, while performance on the unrelated addition and reading items provided a measure of procedural skill. The results indicated that the children's ability to use conceptual relations to solve both reading and addition problems enhanced speed and accuracy levels, increased with age, and was related to procedural skill. However, regression analyses revealed that domain-specific competencies can best explain the use of conceptual relations in both reading and addition. Moreover, a cluster analysis revealed that children differ according to the academic domain in which they first apply conceptual relations and these differences are related to individual variation in their procedural skills within these particular domains. These results highlight the developmental significance of relational reasoning in the context of reading and addition and underscore the importance of concept-procedure links in explaining children's literacy and arithmetical development.

Research in the design of high-performance reconfigurable systems

NASA Technical Reports Server (NTRS)

Slotnick, D. L.; Mcewan, S. D.; Spry, A. J.

1984-01-01

An initial design for the Bit Processor (BP) referred to in prior reports as the Processing Element or PE has been completed. Eight BP's, together with their supporting random-access memory, a 64 k x 9 ROM to perform addition, routing logic, and some additional logic, constitute the components of a single stage. An initial stage design is given. Stages may be combined to perform high-speed fixed or floating point arithmetic. Stages can be configured into a range of arithmetic modules that includes bit-serial one or two-dimensional arrays; one or two dimensional arrays fixed or floating point processors; and specialized uniprocessors, such as long-word arithmetic units. One to eight BP's represent a likely initial chip level. The Stage would then correspond to a first-level pluggable module. As both this project and VLSI CAD/CAM progress, however, it is expected that the chip level would migrate upward to the stage and, perhaps, ultimately the box level. The BP RAM, consisting of two banks, holds only operands and indices. Programs are at the box (high-level function) and system level. At the system level initial effort has been concentrated on specifying the tools needed to evaluate design alternatives.

Costs of Military Pay and Benefits in the Defense Budget

DTIC Science & Technology

2012-11-01

arithmetic reasoning, mathematics knowledge, paragraph comprehension, and word knowledge. Percentile scores measure aptitude relative to the entire...is not actuarially fair—it does not financially compensate the military retiree for what could easily be four decades of smaller annuity pay- ments...during a month in which the member is serving in a designated combat zone.37 One report estimates that to achieve an actuarially fair out- come, the

Working Memory Training Does Not Improve Performance on Measures of Intelligence or Other Measures of “Far Transfer”

PubMed Central

Melby-Lervåg, Monica; Redick, Thomas S.; Hulme, Charles

2016-01-01

It has been claimed that working memory training programs produce diverse beneficial effects. This article presents a meta-analysis of working memory training studies (with a pretest-posttest design and a control group) that have examined transfer to other measures (nonverbal ability, verbal ability, word decoding, reading comprehension, or arithmetic; 87 publications with 145 experimental comparisons). Immediately following training there were reliable improvements on measures of intermediate transfer (verbal and visuospatial working memory). For measures of far transfer (nonverbal ability, verbal ability, word decoding, reading comprehension, arithmetic) there was no convincing evidence of any reliable improvements when working memory training was compared with a treated control condition. Furthermore, mediation analyses indicated that across studies, the degree of improvement on working memory measures was not related to the magnitude of far-transfer effects found. Finally, analysis of publication bias shows that there is no evidential value from the studies of working memory training using treated controls. The authors conclude that working memory training programs appear to produce short-term, specific training effects that do not generalize to measures of “real-world” cognitive skills. These results seriously question the practical and theoretical importance of current computerized working memory programs as methods of training working memory skills. PMID:27474138

The Arithmetic Project Course for Teachers - 16. Topic: Composition (continued). Supplement: More Problems With Composition of Number Line Rules.

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…

Fault-tolerant arithmetic via time-shared TMR

NASA Astrophysics Data System (ADS)

Swartzlander, Earl E.

1999-11-01

Fault tolerance is increasingly important as society has come to depend on computers for more and more aspects of daily life. The current concern about the Y2K problems indicates just how much we depend on accurate computers. This paper describes work on time- shared TMR, a technique which is used to provide arithmetic operations that produce correct results in spite of circuit faults.

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.

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

Individual strategy ratings improve the control for task difficulty effects in arithmetic problem solving paradigms.

PubMed

Tschentscher, Nadja; Hauk, Olaf

2015-01-01

Mental arithmetic is a powerful paradigm to study problem solving using neuroimaging methods. However, the evaluation of task complexity varies significantly across neuroimaging studies. Most studies have parameterized task complexity by objective features such as the number size. Only a few studies used subjective rating procedures. In fMRI, we provided evidence that strategy self-reports control better for task complexity across arithmetic conditions than objective features (Tschentscher and Hauk, 2014). Here, we analyzed the relative predictive value of self-reported strategies and objective features for performance in addition and multiplication tasks, by using a paradigm designed for neuroimaging research. We found a superiority of strategy ratings as predictor of performance above objective features. In a Principal Component Analysis on reaction times, the first component explained over 90 percent of variance and factor loadings reflected percentages of self-reported strategies well. In multiple regression analyses on reaction times, self-reported strategies performed equally well or better than objective features, depending on the operation type. A Receiver Operating Characteristic (ROC) analysis confirmed this result. Reaction times classified task complexity better when defined by individual ratings. This suggests that participants' strategy ratings are reliable predictors of arithmetic complexity and should be taken into account in neuroimaging research.

Individual strategy ratings improve the control for task difficulty effects in arithmetic problem solving paradigms

PubMed Central

Tschentscher, Nadja; Hauk, Olaf

2015-01-01

Mental arithmetic is a powerful paradigm to study problem solving using neuroimaging methods. However, the evaluation of task complexity varies significantly across neuroimaging studies. Most studies have parameterized task complexity by objective features such as the number size. Only a few studies used subjective rating procedures. In fMRI, we provided evidence that strategy self-reports control better for task complexity across arithmetic conditions than objective features (Tschentscher and Hauk, 2014). Here, we analyzed the relative predictive value of self-reported strategies and objective features for performance in addition and multiplication tasks, by using a paradigm designed for neuroimaging research. We found a superiority of strategy ratings as predictor of performance above objective features. In a Principal Component Analysis on reaction times, the first component explained over 90 percent of variance and factor loadings reflected percentages of self-reported strategies well. In multiple regression analyses on reaction times, self-reported strategies performed equally well or better than objective features, depending on the operation type. A Receiver Operating Characteristic (ROC) analysis confirmed this result. Reaction times classified task complexity better when defined by individual ratings. This suggests that participants’ strategy ratings are reliable predictors of arithmetic complexity and should be taken into account in neuroimaging research. PMID:26321997

Mathematical modelling of Bit-Level Architecture using Reciprocal Quantum Logic

NASA Astrophysics Data System (ADS)

Narendran, S.; Selvakumar, J.

2018-04-01

Efficiency of high-performance computing is on high demand with both speed and energy efficiency. Reciprocal Quantum Logic (RQL) is one of the technology which will produce high speed and zero static power dissipation. RQL uses AC power supply as input rather than DC input. RQL has three set of basic gates. Series of reciprocal transmission lines are placed in between each gate to avoid loss of power and to achieve high speed. Analytical model of Bit-Level Architecture are done through RQL. Major drawback of reciprocal Quantum Logic is area, because of lack in proper power supply. To achieve proper power supply we need to use splitters which will occupy large area. Distributed arithmetic uses vector- vector multiplication one is constant and other is signed variable and each word performs as a binary number, they rearranged and mixed to form distributed system. Distributed arithmetic is widely used in convolution and high performance computational devices.

Self-Regulation as an Aid to Human Effectiveness and Biocybernetics Technology and Behavior

DTIC Science & Technology

1976-01-01

feedback and two measures of information-processing capacity: short-term memory for digits and choice-reaction times. In this study, Beatty selected...Kamiya, like Beatty, found EEG activity unrelated to both memory for words and a simple reaction-time test. In another study, Kamiya (1972...creative intelligence, visual memory , mental arithmetic, digit memory span, and i,une tracking. The results were negative. Kamiya concluded that the self

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.

Neural predictors of individual differences in response to math tutoring in primary-grade school children

PubMed Central

Supekar, Kaustubh; Swigart, Anna G.; Tenison, Caitlin; Jolles, Dietsje D.; Rosenberg-Lee, Miriam; Fuchs, Lynn; Menon, Vinod

2013-01-01

Now, more than ever, the ability to acquire mathematical skills efficiently is critical for academic and professional success, yet little is known about the behavioral and neural mechanisms that drive some children to acquire these skills faster than others. Here we investigate the behavioral and neural predictors of individual differences in arithmetic skill acquisition in response to 8-wk of one-to-one math tutoring. Twenty-four children in grade 3 (ages 8–9 y), a critical period for acquisition of basic mathematical skills, underwent structural and resting-state functional MRI scans pretutoring. A significant shift in arithmetic problem-solving strategies from counting to fact retrieval was observed with tutoring. Notably, the speed and accuracy of arithmetic problem solving increased with tutoring, with some children improving significantly more than others. Next, we examined whether pretutoring behavioral and brain measures could predict individual differences in arithmetic performance improvements with tutoring. No behavioral measures, including intelligence quotient, working memory, or mathematical abilities, predicted performance improvements. In contrast, pretutoring hippocampal volume predicted performance improvements. Furthermore, pretutoring intrinsic functional connectivity of the hippocampus with dorsolateral and ventrolateral prefrontal cortices and the basal ganglia also predicted performance improvements. Our findings provide evidence that individual differences in morphometry and connectivity of brain regions associated with learning and memory, and not regions typically involved in arithmetic processing, are strong predictors of responsiveness to math tutoring in children. More generally, our study suggests that quantitative measures of brain structure and intrinsic brain organization can provide a more sensitive marker of skill acquisition than behavioral measures. PMID:23630286

Neural predictors of individual differences in response to math tutoring in primary-grade school children.

PubMed

Supekar, Kaustubh; Swigart, Anna G; Tenison, Caitlin; Jolles, Dietsje D; Rosenberg-Lee, Miriam; Fuchs, Lynn; Menon, Vinod

2013-05-14

Now, more than ever, the ability to acquire mathematical skills efficiently is critical for academic and professional success, yet little is known about the behavioral and neural mechanisms that drive some children to acquire these skills faster than others. Here we investigate the behavioral and neural predictors of individual differences in arithmetic skill acquisition in response to 8-wk of one-to-one math tutoring. Twenty-four children in grade 3 (ages 8-9 y), a critical period for acquisition of basic mathematical skills, underwent structural and resting-state functional MRI scans pretutoring. A significant shift in arithmetic problem-solving strategies from counting to fact retrieval was observed with tutoring. Notably, the speed and accuracy of arithmetic problem solving increased with tutoring, with some children improving significantly more than others. Next, we examined whether pretutoring behavioral and brain measures could predict individual differences in arithmetic performance improvements with tutoring. No behavioral measures, including intelligence quotient, working memory, or mathematical abilities, predicted performance improvements. In contrast, pretutoring hippocampal volume predicted performance improvements. Furthermore, pretutoring intrinsic functional connectivity of the hippocampus with dorsolateral and ventrolateral prefrontal cortices and the basal ganglia also predicted performance improvements. Our findings provide evidence that individual differences in morphometry and connectivity of brain regions associated with learning and memory, and not regions typically involved in arithmetic processing, are strong predictors of responsiveness to math tutoring in children. More generally, our study suggests that quantitative measures of brain structure and intrinsic brain organization can provide a more sensitive marker of skill acquisition than behavioral measures.

Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications.

PubMed

Zimmerman, Federico; Shalom, Diego; Gonzalez, Pablo A; Garrido, Juan Manuel; Alvarez Heduan, Facundo; Dehaene, Stanislas; Sigman, Mariano; Rieznik, Andres

2016-01-01

We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the main principles derived in a long tradition of investigation: size effect, tie effect, size-tie interaction effect, five-effect, RTs and error rates correlation effect, and most common error effect. Our dataset allowed us to perform a robust analysis of order effects for each individual problem, for which there is controversy both in experimental findings and in the predictions of theoretical models. For addition problems, the order effect was dominated by a max-then-min structure (i.e 7+4 is easier than 4+7). This result is predicted by models in which additions are performed as a translation starting from the first addend, with a distance given by the second addend. In multiplication, we observed a dominance of two effects: (1) a max-then-min pattern that can be accounted by the fact that it is easier to perform fewer additions of the largest number (i.e. 8x3 is easier to compute as 8+8+8 than as 3+3+…+3) and (2) a phonological effect by which problems for which there is a rhyme (i.e. "seis por cuatro es veinticuatro") are performed faster. Above and beyond these results, our study bares an important practical conclusion, as proof of concept, that participants can be motivated to perform substantial arithmetic training simply by presenting it in a gamified format.

Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications

PubMed Central

Zimmerman, Federico; Shalom, Diego; Gonzalez, Pablo A.; Garrido, Juan Manuel; Alvarez Heduan, Facundo; Dehaene, Stanislas; Sigman, Mariano; Rieznik, Andres

2016-01-01

We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the main principles derived in a long tradition of investigation: size effect, tie effect, size-tie interaction effect, five-effect, RTs and error rates correlation effect, and most common error effect. Our dataset allowed us to perform a robust analysis of order effects for each individual problem, for which there is controversy both in experimental findings and in the predictions of theoretical models. For addition problems, the order effect was dominated by a max-then-min structure (i.e 7+4 is easier than 4+7). This result is predicted by models in which additions are performed as a translation starting from the first addend, with a distance given by the second addend. In multiplication, we observed a dominance of two effects: (1) a max-then-min pattern that can be accounted by the fact that it is easier to perform fewer additions of the largest number (i.e. 8x3 is easier to compute as 8+8+8 than as 3+3+…+3) and (2) a phonological effect by which problems for which there is a rhyme (i.e. "seis por cuatro es veinticuatro") are performed faster. Above and beyond these results, our study bares an important practical conclusion, as proof of concept, that participants can be motivated to perform substantial arithmetic training simply by presenting it in a gamified format. PMID:28033357

The Adidactic Interaction with the Procedures of Peers in the Transition from Arithmetic to Algebra: A "Milieu" for the Emergence of New Questions

ERIC Educational Resources Information Center

Sadovsky, Patricia; Sessa, Carmen

2005-01-01

The purpose of the present article is to give an account of the emergence of knowledge pertaining to the transition from arithmetic to algebra in the course of a debate in a grade 7 classroom. This debate follows two other instances of work: (1) the adidactic interaction between each student and a given problem, (2) the adidactic interaction of…

Students creative thinking skills in solving two dimensional arithmetic series through research-based learning

NASA Astrophysics Data System (ADS)

Tohir, M.; Abidin, Z.; Dafik; Hobri

2018-04-01

Arithmetics is one of the topics in Mathematics, which deals with logic and detailed process upon generalizing formula. Creativity and flexibility are needed in generalizing formula of arithmetics series. This research aimed at analyzing students creative thinking skills in generalizing arithmetic series. The triangulation method and research-based learning was used in this research. The subjects were students of the Master Program of Mathematics Education in Faculty of Teacher Training and Education at Jember University. The data was collected by giving assignments to the students. The data collection was done by giving open problem-solving task and documentation study to the students to arrange generalization pattern based on the dependent function formula i and the function depend on i and j. Then, the students finished the next problem-solving task to construct arithmetic generalization patterns based on the function formula which depends on i and i + n and the sum formula of functions dependent on i and j of the arithmetic compiled. The data analysis techniques operative in this study was Miles and Huberman analysis model. Based on the result of data analysis on task 1, the levels of students creative thinking skill were classified as follows; 22,22% of the students categorized as “not creative” 38.89% of the students categorized as “less creative” category; 22.22% of the students categorized as “sufficiently creative” and 16.67% of the students categorized as “creative”. By contrast, the results of data analysis on task 2 found that the levels of students creative thinking skills were classified as follows; 22.22% of the students categorized as “sufficiently creative”, 44.44% of the students categorized as “creative” and 33.33% of the students categorized as “very creative”. This analysis result can set the basis for teaching references and actualizing a better teaching model in order to increase students creative thinking skills.

Lack of interaction between a new antihistamine, mizolastine, and lorazepam on psychomotor performance and memory in healthy volunteers.

PubMed

Patat, A; Perault, M C; Vandel, B; Ulliac, N; Zieleniuk, I; Rosenzweig, P

1995-01-01

1. The possible interaction between a new H1 antihistamine, mizolastine, and lorazepam was assessed in a randomised, double-blind, cross-over, placebo-controlled study involving 16 healthy young male volunteers who received mizolastine 10 mg or placebo once daily for 8 days with a 1 week wash-out interval. The interaction of mizolastine, at steady-state, with a single oral dose of lorazepam or placebo was assessed on days 6 or 8 of each treatment period. 2. Psychomotor performance and cognitive function were evaluated using objective tests (critical flicker fusion threshold, choice reaction time, tapping, arithmetic calculation, body sway) and self-ratings (visual analogue scale, ARCI) before and at 2, 4, 6 and 8 h after dosing. Short-term memory (Sternberg memory scanning immediate free recall of a word list) and long-term memory (delayed free recall and recognition of words and pictures) were assessed before and at 3 h after dosing. Pharmacodynamic interactions were evaluated by repeated measures ANOVA in a 2 x 2 factorial interaction model. 3. Mizolastine, 10 mg once daily, at steady-state, was devoid of sedation and detrimental effect on skilled performance and memory. 4. In contrast, a single 2 mg dose of lorazepam produced marked impairment of psychomotor performance, cognitive functions (significant reduction in flicker fusion threshold, tapping and arithmetic calculation and increase in reaction times and body sway) and subjective sedation from 2 to 8 h after dosing. In addition, lorazepam induced an anterograde amnesia, characterised by a decrease in delayed free recall and recognition, and a deficit in short term memory.(ABSTRACT TRUNCATED AT 250 WORDS)

Technical Mathematics.

ERIC Educational Resources Information Center

Flannery, Carol A.

This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…

Learning disability subtypes and the role of attention during the naming of pictures and words: an event-related potential analysis.

PubMed

Greenham, Stephanie L; Stelmack, Robert M; van der Vlugt, Harry

2003-01-01

The role of attention in the processing of pictures and words was investigated for a group of normally achieving children and for groups of learning disability sub-types that were defined by deficient performance on tests of reading and spelling (Group RS) and of arithmetic (Group A). An event-related potential (ERP) recording paradigm was employed in which the children were required to attend to and name either pictures or words that were presented individually or in superimposed picture-word arrays that varied in degree of semantic relation. For Group RS, the ERP waves to words, both presented individually or attended in the superimposed array, exhibited reduced N450 amplitude relative to controls, whereas their ERP waves to pictures were normal. This suggests that the word-naming deficiency for Group RS is not a selective attention deficit but rather a specific linguistic deficit that develops at a later stage of processing. In contrast to Group RS and controls, Group A did not exhibit reliable early frontal negative waves (N280) to the super-imposed pictures and words, an effect that may reflect a selective attention deficit for these children that develops at an early stage of visuo-spatial processing. These early processing differences were also evident in smaller amplitude N450 waves for Group A when naming either pictures or words in the superimposed arrays.

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.

Dyscalculia and Other Learning Problems in Arithmetic: A Historical Perspective.

ERIC Educational Resources Information Center

Sharma, Mahesh C.

1986-01-01

Evidence on learning problems due to dyscalculia is surveyed. Definitions, factors responsible for dyscalculia, split-brain research and hemispheric roles, mathematics learning problems and personality, materials for instruction, and levels of knowing mathematics are among the topics discussed with an extensive list of references. (MNS)

Working Memory Training Does Not Improve Performance on Measures of Intelligence or Other Measures of "Far Transfer": Evidence From a Meta-Analytic Review.

PubMed

Melby-Lervåg, Monica; Redick, Thomas S; Hulme, Charles

2016-07-01

It has been claimed that working memory training programs produce diverse beneficial effects. This article presents a meta-analysis of working memory training studies (with a pretest-posttest design and a control group) that have examined transfer to other measures (nonverbal ability, verbal ability, word decoding, reading comprehension, or arithmetic; 87 publications with 145 experimental comparisons). Immediately following training there were reliable improvements on measures of intermediate transfer (verbal and visuospatial working memory). For measures of far transfer (nonverbal ability, verbal ability, word decoding, reading comprehension, arithmetic) there was no convincing evidence of any reliable improvements when working memory training was compared with a treated control condition. Furthermore, mediation analyses indicated that across studies, the degree of improvement on working memory measures was not related to the magnitude of far-transfer effects found. Finally, analysis of publication bias shows that there is no evidential value from the studies of working memory training using treated controls. The authors conclude that working memory training programs appear to produce short-term, specific training effects that do not generalize to measures of "real-world" cognitive skills. These results seriously question the practical and theoretical importance of current computerized working memory programs as methods of training working memory skills. © The Author(s) 2016.

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

Translation of one high-level language to another: COBOL to ADA, an example

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

Hill, J.A.

1986-01-01

This dissertation discusses the difficulties encountered in, and explores possible solutions to, the task of automatically converting programs written in one HLL, COBOL, into programs written in another HLL, Ada, and still maintain readability. This paper presents at least one set of techniques and algorithms to solve many of the problems that were encountered. The differing view of records is solved by isolating those instances where it is a problem, then using the RENAMES option of Ada. Several solutions to doing the decimal-arithmetic translation are discussed. One method used is to emulate COBOL arithmetic in an arithmetic package. Another partialmore » solution suggested is to convert the values to decimal-scaled integers and use modular arithmetic. Conversion to fixed-point type and floating-point type are the third and fourth methods. The work of another researcher, Bobby Othmer, is utilized to correct any unstructured code, to remap statements not directly translatable such as ALTER, and to pull together isolated code sections. Algorithms are then presented to convert this restructured COBOL code into Ada code with local variables, parameters, and packages. The input/output requirements are partially met by mapping them to a series of procedure calls that interface with Ada's standard input-output package. Several examples are given of hand translations of COBOL programs. In addition, a possibly new method is shown for measuring the readability of programs.« less

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 .

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

ABC Problem in Elementary Mathematics Education: Arithmetic "before" Comprehension

ERIC Educational Resources Information Center

Boote, Stacy K.; Boote, David N.

2018-01-01

Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a…

Cognitive Functioning in Children with Learning Problems

ERIC Educational Resources Information Center

Schwenck, Christina; Dummert, Friederike; Endlich, Darius; Schneider, Wolfgang

2015-01-01

Several cognitive deficits associated with reading and mathematics problems have been identified. However, only few studies assessed the impact of these variables in children with combined problems in reading and arithmetics, and none of these studies included children with low IQ. This longitudinal study was designed to assess the impact of…

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.

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.

Do calendrical savants use calculation to answer date questions? A functional magnetic resonance imaging study

PubMed Central

Cowan, Richard; Frith, Chris

2009-01-01

Calendrical savants can name the weekdays for dates from different years with remarkable speed and accuracy. Whether calculation rather than just memory is involved is disputed. Grounds for doubting whether they can calculate are reviewed and criteria for attributing date calculation skills to them are discussed. At least some calendrical savants possess date calculation skills. A behavioural characteristic observed in many calendrical savants is increased response time for questions about more remote years. This may be because more remote years require more calculation or because closer years are more practised. An experiment is reported that used functional magnetic resonance imaging to attempt to discriminate between these explanations. Only two savants could be scanned and excessive head movement corrupted one savant's mental arithmetic data. Nevertheless, there was increased parietal activation during both mental arithmetic and date questions and this region showed increased activity with more remote dates. These results suggest that the calendrical skills observed in savants result from intensive practice with calculations used in solving mental arithmetic problems. The mystery is not how they solve these problems, but why. PMID:19528025

The Effects of Schema-Broadening Instruction on Second Graders’ Word-Problem Performance and Their Ability to Represent Word Problems with Algebraic Equations: A Randomized Control Study

PubMed Central

Fuchs, Lynn S.; Zumeta, Rebecca O.; Schumacher, Robin Finelli; Powell, Sarah R.; Seethaler, Pamela M.; Hamlett, Carol L.; Fuchs, Douglas

2010-01-01

The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders’ word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which taught students to represent the structural, defining features of word problems with overarching equations. Intervention lasted 16 weeks. We pretested and posttested 270 students on measures of word-problem skill; analyses that accounted for the nested structure of the data indicated superior word-problem learning for SBI students. Descriptive analyses of students’ word-problem work indicated that SBI helped students represent the structure of word problems with algebraic equations, suggesting that SBI promoted this aspect of students’ emerging algebraic reasoning. PMID:20539822

Ittigahat wa Nozom at-Ta lim fi al-Gonhouriyyah al-Arabiyyah al-Mouttahidah wa Makanat at-ta lim at-tougari fiha (Education in the United Arab Republic: Its Structure and Orientation, and the Position of Commercial Studies within the Educational System).

ERIC Educational Resources Information Center

Ministry of Education, Cairo (United Arab Republic).

This document is an English-language abstract (approximately 1,500 words) surveying Egyptian education. Elementary education is compulsory. It begins between the ages of six and eight and lasts six years. The curriculum includes Arabic, religion, social subjects, hygiene, arithmetic, community singing, music, physical education, drawing and…

Military Personnel. Military and Civilian Pay Comparisons Present Challenges and Are One of Many Tools in Assessing Compensation

DTIC Science & Technology

2010-04-01

generally determined by the results of a series of tests that measure word knowledge, paragraph comprehension, arithmetic reasoning, and mathematics ...significant cost to the department, according to the department’s Office of the Actuary , only 15 percent of enlisted and 47 percent of officers become...to value retiree health care as it did retiree pension, DOD’s Office of the Actuary is required by statute to review valuations of the fund and to

Spacing and the Transition from Calculation to Retrieval

ERIC Educational Resources Information Center

Rickard, Timothy C.; Lau, Jonas; Pashler, Harold

2008-01-01

Many arithmetic problems can be solved in two ways: by a calculation involving several steps, and by direct retrieval of the answer. With practice on particular problems, memory retrieval tends to supplant calculation--an important aspect of skill learning. We asked how the distribution of practice on particular problems affects this kind of…

The Problem-Solving Nemesis: Mindless Manipulation.

ERIC Educational Resources Information Center

Hawkins, Vincent J.

1987-01-01

Indicates that only 21% of respondents (secondary school math teachers) used computer-assisted instruction for tutorial work, physical models to interpret abstract concepts, or real-life application of the arithmetic or algebraic manipulation. Recommends that creative teaching methods be applied to problem solving. (NKA)

Math, monkeys, and the developing brain.

PubMed

Cantlon, Jessica F

2012-06-26

Thirty thousand years ago, humans kept track of numerical quantities by carving slashes on fragments of bone. It took approximately 25,000 y for the first iconic written numerals to emerge among human cultures (e.g., Sumerian cuneiform). Now, children acquire the meanings of verbal counting words, Arabic numerals, written number words, and the procedures of basic arithmetic operations, such as addition and subtraction, in just 6 y (between ages 2 and 8). What cognitive abilities enabled our ancestors to record tallies in the first place? Additionally, what cognitive abilities allow children to rapidly acquire the formal mathematics knowledge that took our ancestors many millennia to invent? Current research aims to discover the origins and organization of numerical information in humans using clues from child development, the organization of the human brain, and animal cognition.

Young children's use of derived fact strategies for addition and subtraction

PubMed Central

Dowker, Ann

2014-01-01

Forty-four children between 6;0 and 7;11 took part in a study of derived fact strategy use. They were assigned to addition and subtraction levels on the basis of calculation pretests. They were then given Dowker's (1998) test of derived fact strategies in addition, involving strategies based on the Identity, Commutativity, Addend +1, Addend −1, and addition/subtraction Inverse principles; and test of derived fact strategies in subtraction, involving strategies based on the Identity, Minuend +1, Minuend −1, Subtrahend +1, Subtrahend −1, Complement and addition/subtraction Inverse principles. The exact arithmetic problems given varied according to the child's previously assessed calculation level and were selected to be just a little too difficult for the child to solve unaided. Children were given the answer to a problem and then asked to solve another problem that could be solved quickly by using this answer, together with the principle being assessed. The children also took the WISC Arithmetic subtest. Strategies differed greatly in difficulty, with Identity being the easiest, and the Inverse and Complement principles being most difficult. The Subtrahend +1 and Subtrahend −1 problems often elicited incorrect strategies based on an overextension of the principles of addition to subtraction. It was concluded that children may have difficulty with understanding and applying the relationships between addition and subtraction. Derived fact strategy use was significantly related to both calculation level and to WISC Arithmetic scaled score. PMID:24431996

Syntactic processing in the absence of awareness and semantics.

PubMed

Hung, Shao-Min; Hsieh, Po-Jang

2015-10-01

The classical view that multistep rule-based operations require consciousness has recently been challenged by findings that both multiword semantic processing and multistep arithmetic equations can be processed unconsciously. It remains unclear, however, whether pure rule-based cognitive processes can occur unconsciously in the absence of semantics. Here, after presenting 2 words consciously, we suppressed the third with continuous flash suppression. First, we showed that the third word in the subject-verb-verb format (syntactically incongruent) broke suppression significantly faster than the third word in the subject-verb-object format (syntactically congruent). Crucially, the same effect was observed even with sentences composed of pseudowords (pseudo subject-verb-adjective vs. pseudo subject-verb-object) without any semantic information. This is the first study to show that syntactic congruency can be processed unconsciously in the complete absence of semantics. Our findings illustrate how abstract rule-based processing (e.g., syntactic categories) can occur in the absence of visual awareness, even when deprived of semantics. (c) 2015 APA, all rights reserved).

Pictorial Representations of Simple Arithmetic Problems Are Not Always Helpful: A Cognitive Load Perspective

ERIC Educational Resources Information Center

van Lieshout, Ernest C. D. M.; Xenidou-Dervou, Iro

2018-01-01

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

Solving Classical Insight Problems without Aha! Experience: 9 Dot, 8 Coin, and Matchstick Arithmetic Problems

ERIC Educational Resources Information Center

Danek, Amory H.; Wiley, Jennifer; Öllinger, Michael

2016-01-01

Insightful problem solving is a vital part of human thinking, yet very difficult to grasp. Traditionally, insight has been investigated by using a set of established "insight tasks," assuming that insight has taken place if these problems are solved. Instead of assuming that insight takes place during every solution of the 9 Dot, 8 Coin,…

Arithmetic Problems at School: When There Is an Apparent Contradiction between the Situation Model and the Problem Model

ERIC Educational Resources Information Center

Coquin-Viennot, Daniele; Moreau, Stephanie

2007-01-01

Background: Understanding and solving problems involves different levels of representation. On the one hand, there are logico-mathematical representations, or problem models (PMs), which contain information such as "the size of the flock changed from 31 sheep to 42" while, on the other hand, there are more qualitative representations, or…

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

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.

A structural equation modeling of executive functions, IQ and mathematical skills in primary students: Differential effects on number production, mental calculus and arithmetical problems.

PubMed

Arán Filippetti, Vanessa; Richaud, María Cristina

2017-10-01

Though the relationship between executive functions (EFs) and mathematical skills has been well documented, little is known about how both EFs and IQ differentially support diverse math domains in primary students. Inconsistency of results may be due to the statistical techniques employed, specifically, if the analysis is conducted with observed variables, i.e., regression analysis, or at the latent level, i.e., structural equation modeling (SEM). The current study explores the contribution of both EFs and IQ in mathematics through an SEM approach. A total of 118 8- to 12-year-olds were administered measures of EFs, crystallized (Gc) and fluid (Gf) intelligence, and math abilities (i.e., number production, mental calculus and arithmetical problem-solving). Confirmatory factor analysis (CFA) offered support for the three-factor solution of EFs: (1) working memory (WM), (2) shifting, and (3) inhibition. Regarding the relationship among EFs, IQ and math abilities, the results of the SEM analysis showed that (i) WM and age predict number production and mental calculus, and (ii) shifting and sex predict arithmetical problem-solving. In all of the SEM models, EFs partially or totally mediated the relationship between IQ, age and math achievement. These results suggest that EFs differentially supports math abilities in primary-school children and is a more significant predictor of math achievement than IQ level.

Aging effects in sequential modulations of poorer-strategy effects during execution of memory strategies.

PubMed

Hinault, Thomas; Lemaire, Patrick; Touron, Dayna

2017-02-01

In this study, we asked young adults and older adults to encode pairs of words. For each item, they were told which strategy to use, interactive imagery or rote repetition. Data revealed poorer-strategy effects in both young adults and older adults: Participants obtained better performance when executing better strategies (i.e., interactive-imagery strategy to encode pairs of concrete words; rote-repetition strategy on pairs of abstract words) than with poorer strategies (i.e., interactive-imagery strategy on pairs of abstract words; rote-repetition strategy on pairs of concrete words). Crucially, we showed that sequential modulations of poorer-strategy effects (i.e., poorer-strategy effects being larger when previous items were encoded with better relative to poorer strategies), previously demonstrated in arithmetic, generalise to memory strategies. We also found reduced sequential modulations of poorer-strategy effects in older adults relative to young adults. Finally, sequential modulations of poorer-strategy effects correlated with measures of cognitive control processes, suggesting that these processes underlie efficient trial-to-trial modulations during strategy execution. Differences in correlations with cognitive control processes were also found between older adults and young adults. These findings have important implications regarding mechanisms underlying memory strategy execution and age differences in memory performance.

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training

PubMed Central

Boonen, Anton J. H.; de Koning, Björn B.; Jolles, Jelle; van der Schoot, Menno

2016-01-01

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME. PMID:26925012

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training.

PubMed

Boonen, Anton J H; de Koning, Björn B; Jolles, Jelle; van der Schoot, Menno

2016-01-01

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME.

You'll See What You Mean: Students Encode Equations Based on Their Knowledge of Arithmetic

ERIC Educational Resources Information Center

McNeil, Nicole M.; Alibali, Martha W.

2004-01-01

This study investigated the roles of problem structure and strategy use in problem encoding. Fourth-grade students solved and explained a set of typical addition problems (e.g., 5 + 4 + 9 + 5 = ?) and mathematical equivalence problems (e.g., 4 + 3 + 6 = 4 + ? or 6 + 4 + 5 = ? + 5). Next, they completed an encoding task in which they reconstructed…

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

Solving Math Problems Approximately: A Developmental Perspective

PubMed Central

Ganor-Stern, Dana

2016-01-01

Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224

Impact of ageing on problem size and proactive interference in arithmetic facts solving.

PubMed

Archambeau, Kim; De Visscher, Alice; Noël, Marie-Pascale; Gevers, Wim

2018-02-01

Arithmetic facts (AFs) are required when solving problems such as "3 × 4" and refer to calculations for which the correct answer is retrieved from memory. Currently, two important effects that modulate the performance in AFs have been highlighted: the problem size effect and the proactive interference effect. The aim of this study is to investigate possible age-related changes of the problem size effect and the proactive interference effect in AF solving. To this end, the performance of young and older adults was compared in a multiplication production task. Furthermore, an independent measure of proactive interference was assessed to further define the architecture underlying this effect in multiplication solving. The results indicate that both young and older adults were sensitive to the effects of interference and of the problem size. That is, both interference and problem size affected performance negatively: the time needed to solve a multiplication problem increases as the level of interference and the size of the problem increase. Regarding the effect of ageing, the problem size effect remains constant with age, indicating a preserved AF network in older adults. Interestingly, sensitivity to proactive interference in multiplication solving was less pronounced in older than in younger adults suggesting that part of the proactive interference has been overcome with age.

In Search of Structures: How Does the Mind Explore Infinity?

ERIC Educational Resources Information Center

Singer, Florence Mihaela; Voica, Cristian

2010-01-01

When reasoning about infinite sets, children seem to activate four categories of conceptual structures: geometric (g-structures), arithmetic (a-structures), fractal-type (f-structures), and density-type (d-structures). Students select different problem-solving strategies depending on the structure they recognize within the problem domain. They…

Online with Integers

ERIC Educational Resources Information Center

Siegel, Jonathan W.; Siegel, P. B.

2011-01-01

Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…

Can Dyscalculics Estimate the Results of Arithmetic Problems?

ERIC Educational Resources Information Center

Ganor-Stern, Dana

2017-01-01

The present study is the first to examine the computation estimation skills of dyscalculics versus controls using the estimation comparison task. In this task, participants judged whether an estimated answer to a multidigit multiplication problem was larger or smaller than a given reference number. While dyscalculics were less accurate than…

Reading, Writing, … and Arithmetic?

ERIC Educational Resources Information Center

Sussman, Dan

2017-01-01

How can the best of mathematical problem-based learning be applied toward literature classes? Daniel Sussman, an English teacher at Moorestown Friends School in New Jersey, discusses how he uses problem solving tactics to encourage close, critical reading of fiction texts in his Jewish literature and poetry classes. He explores the challenges of…

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

A Learning Trajectory for Teaching Social Arithmetic using RME Approach

NASA Astrophysics Data System (ADS)

Fauzan, A.; Armiati, A.; Ceria, C.

2018-04-01

This paper discusses the role of a learning trajectory (LT) in promoting students’ reasoning when they learn social arithmetic using Realistic Mathematics Education (RME) approach. In our LT, we built the intertwining of the concepts such as profit, loss, percentage, discount, and interest rate, so that the students understand the relations among them. The LT was developed through a design research that consisted of a cyclic process of preparing for the experiment, conducting the experiment, and retrospective analysis. The research’s subject was 32 students at grade 7 MTsN Sintoga, Pariaman, Indonesia. Data were collected through observations, interviews, checklist, videotaping, and analyzing the students' works. The results showed that the LT could help the students to reinvent the concepts in social arithmetic. The students had more confidence to use their own strategies in solving contextual problems. The most important thing, we discovered the growth in the students’ mathematical reasoning.

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.

Procedural and Conceptual Changes in Young Children's Problem Solving

ERIC Educational Resources Information Center

Voutsina, Chronoula

2012-01-01

This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach,…

Transitions in Learning: Evidence for Simultaneously Activated Strategies.

ERIC Educational Resources Information Center

Goldin-Meadow, Susan; And Others

Children rarely cite more than one strategy when asked to explain how they solved a particular arithmetic problem, hence their verbal explanations will not necessarily reveal whether they have considered multiple strategies on that problem. However, previous work has shown that, when asked to explain their performance on a task, children often use…

Analyzing Algebraic Thinking Using "Guess My Number" Problems

ERIC Educational Resources Information Center

Patton, Barba; De Los Santos, Estella

2012-01-01

The purpose of this study was to assess student knowledge of numeric, visual and algebraic representations. A definite gap between arithmetic and algebra has been documented in the research. The researchers' goal was to identify a link between the two. Using four "Guess My Number" problems, seventh and tenth grade students were asked to write…

Analyzing the Responses of 7-8 Year Olds When Solving Partitioning Problems

ERIC Educational Resources Information Center

Badillo, Edelmira; Font, Vicenç; Edo, Mequè

2015-01-01

We analyze the mathematical solutions of 7- to 8-year-old pupils while individually solving an arithmetic problem. The analysis was based on the "configuration of objects," an instrument derived from the onto-semiotic approach to mathematical knowledge. Results are illustrated through a number of cases. From the analysis of mathematical…

Investigating the Relationship between Conceptual and Procedural Errors in the Domain of Probability Problem-Solving.

ERIC Educational Resources Information Center

O'Connell, Ann Aileen

The relationships among types of errors observed during probability problem solving were studied. Subjects were 50 graduate students in an introductory probability and statistics course. Errors were classified as text comprehension, conceptual, procedural, and arithmetic. Canonical correlation analysis was conducted on the frequencies of specific…

No Generalization of Practice for Nonzero Simple Addition

ERIC Educational Resources Information Center

Campbell, Jamie I. D.; Beech, Leah C.

2014-01-01

Several types of converging evidence have suggested recently that skilled adults solve very simple addition problems (e.g., 2 + 1, 4 + 2) using a fast, unconscious counting algorithm. These results stand in opposition to the long-held assumption in the cognitive arithmetic literature that such simple addition problems normally are solved by fact…

Investigating middle school students’ difficulties in mathematical literacy problems level 1 and 2

NASA Astrophysics Data System (ADS)

Setiawati, S.; Herman, T.; Jupri, A.

2017-11-01

The background of this study is the lack of mathematical literacy skills of students. The proficiency of students’ mathematical literacy skills based on the results of the PISA 2015 study shows that Indonesian students at the proficiency level 1. This fact gave rise to this study which aims to investigate middle school students’ difficulties in mathematical literacy problems level 1 and 2. Qualitative research was used in this study. An individual written test on mathematical literacy problems was administered, followed by interviews. The subjects of the study were 61 students grade VII in Bandung and 26 of them were interviewed afterward. Data analysis revealed that students’ error in performing arithmetic most frequently observed. Other observed difficulties concerned understanding about algebra concept, applying arithmetic operation in algebraic expressions, and interpreting symbols to represent the unknown. In solving mathematical literacy problems, students use their prior knowledge, although sometimes not relevant to the questions. Based on the results, we suggest that mathematics learning in contextual learning and which invites students to participate in the processes of understanding the concepts.

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's Understanding of the Arithmetic Concepts of Inversion and Associativity

ERIC Educational Resources Information Center

Robinson, Katherine M.; Ninowski, Jerilyn E.; Gray, Melissa L.

2006-01-01

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

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.

A new compound arithmetic crossover-based genetic algorithm for constrained optimisation in enterprise systems

NASA Astrophysics Data System (ADS)

Jin, Chenxia; Li, Fachao; Tsang, Eric C. C.; Bulysheva, Larissa; Kataev, Mikhail Yu

2017-01-01

In many real industrial applications, the integration of raw data with a methodology can support economically sound decision-making. Furthermore, most of these tasks involve complex optimisation problems. Seeking better solutions is critical. As an intelligent search optimisation algorithm, genetic algorithm (GA) is an important technique for complex system optimisation, but it has internal drawbacks such as low computation efficiency and prematurity. Improving the performance of GA is a vital topic in academic and applications research. In this paper, a new real-coded crossover operator, called compound arithmetic crossover operator (CAC), is proposed. CAC is used in conjunction with a uniform mutation operator to define a new genetic algorithm CAC10-GA. This GA is compared with an existing genetic algorithm (AC10-GA) that comprises an arithmetic crossover operator and a uniform mutation operator. To judge the performance of CAC10-GA, two kinds of analysis are performed. First the analysis of the convergence of CAC10-GA is performed by the Markov chain theory; second, a pair-wise comparison is carried out between CAC10-GA and AC10-GA through two test problems available in the global optimisation literature. The overall comparative study shows that the CAC performs quite well and the CAC10-GA defined outperforms the AC10-GA.

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.

Distinct representations of subtraction and multiplication in the neural systems for numerosity and language

PubMed Central

Prado, Jérôme; Mutreja, Rachna; Zhang, Hongchuan; Mehta, Rucha; Desroches, Amy S.; Minas, Jennifer E.; Booth, James R.

2010-01-01

It has been proposed that recent cultural inventions such as symbolic arithmetic recycle evolutionary older neural mechanisms. A central assumption of this hypothesis is that the degree to which a pre-existing mechanism is recycled depends upon the degree of similarity between its initial function and the novel task. To test this assumption, we investigated whether the brain region involved in magnitude comparison in the intraparietal sulcus (IPS), localized by a numerosity comparison task, is recruited to a greater degree by arithmetic problems that involve number comparison (single-digit subtractions) than by problems that involve retrieving facts from memory (single-digit multiplications). Our results confirmed that subtractions are associated with greater activity in the IPS than multiplications, whereas multiplications elicit greater activity than subtractions in regions involved in verbal processing including the middle temporal gyrus and inferior frontal gyrus that were localized by a phonological processing task. Pattern analyses further indicated that the neural mechanisms more active for subtraction than multiplication in the IPS overlap with those involved in numerosity comparison, and that the strength of this overlap predicts inter-individual performance in the subtraction task. These findings provide novel evidence that elementary arithmetic relies on the co-option of evolutionary older neural circuits. PMID:21246667

Specific Preschool Executive Functions Predict Unique Aspects of Mathematics Development: A 3-Year Longitudinal Study.

PubMed

Simanowski, Stefanie; Krajewski, Kristin

2017-08-10

This study assessed the extent to which executive functions (EF), according to their factor structure in 5-year-olds (N = 244), influenced early quantity-number competencies, arithmetic fluency, and mathematics school achievement throughout first and second grades. A confirmatory factor analysis resulted in updating as a first, and inhibition and shifting as a combined second factor. In the structural equation model, updating significantly affected knowledge of the number word sequence, suggesting a facilitatory effect on basic encoding processes in numerical materials that can be learnt purely by rote. Shifting and inhibition significantly influenced quantity to number word linkages, indicating that these processes promote developing a profound understanding of numbers. These results show the supportive role of specific EF for specific aspects of a numerical foundation. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

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

Children's Solution Processes in Elementary Arithmetic Problems: Analysis and Improvement. Report No. 19.

ERIC Educational Resources Information Center

De Corte, Erik; Verschaffel, Lieven

Design and results of an investigation attempting to analyze and improve children's solution processes in elementary addition and subtraction problems are described. As background for the study, a conceptual model was developed based on previous research. One dimension of the model relates to the characteristics of the tasks (numerical versus word…

Brain Hyper-Connectivity and Operation-Specific Deficits during Arithmetic Problem Solving in Children with Developmental Dyscalculia

ERIC Educational Resources Information Center

Rosenberg-Lee, Miriam; Ashkenazi, Sarit; Chen, Tianwen; Young, Christina B.; Geary, David C.; Menon, Vinod

2015-01-01

Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who…

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…

Elastic, Cottage Cheese, and Gasoline: Visualizing Division of Fractions

ERIC Educational Resources Information Center

Peck, Sallie; Wood, Japheth

2008-01-01

Teachers must be prepared to recognize valid alternative representations of arithmetic problems. Challenging examples involving mixed fractions and division are presented along with teacher's discussion from a professional development workshop. (Contains 6 figures and 1 table.)

Arithmetic and algebraic problem solving and resource allocation: the distinct impact of fluid and numerical intelligence.

PubMed

Dix, Annika; van der Meer, Elke

2015-04-01

This study investigates cognitive resource allocation dependent on fluid and numerical intelligence in arithmetic/algebraic tasks varying in difficulty. Sixty-six 11th grade students participated in a mathematical verification paradigm, while pupil dilation as a measure of resource allocation was collected. Students with high fluid intelligence solved the tasks faster and more accurately than those with average fluid intelligence, as did students with high compared to average numerical intelligence. However, fluid intelligence sped up response times only in students with average but not high numerical intelligence. Further, high fluid but not numerical intelligence led to greater task-related pupil dilation. We assume that fluid intelligence serves as a domain-general resource that helps to tackle problems for which domain-specific knowledge (numerical intelligence) is missing. The allocation of this resource can be measured by pupil dilation. Copyright © 2014 Society for Psychophysiological Research.

Solving Word Problems using Schemas: A Review of the Literature

PubMed Central

Powell, Sarah R.

2011-01-01

Solving word problems is a difficult task for students at-risk for or with learning disabilities (LD). One instructional approach that has emerged as a valid method for helping students at-risk for or with LD to become more proficient at word-problem solving is using schemas. A schema is a framework for solving a problem. With a schema, students are taught to recognize problems as falling within word-problem types and to apply a problem solution method that matches that problem type. This review highlights two schema approaches for 2nd- and 3rd-grade students at-risk for or with LD: schema-based instruction and schema-broadening instruction. A total of 12 schema studies were reviewed and synthesized. Both types of schema approaches enhanced the word-problem skill of students at-risk for or with LD. Based on the review, suggestions are provided for incorporating word-problem instruction using schemas. PMID:21643477

A VLSI architecture for performing finite field arithmetic with reduced table look-up

NASA Technical Reports Server (NTRS)

Hsu, I. S.; Truong, T. K.; Reed, I. S.

1986-01-01

A new table look-up method for finding the log and antilog of finite field elements has been developed by N. Glover. In his method, the log and antilog of a field element is found by the use of several smaller tables. The method is based on a use of the Chinese Remainder Theorem. The technique often results in a significant reduction in the memory requirements of the problem. A VLSI architecture is developed for a special case of this new algorithm to perform finite field arithmetic including multiplication, division, and the finding of an inverse element in the finite field.

Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners.

PubMed

Powell, Sarah R; Fuchs, Lynn S; Cirino, Paul T; Fuchs, Douglas; Compton, Donald L; Changas, Paul C

2015-07-01

The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2 nd -grade students at risk for mathematics difficulty. Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation RTI, word-problem RTI, and business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word-problem outcomes; word-problem RTI enhanced proximal word-problem outcomes as well as performance on some calculation outcomes; and word-problem RTI provided a stronger route than calculation RTI to pre-algebraic knowledge.

Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.; Cirino, Paul T.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

2014-01-01

The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2nd-grade students at risk for mathematics difficulty. Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation RTI, word-problem RTI, and business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word-problem outcomes; word-problem RTI enhanced proximal word-problem outcomes as well as performance on some calculation outcomes; and word-problem RTI provided a stronger route than calculation RTI to pre-algebraic knowledge. PMID:26097244

Culturally and Linguistically Responsive Schema Intervention: Improving Word Problem Solving for English Language Learners with Mathematics Difficulty

ERIC Educational Resources Information Center

Driver, Melissa K.; Powell, Sarah R.

2017-01-01

Word problems are prevalent on high-stakes assessments, and success on word problems has implications for grade promotion and graduation. Unfortunately, English Language Learners (ELLs) continue to perform significantly below their native English-speaking peers on mathematics assessments featuring word problems. Little is known about the…

Contribution of Equal-Sign Instruction beyond Word-Problem Tutoring for Third-Grade Students with Mathematics Difficulty.

PubMed

Powell, Sarah R; Fuchs, Lynn S

2010-05-01

Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for higher-order mathematics skills including word problems. Research indicates equal-sign instruction can alter how typically-developing students use the equal sign, but no study has examined effects for students with mathematics difficulty (MD) or how equal-sign instruction contributes to word-problem skill for students with or without MD. The present study assessed the efficacy of equal-sign instruction within word-problem tutoring. Third-grade students with MD (n = 80) were assigned to word-problem tutoring, word-problem tutoring plus equal-sign instruction (combined) tutoring, or no-tutoring control. Combined tutoring produced better improvement on equal sign tasks and open equations compared to the other 2 conditions. On certain forms of word problems, combined tutoring but not word-problem tutoring alone produced better improvement than control. When compared at posttest to 3(rd)-grade students without MD on equal sign tasks and open equations, only combined tutoring students with MD performed comparably.

The MONGOOSE Rational Arithmetic Toolbox.

PubMed

Le, Christopher; Chindelevitch, Leonid

2018-01-01

The modeling of metabolic networks has seen a rapid expansion following the complete sequencing of thousands of genomes. The constraint-based modeling framework has emerged as one of the most popular approaches to reconstructing and analyzing genome-scale metabolic models. Its main assumption is that of a quasi-steady-state, requiring that the production of each internal metabolite be balanced by its consumption. However, due to the multiscale nature of the models, the large number of reactions and metabolites, and the use of floating-point arithmetic for the stoichiometric coefficients, ensuring that this assumption holds can be challenging.The MONGOOSE toolbox addresses this problem by using rational arithmetic, thus ensuring that models are analyzed in a reproducible manner and consistently with modeling assumptions. In this chapter we present a protocol for the complete analysis of a metabolic network model using the MONGOOSE toolbox, via its newly developed GUI, and describe how it can be used as a model-checking platform both during and after the model construction process.

An exact arithmetic toolbox for a consistent and reproducible structural analysis of metabolic network models

PubMed Central

Chindelevitch, Leonid; Trigg, Jason; Regev, Aviv; Berger, Bonnie

2014-01-01

Constraint-based models are currently the only methodology that allows the study of metabolism at the whole-genome scale. Flux balance analysis is commonly used to analyse constraint-based models. Curiously, the results of this analysis vary with the software being run, a situation that we show can be remedied by using exact rather than floating-point arithmetic. Here we introduce MONGOOSE, a toolbox for analysing the structure of constraint-based metabolic models in exact arithmetic. We apply MONGOOSE to the analysis of 98 existing metabolic network models and find that the biomass reaction is surprisingly blocked (unable to sustain non-zero flux) in nearly half of them. We propose a principled approach for unblocking these reactions and extend it to the problems of identifying essential and synthetic lethal reactions and minimal media. Our structural insights enable a systematic study of constraint-based metabolic models, yielding a deeper understanding of their possibilities and limitations. PMID:25291352

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.

Embedding Number-Combinations Practice Within Word-Problem Tutoring

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Douglas

2012-01-01

Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems. PMID:22661880

Embedding Number-Combinations Practice Within Word-Problem Tutoring.

PubMed

Powell, Sarah R; Fuchs, Lynn S; Fuchs, Douglas

2010-09-01

Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems.

Does Early Algebraic Reasoning Differ as a Function of Students’ Difficulty with Calculations versus Word Problems?

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.

2014-01-01

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2nd- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044

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

Solving fully fuzzy transportation problem using pentagonal fuzzy numbers

NASA Astrophysics Data System (ADS)

Maheswari, P. Uma; Ganesan, K.

2018-04-01

In this paper, we propose a simple approach for the solution of fuzzy transportation problem under fuzzy environment in which the transportation costs, supplies at sources and demands at destinations are represented by pentagonal fuzzy numbers. The fuzzy transportation problem is solved without converting to its equivalent crisp form using a robust ranking technique and a new fuzzy arithmetic on pentagonal fuzzy numbers. To illustrate the proposed approach a numerical example is provided.

Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

DOEpatents

Van Benthem, Mark H.; Keenan, Michael R.

2008-11-11

A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.

Levels of Arithmetic Reasoning in Solving an Open-Ended Problem

ERIC Educational Resources Information Center

Kosyvas, Georgios

2016-01-01

This paper presents the results of an experimental teaching carried out on 12-year-old students. An open-ended task was given to them and they had not been taught the algorithmic process leading to the solution. The formal solution to the problem refers to a system of two linear equations with two unknown quantities. In this mathematical activity,…

The role of physical digit representation and numerical magnitude representation in children's multiplication fact retrieval.

PubMed

De Visscher, Alice; Noël, Marie-Pascale; De Smedt, Bert

2016-12-01

Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (M age =9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

How Can One Learn Mathematical Word Problems in a Second Language? A Cognitive Load Perspective

ERIC Educational Resources Information Center

Moussa-Inaty, Jase; Causapin, Mark; Groombridge, Timothy

2015-01-01

Language may ordinarily account for difficulties in solving word problems and this is particularly true if mathematical word problems are taught in a language other than one's native language. Research into cognitive load may offer a clear theoretical framework when investigating word problems because memory, specifically working memory, plays a…

Do word-problem features differentially affect problem difficulty as a function of students' mathematics difficulty with and without reading difficulty?

PubMed

Powell, Sarah R; Fuchs, Lynn S; Fuchs, Douglas; Cirino, Paul T; Fletcher, Jack M

2009-01-01

This study examined whether and, if so, how word-problem features differentially affect problem difficulty as a function of mathematics difficulty (MD) status: no MD (n = 109), MD only (n = 109), or MD in combination with reading difficulties (MDRD; n = 109). The problem features were problem type (total, difference, or change) and position of missing information in the number sentence representing the word problem (first, second, or third position). Students were assessed on 14 word problems near the beginning of third grade. Consistent with the hypothesis that mathematical cognition differs as a function of MD subtype, problem type affected problem difficulty differentially for MDRD versus MD-only students; however, the position of missing information in word problems did not. Implications for MD subtyping and for instruction are discussed.

Contribution of Equal-Sign Instruction beyond Word-Problem Tutoring for Third-Grade Students with Mathematics Difficulty

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.

2010-01-01

Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for higher-order mathematics skills including word problems. Research indicates equal-sign instruction can alter how typically-developing students use the equal sign, but no study has examined effects for students with mathematics difficulty (MD) or how equal-sign instruction contributes to word-problem skill for students with or without MD. The present study assessed the efficacy of equal-sign instruction within word-problem tutoring. Third-grade students with MD (n = 80) were assigned to word-problem tutoring, word-problem tutoring plus equal-sign instruction (combined) tutoring, or no-tutoring control. Combined tutoring produced better improvement on equal sign tasks and open equations compared to the other 2 conditions. On certain forms of word problems, combined tutoring but not word-problem tutoring alone produced better improvement than control. When compared at posttest to 3rd-grade students without MD on equal sign tasks and open equations, only combined tutoring students with MD performed comparably. PMID:20640240

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...

Classroom Capsules.

ERIC Educational Resources Information Center

Page, Warren, Ed.

1988-01-01

Presents ideas that are intended to convey new insights on familiar topics and to enhance pedagogy. The mathematical topics addressed are applications of transformations to numerical integration, the golden ratio, Cramer's rule, a counting problem, and the general form of the arithmetic-geometric mean inequality. (PK)

Does understanding relational terminology mediate effects of intervention on compare word problems?

PubMed

Schumacher, Robin F; Fuchs, Lynn S

2012-04-01

The purpose of this study was to assess whether understanding relational terminology (i.e., more, less, and fewer) mediates the effects of intervention on compare word problems. Second-grade classrooms (N=31) were randomly assigned to one of three conditions: researcher-designed word-problem intervention, researcher-designed calculation intervention, or business-as-usual (teacher-designed) control. Students in word-problem intervention classrooms received instruction on the compare problem type, which included a focus on understanding relational terminology within compare word problems. Analyses, which accounted for variance associated with classroom clustering, indicated that (a) compared with the calculation intervention and business-as-usual conditions, word-problem intervention significantly increased performance on all three subtypes of compare problems and on understanding relational terminology, and (b) the intervention effect was fully mediated by students' understanding of relational terminology for one subtype of compare problems and partially mediated by students' understanding of relational terminology for the other two subtypes. Copyright © 2011 Elsevier Inc. All rights reserved.

Academic Achievement in Adults with a History of Childhood Attention-Deficit/Hyperactivity Disorder: A Population-Based Prospective Study.

PubMed

Voigt, Robert G; Katusic, Slavica K; Colligan, Robert C; Killian, Jill M; Weaver, Amy L; Barbaresi, William J

2017-01-01

Previous research on the developmental course of attention-deficit/hyperactivity disorder (ADHD) is limited by biased clinic-referred samples and other methodological problems. Thus, questions about adult academic outcomes associated with childhood ADHD remain unanswered. Thus, the objective of this study was to describe academic outcomes in adulthood among incident cases of research-identified childhood ADHD versus non-ADHD referents from a population-based birth cohort. Young adults with research-identified childhood ADHD (N = 232; mean age 27.0 yr; 72.0% men) and referents (N = 335; mean age 28.6 yr; 62.7% men) from a 1976 to 1982 birth cohort (N = 5699) were invited to participate in a followup study and were administered an academic achievement battery consisting of the basic reading component of the Woodcock-Johnson III Tests of Achievement (WJ-III) and the arithmetic subtest of the Wide Range Achievement Test-Third Edition (WRAT-3). Outcomes were compared between the 2 groups using linear regression models, adjusted for age, sex, and comorbid learning disability status. Childhood ADHD cases scored from 3 to 5 grade equivalents lower on all academic tests compared with referents, with mean (SD) standard scores of 95.7 (8.4) versus 101.8 (8.1) in basic reading; 95.0 (9.3) versus 101.9 (8.5) in letterword identification; 98.2 (8.6) versus 103.2 (9.2) in passage comprehension; 95.7 (9.1) versus 100.9 (9.0) in word attack; and 87.8 (12.9) versus 98.0 (12.0) in arithmetic. This is the first prospective, population-based study of adult academic outcomes of childhood ADHD. Our data provide evidence that childhood onset ADHD is associated with long-term underachievement in reading and math that may negatively impact ultimate educational attainment and occupational functioning in adulthood.

Efficient solution of a multi objective fuzzy transportation problem

NASA Astrophysics Data System (ADS)

Vidhya, V.; Ganesan, K.

2018-04-01

In this paper we present a methodology for the solution of multi-objective fuzzy transportation problem when all the cost and time coefficients are trapezoidal fuzzy numbers and the supply and demand are crisp numbers. Using a new fuzzy arithmetic on parametric form of trapezoidal fuzzy numbers and a new ranking method all efficient solutions are obtained. The proposed method is illustrated with an example.

How Do We Choose among Strategies to Accomplish Cognitive Tasks? Evidence from Behavioral and Event-Related Potential Data in Arithmetic Problem Solving

ERIC Educational Resources Information Center

Taillan, Julien; Dufau, Stéphane; Lemaire, Patrick

2015-01-01

We used event-related potentials (ERPs) to determine the time course of mechanisms underlying strategy selection. Participants had to select the better strategy on multiplication problems (i.e., 51 × 27) to find approximate products. They could choose between rounding up and rounding down both operands to their nearest decades. Two types of…

Contextual Processing of Abstract Concepts Reveals Neural Representations of Non-Linguistic Semantic Content

PubMed Central

Wilson-Mendenhall, Christine D.; Simmons, W. Kyle; Martin, Alex; Barsalou, Lawrence W.

2014-01-01

Concepts develop for many aspects of experience, including abstract internal states and abstract social activities that do not refer to concrete entities in the world. The current study assessed the hypothesis that, like concrete concepts, distributed neural patterns of relevant, non-linguistic semantic content represent the meanings of abstract concepts. In a novel neuroimaging paradigm, participants processed two abstract concepts (convince, arithmetic) and two concrete concepts (rolling, red) deeply and repeatedly during a concept-scene matching task that grounded each concept in typical contexts. Using a catch trial design, neural activity associated with each concept word was separated from neural activity associated with subsequent visual scenes to assess activations underlying the detailed semantics of each concept. We predicted that brain regions underlying mentalizing and social cognition (e.g., medial prefrontal cortex, superior temporal sulcus) would become active to represent semantic content central to convince, whereas brain regions underlying numerical cognition (e.g., bilateral intraparietal sulcus) would become active to represent semantic content central to arithmetic. The results supported these predictions, suggesting that the meanings of abstract concepts arise from distributed neural systems that represent concept-specific content. PMID:23363408

Language processing within the striatum: evidence from a PET correlation study in Huntington's disease.

PubMed

Teichmann, Marc; Gaura, Véronique; Démonet, Jean-François; Supiot, Frédéric; Delliaux, Marie; Verny, Christophe; Renou, Pierre; Remy, Philippe; Bachoud-Lévi, Anne-Catherine

2008-04-01

The role of sub-cortical structures in language processing, and more specifically of the striatum, remains controversial. In line with psycholinguistic models stating that language processing implies both the recovery of lexical information and the application of combinatorial rules, the striatum has been claimed to be involved either in the former component or in the latter. The present study reconciles these conflicting views by showing the striatum's involvement in both language processes, depending on distinct striatal sub-regions. Using PET scanning in a model of striatal disorders, namely Huntington's disease (HD), we correlated metabolic data of 31 early stage HD patients regarding different striatal sub-regions with behavioural scores on three rule/lexicon tasks drawn from word morphology, syntax and from a non-linguistic domain, namely arithmetic. Behavioural results reflected impairment on both processing aspects, while deficits predominated on rule application. Both correlated with the left striatum but involved distinct striatal sub-regions. We suggest that the left striatum encompasses linguistic and arithmetic circuits, which differ with respect to their anatomical and functional specification, comprising ventrally located regions dedicated to rule computations and more dorsal portions pertaining to lexical devices.

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'.

Three-M in Word Problem Solving

ERIC Educational Resources Information Center

Hajra, Sayonita Ghosh; Kofman, Victoria

2018-01-01

We describe three activities that help undergraduates (pre-service teachers) to develop scientific vocabulary on measurable attributes and units of measurement. Measurable attributes are important features in understanding a word problem and solving the problem. These activities help students comprehend word problems better by identifying…

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…

Dynamic Assessment of Algebraic Learning in Predicting Third Graders’ Development of Mathematical Problem Solving

PubMed Central

Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Hollenbeck, Kurstin N.; Craddock, Caitlin F.; Hamlett, Carol L.

2008-01-01

Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting 3rd graders’ development of mathematics problem solving. In the fall, 122 3rd-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) was sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment math skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities. PMID:19884957

Software Reviews.

ERIC Educational Resources Information Center

McGrath, Diane, Ed.

1989-01-01

Provides reviews of courseware entitled: "Mystery Matter," which is a series that supplements the basic inquiry process; "Jumping Math Flash," which is an arcade-game program with arithmetic problems; and "Quest for Files: Science Rocks and Minerals The Upper Crust," which is a database program for earth science.…

QUARTERLY TECHNICAL PROGRESS REPORT, JULY, AUGUST, SEPTEMBER 1966.

DTIC Science & Technology

Contents: Circuit research program; Hardware systems research; Software systems research program; Numerical methods, computer arithmetic and...artificial languages; Library automation; Illiac II service , use, and program development; IBM service , use, and program development; Problem specifications; Switching theory and logical design; General laboratory information.

Pupils' over-reliance on linearity: a scholastic effect?

PubMed

Van Dooren, Wim; De Bock, Dirk; Janssens, Dirk; Verschaffel, Lieven

2007-06-01

From upper elementary education on, children develop a tendency to over-use linearity. Particularly, it is found that many pupils assume that if a figure enlarges k times, the area enlarges k times too. However, most research was conducted with traditional, school-like word problems. This study examines whether pupils also over-use linearity if non-linear problems are embedded in meaningful, authentic performance tasks instead of traditional, school-like word problems, and whether this experience influences later behaviour. Ninety-three sixth graders from two primary schools in Flanders, Belgium. Pupils received a pre-test with traditional word problems. Those who made a linear error on the non-linear area problem were subjected to individual interviews. They received one new non-linear problem, in the S-condition (again a traditional, scholastic word problem), D-condition (the same word problem with a drawing) or P-condition (a meaningful performance-based task). Shortly afterwards, pupils received a post-test, containing again a non-linear word problem. Most pupils from the S-condition displayed linear reasoning during the interview. Offering drawings (D-condition) had a positive effect, but presenting the problem as a performance task (P-condition) was more beneficial. Linear reasoning was nearly absent in the P-condition. Remarkably, at the post-test, most pupils from all three groups again applied linear strategies. Pupils' over-reliance on linearity seems partly elicited by the school-like word problem format of test items. Pupils perform much better if non-linear problems are offered as performance tasks. However, a single experience does not change performances on a comparable word problem test afterwards.

Extreme D'Hondt and round-off effects in voting computations

NASA Astrophysics Data System (ADS)

Konstantinov, M. M.; Pelova, G. B.

2015-11-01

D'Hondt (or Jefferson) method and Hare-Niemeyer (or Hamilton) method are widely used worldwide for seat allocation in proportional systems. Everything seems to be well known in this area. However, this is not the case. For example the D'Hondt method can violate the quota rule from above but this effect is not analyzed as a function of the number of parties and/or the threshold used. Also, allocation methods are often implemented automatically as computer codes in machine arithmetic believing that following the IEEE standards for double precision binary arithmetics would guarantee correct results. Unfortunately this may not happen not only for double precision arithmetic (usually producing 15-16 true decimal digits) but also for any relative precision of the underlying binary machine arithmetics. This paper deals with the following new issues.Find conditions (threshold in particular) such that D'Hondt seat allocation violates maximally the quota rule. Analyze possible influence of rounding errors in the automatic implementation of Hare-Niemeyer method in machine arithmetic.Concerning the first issue, it is known that the maximal deviation of D'Hondt allocation from upper quota for the Bulgarian proportional system (240 MP and 4% barrier) is 5. This fact had been established in 1991. A classical treatment of voting issues is the monograph [1], while electoral problems specific for Bulgaria have been treated in [2, 4]. The effect of threshold on extreme seat allocations is also analyzed in [3]. Finally we would like to stress that Voting Theory may sometimes be mathematically trivial but always has great political impact. This is a strong motivation for further investigations in this area.

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

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.

Word Problems: A "Meme" for Our Times.

ERIC Educational Resources Information Center

Leamnson, Robert N.

1996-01-01

Discusses a novel approach to word problems that involves linear relationships between variables. Argues that working stepwise through intermediates is the way our minds actually work and therefore this should be used in solving word problems. (JRH)

Child-Level Predictors of Responsiveness to Evidence-Based Mathematics Intervention.

PubMed

Powell, Sarah R; Cirino, Paul T; Malone, Amelia S

2017-07-01

We identified child-level predictors of responsiveness to 2 types of mathematics (calculation and word-problem) intervention among 2nd-grade children with mathematics difficulty. Participants were 250 children in 107 classrooms in 23 schools pretested on mathematics and general cognitive measures and posttested on mathematics measures. We assigned classrooms randomly assigned to calculation intervention, word-problem intervention, or business-as-usual control. Intervention lasted 17 weeks. Path analyses indicated that scores on working memory and language comprehension assessments moderated responsiveness to calculation intervention. No moderators were identified for responsiveness to word-problem intervention. Across both intervention groups and the control group, attentive behavior predicted both outcomes. Initial calculation skill predicted the calculation outcome, and initial language comprehension predicted word-problem outcomes. These results indicate that screening for calculation intervention should include a focus on working memory, language comprehension, attentive behavior, and calculations. Screening for word-problem intervention should focus on attentive behavior and word problems.

Thinking in Arithmetic.

ERIC Educational Resources Information Center

Resnick, Lauren B.; And Others

This paper discusses a radically different set of assumptions to improve educational outcomes for disadvantaged students. It is argued that disadvantaged children, when exposed to carefully organized thinking-oriented instruction, can acquire the traditional basic skills in the process of reasoning and solving problems. The paper is presented in…

Cryptography: Cracking Codes.

ERIC Educational Resources Information Center

Myerscough, Don; And Others

1996-01-01

Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)

Mapping Students' Spoken Conceptions of Equality

ERIC Educational Resources Information Center

Anakin, Megan

2013-01-01

This study expands contemporary theorising about students' conceptions of equality. A nationally representative sample of New Zealand students' were asked to provide a spoken numerical response and an explanation as they solved an arithmetic additive missing number problem. Students' responses were conceptualised as acts of communication and…

Technical Mathematics: Restructure of Technical Mathematics.

ERIC Educational Resources Information Center

Flannery, Carol A.

Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…

The Psychoeducational Characteristics of Children with Turner Syndrome.

ERIC Educational Resources Information Center

Rovet, Joanne F.

1993-01-01

This study compared psychoeducational characteristics of 67 children (ages 6-16) with Turner syndrome and 27 nonaffected controls. Subjects exhibited selective impairments in visuospatial and memory areas; significant underachievement in arithmetic; poor social competence; and increased behavior problems, particularly in the area of hyperactivity.…

Figurate Numbers in the Classroom.

ERIC Educational Resources Information Center

Norman, F. Alexander

1991-01-01

A series of activities involving figurate numbers that allow students at various levels to integrate numerical, geometric, arithmetic, patterning, measuring, and problem-solving skills are presented. A discussion of the geometric and numerical aspects of figurate numbers is included. Appended are IBM Logo procedures that will create pentagonal…

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...

Using Technology to Meet the Developmental Needs of Deaf Students To Improve Their Mathematical Word Problem Solving Skills.

ERIC Educational Resources Information Center

Kelly, Ronald R.

2003-01-01

Presents "Project Solve," a web-based problem-solving instruction and guided practice for mathematical word problems. Discusses implications for college students for whom reading and comprehension of mathematical word problem solving are difficult, especially learning disabled students. (Author/KHR)

Kodiak: An Implementation Framework for Branch and Bound Algorithms

NASA Technical Reports Server (NTRS)

Smith, Andrew P.; Munoz, Cesar A.; Narkawicz, Anthony J.; Markevicius, Mantas

2015-01-01

Recursive branch and bound algorithms are often used to refine and isolate solutions to several classes of global optimization problems. A rigorous computation framework for the solution of systems of equations and inequalities involving nonlinear real arithmetic over hyper-rectangular variable and parameter domains is presented. It is derived from a generic branch and bound algorithm that has been formally verified, and utilizes self-validating enclosure methods, namely interval arithmetic and, for polynomials and rational functions, Bernstein expansion. Since bounds computed by these enclosure methods are sound, this approach may be used reliably in software verification tools. Advantage is taken of the partial derivatives of the constraint functions involved in the system, firstly to reduce the branching factor by the use of bisection heuristics and secondly to permit the computation of bifurcation sets for systems of ordinary differential equations. The associated software development, Kodiak, is presented, along with examples of three different branch and bound problem types it implements.

Operational momentum in large-number addition and subtraction by 9-month-olds.

PubMed

McCrink, Koleen; Wynn, Karen

2009-08-01

Recent studies on nonsymbolic arithmetic have illustrated that under conditions that prevent exact calculation, adults display a systematic tendency to overestimate the answers to addition problems and underestimate the answers to subtraction problems. It has been suggested that this operational momentum results from exposure to a culture-specific practice of representing numbers spatially; alternatively, the mind may represent numbers in spatial terms from early in development. In the current study, we asked whether operational momentum is present during infancy, prior to exposure to culture-specific representations of numbers. Infants (9-month-olds) were shown videos of events involving the addition or subtraction of objects with three different types of outcomes: numerically correct, too large, and too small. Infants looked significantly longer only at those incorrect outcomes that violated the momentum of the arithmetic operation (i.e., at too-large outcomes in subtraction events and too-small outcomes in addition events). The presence of operational momentum during infancy indicates developmental continuity in the underlying mechanisms used when operating over numerical representations.

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.

The problem of complex eigensystems in the semianalytical solution for advancement of time in solute transport simulations: a new method using real arithmetic

USGS Publications Warehouse

Umari, Amjad M.J.; Gorelick, Steven M.

1986-01-01

In the numerical modeling of groundwater solute transport, explicit solutions may be obtained for the concentration field at any future time without computing concentrations at intermediate times. The spatial variables are discretized and time is left continuous in the governing differential equation. These semianalytical solutions have been presented in the literature and involve the eigensystem of a coefficient matrix. This eigensystem may be complex (i.e., have imaginary components) due to the asymmetry created by the advection term in the governing advection-dispersion equation. Previous investigators have either used complex arithmetic to represent a complex eigensystem or chosen large dispersivity values for which the imaginary components of the complex eigenvalues may be ignored without significant error. It is shown here that the error due to ignoring the imaginary components of complex eigenvalues is large for small dispersivity values. A new algorithm that represents the complex eigensystem by converting it to a real eigensystem is presented. The method requires only real arithmetic.

A Hypergraph and Arithmetic Residue-based Probabilistic Neural Network for classification in Intrusion Detection Systems.

PubMed

Raman, M R Gauthama; Somu, Nivethitha; Kirthivasan, Kannan; Sriram, V S Shankar

2017-08-01

Over the past few decades, the design of an intelligent Intrusion Detection System (IDS) remains an open challenge to the research community. Continuous efforts by the researchers have resulted in the development of several learning models based on Artificial Neural Network (ANN) to improve the performance of the IDSs. However, there exists a tradeoff with respect to the stability of ANN architecture and the detection rate for less frequent attacks. This paper presents a novel approach based on Helly property of Hypergraph and Arithmetic Residue-based Probabilistic Neural Network (HG AR-PNN) to address the classification problem in IDS. The Helly property of Hypergraph was exploited for the identification of the optimal feature subset and the arithmetic residue of the optimal feature subset was used to train the PNN. The performance of HG AR-PNN was evaluated using KDD CUP 1999 intrusion dataset. Experimental results prove the dominance of HG AR-PNN classifier over the existing classifiers with respect to the stability and improved detection rate for less frequent attacks. Copyright © 2017 Elsevier Ltd. All rights reserved.

On the Problem-Size Effect in Small Additions: Can We Really Discard Any Counting-Based Account?

ERIC Educational Resources Information Center

Barrouillet, Pierre; Thevenot, Catherine

2013-01-01

The problem-size effect in simple additions, that is the increase in response times (RTs) and error rates with the size of the operands, is one of the most robust effects in cognitive arithmetic. Current accounts focus on factors that could affect speed of retrieval of the answers from long-term memory such as the occurrence of interference in a…

Aging and sequential modulations of poorer strategy effects: An EEG study in arithmetic problem solving.

PubMed

Hinault, Thomas; Lemaire, Patrick; Phillips, Natalie

2016-01-01

This study investigated age-related differences in electrophysiological signatures of sequential modulations of poorer strategy effects. Sequential modulations of poorer strategy effects refer to decreased poorer strategy effects (i.e., poorer performance when the cued strategy is not the best) on current problem following poorer strategy problems compared to after better strategy problems. Analyses on electrophysiological (EEG) data revealed important age-related changes in time, frequency, and coherence of brain activities underlying sequential modulations of poorer strategy effects. More specifically, sequential modulations of poorer strategy effects were associated with earlier and later time windows (i.e., between 200- and 550 ms and between 850- and 1250 ms). Event-related potentials (ERPs) also revealed an earlier onset in older adults, together with more anterior and less lateralized activations. Furthermore, sequential modulations of poorer strategy effects were associated with theta and alpha frequencies in young adults while these modulations were found in delta frequency and theta inter-hemispheric coherence in older adults, consistent with qualitatively distinct patterns of brain activity. These findings have important implications to further our understanding of age-related differences and similarities in sequential modulations of cognitive control processes during arithmetic strategy execution. Copyright © 2015 Elsevier B.V. All rights reserved.

The Impossibility of "Real-Life" Word Problems (According to Bakhtin, Lacan, Zizek and Baudrillard)

ERIC Educational Resources Information Center

Gerofsky, Susan

2010-01-01

In recent years a great deal of work on mathematical word problems has focused on efforts to bring more of "real life" into the problems themselves and students' uptake of these problems. Following on from earlier studies of the word problem as a pedagogical and literary genre, the author argues that we cannot unproblematically assume an ability…

Procedural versus Content-Related Hints for Word Problem Solving: An Exploratory Study

ERIC Educational Resources Information Center

Kock, W. D.; Harskamp, E. G.

2016-01-01

For primary school students, mathematical word problems are often more difficult to solve than straightforward number problems. Word problems require reading and analysis skills, and in order to explain their situational contexts, the proper mathematical knowledge and number operations have to be selected. To improve students' ability in solving…

Mathematics Framework for California Public Schools, Kindergarten Through Grade Twelve.

ERIC Educational Resources Information Center

California State Dept. of Education, Sacramento.

This report, prepared by a statewide Mathematics Advisory Committee, revises the framework in the Second Strands Report of 1972, expanding it to encompass kindergarten through grade 12. Strands for kindergarten through grade 8 are: arithmetic, numbers, and operations; geometry; measurement, problem solving/ applications; probability and…

Student Math Skills Reference Manual.

ERIC Educational Resources Information Center

Wilson, Odell; And Others

This mathematics support guide is intended for use by vocational students and instructors as a review of essential mathematics concepts and for problem-solving exercises in the vocations. It is designed to accompany the "Mathematical Skills Inventory," which tests mathematics skills, attitudes, and background. A section entitled Arithmetic Skills…

Mathematics for Commercial Foods.

ERIC Educational Resources Information Center

Wersan, Norman

A review of basic mathematics operations is presented with problems and examples applied to activities in the food service industry. The text is divided into eight units: measurement, fractions, arithmetic operations, money and decimals, percentage, ratio and proportion, wages and taxes, and business records. Each unit contains a series of lessons…

Cognitive Consequences of Traditional Apprenticeship Training in West Africa

ERIC Educational Resources Information Center

Lave, Jean

1977-01-01

Addresses the question of the impact of native educational institutions on individual cognitive skills. Examines the Liberian tailor apprenticeship system, and focuses upon tailors' arithmetic skills. Concludes that the inductive teaching learning techniques of apprenticeship training do not prevent the formation of general problem solving…

Students’ Mathematical Literacy in Solving PISA Problems Based on Keirsey Personality Theory

NASA Astrophysics Data System (ADS)

Masriyah; Firmansyah, M. H.

2018-01-01

This research is descriptive-qualitative research. The purpose is to describe students’ mathematical literacy in solving PISA on space and shape content based on Keirsey personality theory. The subjects are four junior high school students grade eight with guardian, artisan, rational or idealist personality. Data collecting methods used test and interview. Data of Keirsey Personality test, PISA test, and interview were analysed. Profile of mathematical literacy of each subject are described as follows. In formulating, guardian subject identified mathematical aspects are formula of rectangle area and sides length; significant variables are terms/conditions in problem and formula of ever encountered question; translated into mathematical language those are measurement and arithmetic operations. In employing, he devised and implemented strategies using ease of calculation on area-subtraction principle; declared truth of result but the reason was less correct; didn’t use and switch between different representations. In interpreting, he declared result as area of house floor; declared reasonableness according measurement estimation. In formulating, artisan subject identified mathematical aspects are plane and sides length; significant variables are solution procedure on both of daily problem and ever encountered question; translated into mathematical language those are measurement, variables, and arithmetic operations as well as symbol representation. In employing, he devised and implemented strategies using two design comparison; declared truth of result without reason; used symbol representation only. In interpreting, he expressed result as floor area of house; declared reasonableness according measurement estimation. In formulating, rational subject identified mathematical aspects are scale and sides length; significant variables are solution strategy on ever encountered question; translated into mathematical language those are measurement, variable, arithmetic operation as well as symbol and graphic representation. In employing, he devised and implemented strategies using additional plane forming on area-subtraction principle; declared truth of result according calculation process; used and switched between symbol and graphic representation. In interpreting, he declared result as house area within terrace and wall; declared reasonableness according measurement estimation. In formulating, idealist subject identified mathematical aspects are sides length; significant variables are terms/condition in problem; translated into mathematical language those are measurement, variables, arithmetic operations as well as symbol and graphic representation. In employing, he devised and implemented strategies using trial and error and two design in process of finding solutions; declared truth of result according the use of two design of solution; used and switched between symbol and graphic representation. In interpreting, he declared result as floor area of house; declared reasonableness according measurement estimation.

Age-related differences in children's strategy repetition: A study in arithmetic.

PubMed

Lemaire, Patrick; Brun, Fleur

2016-10-01

Third and fifth graders (Experiment 1) and fifth and seventh graders (Experiment 2) accomplished computational estimation tasks in which they provided estimates to two-digit arithmetic problems (e.g., 34+68). Participants saw trials, each including three consecutive problems. Each trial was separated by a letter judgment task (i.e., participants needed to say whether a series of four letters included only vowels, only consonants, or both types of letters). On each problem, children were asked to select the better of the following strategies: rounding down (i.e., rounding both operands down to the nearest decades; e.g., 30+60=90) or rounding up (rounding both operands up to the nearest decades; e.g., 40+70=110). Half of the trials were repeated strategy trials (i.e., the better strategy was the same for the first two prime problems and the last target problem) and half were unrepeated strategy trials (i.e., the better strategy was different for prime and target problems). We found that (a) children repeated the same strategy over successive problems, even when they should change strategies to obtain better performance, (b) strategy repetitions decreased with age, (c) repeating the same strategy gave children performance benefits, and (d) these strategy repetition benefits were similar across grades. These effects of strategy repetition during strategy selection and strategy execution have important empirical and theoretical implications regarding how children choose among strategies, how children execute selected strategies on each problem, and how strategic variations change with age. Copyright © 2016 Elsevier Inc. All rights reserved.

Quality of Arithmetic Education for Children with Cerebral Palsy

ERIC Educational Resources Information Center

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

2010-01-01

The aim of this exploratory study was to investigate the quality of arithmetic education for children with cerebral palsy. The use of individual educational plans, amount of arithmetic instruction time, arithmetic instructional grouping, and type of arithmetic teaching method were explored in three groups: children with cerebral palsy (CP) in…

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.

Attentional Cuing in Math Word Problems for Girls At-Risk for ADHD and Their Peers in General Education Settings

ERIC Educational Resources Information Center

Kercood, Suneeta; Zentall, Sydney S.; Vinh, Megan; Tom-Wright, Kinsey

2012-01-01

The purpose of this theoretically-based study was to examine the effects of yellow-highlighting "relevant" words and units within math word problems. Initial differences were documented between 10 girls at-risk for ADHD and 10 comparisons on the performance of group and individual assessments of math computations and word problems, as had…

Teaching Fifth Grade Mathematical Concepts: Effects of Word Problems Used with Traditional Methods.

ERIC Educational Resources Information Center

Coy, Jessica

The view of the researcher is that students in the upper elementary to middle school range need to increase their problem-solving skills by making logical deductions and organizing and structuring their thoughts through the use of word problems. Giving children a daily word problem challenged and introduced them to the lesson. This activity…

A Joint Probabilistic Classification Model of Relevant and Irrelevant Sentences in Mathematical Word Problems

ERIC Educational Resources Information Center

Cetintas, Suleyman; Si, Luo; Xin, Yan Ping; Zhang, Dake; Park, Joo Young; Tzur, Ron

2010-01-01

Estimating the difficulty level of math word problems is an important task for many educational applications. Identification of relevant and irrelevant sentences in math word problems is an important step for calculating the difficulty levels of such problems. This paper addresses a novel application of text categorization to identify two types of…

Process Inquiry: Analysis of Oral Problem-Solving Skills in Mathematics of Engineering Students

ERIC Educational Resources Information Center

Trance, Naci John C.

2013-01-01

This paper presents another effort in determining the difficulty of engineering students in terms of solving word problems. Students were presented with word problems in algebra. Then, they were asked to solve the word problems orally; that is, before they presented their written solutions, they were required to explain how they understood the…

The relation between children’s constructive play activities, spatial ability, and mathematical word problem-solving performance: a mediation analysis in sixth-grade students

PubMed Central

Oostermeijer, Meike; Boonen, Anton J. H.; Jolles, Jelle

2014-01-01

The scientific literature shows that constructive play activities are positively related to children’s spatial ability. Likewise, a close positive relation is found between spatial ability and mathematical word problem-solving performances. The relation between children’s constructive play and their performance on mathematical word problems is, however, not reported yet. The aim of the present study was to investigate whether spatial ability acted as a mediator in the relation between constructive play and mathematical word problem-solving performance in 128 sixth-grade elementary school children. This mediating role of spatial ability was tested by utilizing the current mediation approaches suggested by Preacher and Hayes (2008). Results showed that 38.16% of the variance in mathematical word problem-solving performance is explained by children’s constructive play activities and spatial ability. More specifically, spatial ability acted as a partial mediator, explaining 31.58% of the relation between constructive play and mathematical word problem-solving performance. PMID:25101038

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

Mathematics for the Middle Grades (5-9). 1982 Yearbook.

ERIC Educational Resources Information Center

Silvey, Linda, Ed.; Smart, James R., Ed.

This yearbook for teachers of mathematics in grades 5-9 contains three sections: (1) critical issues; (2) learning activities; and (3) games, contests, and student presentations. The first section includes articles on sex-related differences, learning disabled students, computer literacy, mental arithmetic, rational numbers, and problem solving.…

Critical Skills Survey

ERIC Educational Resources Information Center

Education Digest: Essential Readings Condensed for Quick Review, 2010

2010-01-01

As the U.S. economy begins to show signs of improvement, executives say they need a workforce fully equipped with skills beyond just the basics of reading, writing, and arithmetic (the three Rs). Skills such as critical thinking and problem solving, communication, collaboration, and creativity and innovation (the four Cs) will become even more…

Mathematics Difficulties: Does One Approach Fit All?

ERIC Educational Resources Information Center

Gifford, Sue; Rockliffe, Freda

2012-01-01

This article reviews the nature of learning difficulties in mathematics and, in particular, the nature and prevalence of dyscalculia, a condition that affects the acquisition of arithmetical skills. The evidence reviewed suggests that younger children (under the age of 10) often display a combination of problems, including minor physical…

A New Approach to Teaching Business Oriented Students.

ERIC Educational Resources Information Center

Merchant, Ronald

1980-01-01

Describes a competency based business mathematics course offered at Spokane Falls Community College (Washington) in which students, through the use of calculators, master mathematical concepts without having to mentally add columns of figures or perform complex arithmetic problems on paper. Examines both the mathematical and 10-key skills…

High and Low Visualization Skills and Pedagogical Decision of Preservice Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Unal, Hasan

2011-01-01

The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers…

Conservation II. Science Activities in Energy. [Student's and] Teacher's Guide.

ERIC Educational Resources Information Center

Oak Ridge Associated Universities, TN.

Designed for science students in fourth, fifth, and sixth grades, the activities in this unit illustrate principles and problems related to the conservation of energy. Eleven student activities using art, economics, arithmetic, and other skills and disciplines help teachers directly involve students in exploring scientific questions and making…

The Virginia History Standards and the Cold War

ERIC Educational Resources Information Center

Altschuler, Glenn C.; Rauchway, Eric

2002-01-01

President George W. Bush's approach to education policy has earned him cautious plaudits from otherwise hostile critics, who see much to admire in the implementation of standards for education. However useful such standards for testing students' technical skills like arithmetic and reading, they create problems for less-standardized processes like…

Pacemaker Primary Curriculum; Lesson Book Level C.

ERIC Educational Resources Information Center

Ross, Dorothea M.; Ross, Sheila A.

This lesson book, which is the third in a four-level program for young children with learning difficulties, describes the purpose of and equipment and procedures for teaching lessons in the following subject areas on the primary grade level: arithmetic, reading, vocabulary, spelling, printing, listening, planning, problem solving, social behavior,…

Pacemaker Primary Curriculum; Lesson Book Level B.

ERIC Educational Resources Information Center

Ross, Dorothea M.; Ross, Sheila A.

This lesson book, which is the second in a four-level program for young children with learning difficulties, describes the purpose of and equipment and procedures for teaching lessons in the following subjects areas on the primary grade level: arithmetic, reading, vocabulary, listening, planning, problem solving, social behavior, art, music, and…

Pacemaker Primary Curriculum; Lesson Book Level D.

ERIC Educational Resources Information Center

Ross, Dorothea M.; Ross, Sheila A.

This lesson book, which is the last in a four-level program for young children with learning difficulties, describes the purpose of and equipment and procedures for teaching lessons in the following subject areas on the primary level: arithmetic, reading, vocabulary, spelling, printing, listening, planning and problem solving, social behavior,…

Investigations in Mathematics Education. Volume 20, Number 3.

ERIC Educational Resources Information Center

Suydam, Marilyn N., Ed.; Kasten, Margaret L., Ed.

1987-01-01

This issue contains abstracts and critical comments for 10 papers. The reports are concerned with: (1) children's inferencing behavior; (2) instruction related to problem-solving and basic skills for seventh grade students; (3) remediation of children's subtraction errors; (4) investigation of young children's academic arithmetic contexts; (5)…

Business Mathematics Syllabus.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Bureau of Secondary Curriculum Development.

The course is designed to build the knowledge and skills necessary to solve a variety of arithmetic problems that are commonly found in business situations, specifically for occupationally oriented students who have the ultimate objective of gainful employment in offices or stores, or who are preparing for careers in fields such as agriculture,…

Working Memory Capacity and Categorization: Individual Differences and Modeling

ERIC Educational Resources Information Center

Lewandowsky, Stephan

2011-01-01

Working memory is crucial for many higher-level cognitive functions, ranging from mental arithmetic to reasoning and problem solving. Likewise, the ability to learn and categorize novel concepts forms an indispensable part of human cognition. However, very little is known about the relationship between working memory and categorization, and…

Algebra 2u, Mathematics (Experimental): 5216.26.

ERIC Educational Resources Information Center

Crawford, Glenda

The sixth in a series of six guidebooks on minimum course content for second-year algebra, this booklet presents an introduction to sequences, series, permutation, combinations, and probability. Included are arithmetic and geometric progressions and problems solved by counting and factorials. Overall course goals are specified, a course outline is…

Findings of Studies on Dyscalculia--A Synthesis

ERIC Educational Resources Information Center

Raja, B. William Dharma; Kumar, S. Praveen

2012-01-01

Children with learning disabilities face problems in acquiring the basic skills needed for learning. Dyscalculia is one among those learning disorders which affects the ability to acquire arithmetic skills that are needed to perform mathematical calculations. However this is a learning difficulty which is often not recognized. The objectives of…

Treating Dyslexic and Dyscalculic Students

ERIC Educational Resources Information Center

Kumar, S. Praveen; Raja, B. William Dharma

2009-01-01

This article focusses on the specific learning disabilities found in schools such as Dyslexia and Dyscalculia, the influence of dyslexia on dyscalculia and the need to adopt certain strategies that help cope with this problem. Learners with multifarious language-related or arithmetic-related disabilities are found in most schools. These children…

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.

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.

The Association between Mathematical Word Problems and Reading Comprehension

ERIC Educational Resources Information Center

Vilenius-Tuohimaa, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik

2008-01-01

This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9-10 (Grade 4). The children's text comprehension and mathematical word problem-solving performance was tested. Technical reading skills were investigated in order to categorise participants as…

Bilingual College Writers' Collaborative Writing of Word Problems

ERIC Educational Resources Information Center

Esquinca, Alberto

2011-01-01

Numerous researchers have studied bilingual students' performance on word problems given that reading and writing these requires that they draw on linguistic and mathematical knowledge (Barwell, 2009a, 2009b). Some researchers have studied how bilinguals write word problems in the second language, but few have considered how bilinguals use their…

Cognitive Strategy Instruction for Teaching Word Problems to Primary-Level Struggling Students

ERIC Educational Resources Information Center

Pfannenstiel, Kathleen Hughes; Bryant, Diane Pedrotty; Bryant, Brian R.; Porterfield, Jennifer A.

2015-01-01

Students with mathematics difficulties and learning disabilities (LD) typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to utilize when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word…

How number line estimation skills relate to neural activations in single digit subtraction problems

PubMed Central

Berteletti, I.; Man, G.; Booth, J.R.

2014-01-01

The Number Line (NL) task requires judging the relative numerical magnitude of a number and estimating its value spatially on a continuous line. Children's skill on this task has been shown to correlate with and predict future mathematical competence. Neurofunctionally, this task has been shown to rely on brain regions involved in numerical processing. However, there is no direct evidence that performance on the NL task is related to brain areas recruited during arithmetical processing and that these areas are domain-specific to numerical processing. In this study, we test whether 8- to 14-year-old's behavioral performance on the NL task is related to fMRI activation during small and large single-digit subtraction problems. Domain-specific areas for numerical processing were independently localized through a numerosity judgment task. Results show a direct relation between NL estimation performance and the amount of the activation in key areas for arithmetical processing. Better NL estimators showed a larger problem size effect than poorer NL estimators in numerical magnitude (i.e., intraparietal sulcus) and visuospatial areas (i.e., posterior superior parietal lobules), marked by less activation for small problems. In addition, the direction of the activation with problem size within the IPS was associated to differences in accuracies for small subtraction problems. This study is the first to show that performance in the NL task, i.e. estimating the spatial position of a number on an interval, correlates with brain activity observed during single-digit subtraction problem in regions thought to be involved numerical magnitude and spatial processes. PMID:25497398

Mathematical Word Problem Solving Ability of Children with Autism Spectrum Disorder and their Typically Developing Peers.

PubMed

Bae, Young Seh; Chiang, Hsu-Min; Hickson, Linda

2015-07-01

This study examined the difference between children with autism spectrum disorders (ASD) and children with typical development (TD) in mathematical word problem solving ability and the factors associated with these children's word problem-solving ability. A total of 20 children with ASD and 20 children with TD participated in this study. Independent sample t tests and Spearman's rho correlations were used for data analysis. This study found: (a) Children with TD had higher word problem solving ability than did children with ASD; (b) Sentence comprehension, math vocabulary, computation, and everyday mathematical knowledge were associated with word problem solving ability of children with ASD and children with TD; and (c) Children with TD had higher everyday mathematical knowledge than did children with ASD.

Sources of difficulty in the solution of verbal arithmetic problems by mentally retarded and nonretarded individuals.

PubMed

Bilsky, L H; Judd, T

1986-01-01

Effects of several logical (i.e., operation type and amount of extraneous information), memory (i.e., availability of memory aids and number of problem presentations), and semantic variables (i.e., problem text type) on verbal math problem-solving performance were assessed. Results revealed that the overall problem-solving performance of mildly mentally retarded adolescents was inferior to that of nonretarded fourth graders in spite of comparable performance on a computational screening test. Although the retarded individuals experienced particular difficulty with subtraction and static problem texts, the two groups responded similarly to the other experimental variables. The possibly important role of comprehension in problem-solving was discussed.

The effect of problem structure on problem-solving: an fMRI study of word versus number problems.

PubMed

Newman, Sharlene D; Willoughby, Gregory; Pruce, Benjamin

2011-09-02

It has long been thought that word problems are more difficult to solve than number/equation problems. However, recent findings have begun to bring this broadly believed idea into question. The current study examined the processing differences between these two types of problems. The behavioral results presented here failed to show an overwhelming advantage for number problems. In fact, there were more errors for the number problems than the word problems. The neuroimaging results reported demonstrate that there is significant overlap in the processing of what, on the surface, appears to be completely different problems that elicit different problem-solving strategies. Word and number problems rely on a general network responsible for problem-solving that includes the superior posterior parietal cortex, the horizontal segment of the intraparietal sulcus which is hypothesized to be involved in problem representation and calculation as well as the regions that have been linked to executive aspects of working memory such as the pre-SMA and basal ganglia. While overlap was observed, significant differences were also found primarily in language processing regions such as Broca's and Wernicke's areas for the word problems and the horizontal segment of the intraparietal sulcus for the number problems. Copyright © 2011 Elsevier B.V. All rights reserved.

The role of language in mathematical development: evidence from children with specific language impairments.

PubMed

Donlan, Chris; Cowan, Richard; Newton, Elizabeth J; Lloyd, Delyth

2007-04-01

A sample (n=48) of eight-year-olds with specific language impairments is compared with age-matched (n=55) and language matched controls (n=55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of the count word sequence and basic calculation and significant deficits in understanding of the place-value principle in Hindu-Arabic notation. Only in understanding of arithmetic principles does SLI performance approximate that of age-matched-controls, indicating that principled understanding can develop even where number sequence production and other aspects of number processing are severely compromised.

A polymorphic reconfigurable emulator for parallel simulation

NASA Technical Reports Server (NTRS)

Parrish, E. A., Jr.; Mcvey, E. S.; Cook, G.

1980-01-01

Microprocessor and arithmetic support chip technology was applied to the design of a reconfigurable emulator for real time flight simulation. The system developed consists of master control system to perform all man machine interactions and to configure the hardware to emulate a given aircraft, and numerous slave compute modules (SCM) which comprise the parallel computational units. It is shown that all parts of the state equations can be worked on simultaneously but that the algebraic equations cannot (unless they are slowly varying). Attempts to obtain algorithms that will allow parellel updates are reported. The word length and step size to be used in the SCM's is determined and the architecture of the hardware and software is described.

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.

Developmental amnesia: a new pattern of dissociation with intact episodic memory.

PubMed

Temple, Christine M; Richardson, Paul

2004-01-01

A case of developmental amnesia is reported for a child, CL, of normal intelligence, who has intact episodic memory but impaired semantic memory for both semantic knowledge of facts and semantic knowledge of words, including general world knowledge, knowledge of word meanings and superordinate knowledge of words. In contrast to the deficits in semantic memory, there are no impairments in episodic memory for verbal or visual material, assessed by recall or recognition. Lexical decision was also intact, indicating impairment in semantic knowledge of vocabulary rather than absence of lexical representations. The case forms a double dissociation to the cases of Vargha-Khadem et al. [Science 277 (1997) 376; Episodic memory: new directions in research (2002) 153]; Gadian et al. [Brain 123 (2000) 499] for whom semantic memory was intact but episodic memory was impaired. This double dissociation suggests that semantic memory and episodic memory have the capacity to develop separately and supports models of modularity within memory development and a functional architecture for the developmental disorders within which there is residual normality rather than pervasive abnormality. Knowledge of arithmetical facts is also spared for CL, consistent with adult studies arguing for numeracy knowledge distinct from other semantics. Reading was characterised by difficulty with irregular words and homophones but intact reading of nonwords. CL has surface dyslexia with poor lexico-semantic reading skills but good phonological reading skills. The case was identified following screening from a population of normal schoolchildren suggesting that developmental amnesias may be more pervasive than has been recognised previously.

Non-symbolic approximate arithmetic training improves math performance in preschoolers.

PubMed

Park, Joonkoo; Bermudez, Vanessa; Roberts, Rachel C; Brannon, Elizabeth M

2016-12-01

Math proficiency at early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in preschool-age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher income peers. The majority of existing research-based math intervention programs target symbolic verbal number concepts in young children. However, very little attention has been paid to the preverbal intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we tested the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large arrays of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. In the current study, 3- to 5-year-olds showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared with children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words. Copyright © 2016 Elsevier Inc. All rights reserved.

Non-symbolic approximate arithmetic training improves math performance in preschoolers

PubMed Central

Park, Joonkoo; Bermudez, Vanessa; Roberts, Rachel C.; Brannon, Elizabeth M.

2016-01-01

Math proficiency in early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in pre-school age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher-income peers. The majority of existing research-based math intervention programs target symbolic, verbal number concepts in young children. However, very little attention has been paid to the preverbal, intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we test the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large array of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. Three to five year-old children showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared to children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words. PMID:27596808

Word Problem Strategy for Latino English Language Learners at Risk for Math Disabilities

ERIC Educational Resources Information Center

Orosco, Michael J.

2014-01-01

"English Language Learners" (ELLs) at risk for "math disabilities" (MD) are challenged in solving word problems for numerous reasons such as (a) learning English as a second language, (b) limited experience using math vocabulary, and (c) lack of strategies to improve word-problem-solving skills. As a result of these…

Helping Students with Emotional and Behavioral Disorders Solve Mathematics Word Problems

ERIC Educational Resources Information Center

Alter, Peter

2012-01-01

The author presents a strategy for helping students with emotional and behavioral disorders become more proficient at solving math word problems. Math word problems require students to go beyond simple computation in mathematics (e.g., adding, subtracting, multiplying, and dividing) and use higher level reasoning that includes recognizing relevant…

Does Calculation or Word-Problem Instruction Provide a Stronger Route to Prealgebraic Knowledge?

ERIC Educational Resources Information Center

Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.

2014-01-01

The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and prealgebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other…

Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development

ERIC Educational Resources Information Center

Bae, Young Seh

2013-01-01

Mathematical Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development Young Seh Bae This study investigated mathematical word problem solving and the factors associated with the solution paths adopted by two groups of participants (N=40), students with autism spectrum disorders (ASDs) and typically…

Examining How Students with Diverse Abilities Use Diagrams to Solve Mathematics Word Problems

ERIC Educational Resources Information Center

van Garderen, Delinda; Scheuermann, Amy; Jackson, Christa

2013-01-01

This study examined students' understanding of diagrams and their use of diagrams as tools to solve mathematical word problems. Students with learning disabilities (LD), typically achieving students, and gifted students in Grades 4 through 7 ("N" = 95) participated. Students were presented with novel mathematical word problem-solving…

Why Do Disadvantaged Filipino Children Find Word Problems in English Difficult?

ERIC Educational Resources Information Center

Bautista, Debbie; Mulligan, Joanne

2010-01-01

Young Filipino students are expected to solve mathematical word problems in English, a language that many encounter only in schools. Using individual interviews of 17 Filipino children, we investigated why word problems in English are difficult and the extent to which the language interferes with performance. Results indicate that children could…

Word Problem Solving: A Schema Approach in Year 3

ERIC Educational Resources Information Center

van Klinken, Eduarda

2012-01-01

This article outlines how a Brisbane independent school, Clayfield College, improved the ability of its Year 3 students to solve addition and subtraction word problems by utilising a schematic approach. It was observed that while students could read the words in the text of a written problem, many had difficulty identifying the core information…

Effects of computer-based graphic organizers to solve one-step word problems for middle school students with mild intellectual disability: A preliminary study.

PubMed

Sheriff, Kelli A; Boon, Richard T

2014-08-01

The purpose of this study was to examine the effects of computer-based graphic organizers, using Kidspiration 3© software, to solve one-step word problems. Participants included three students with mild intellectual disability enrolled in a functional academic skills curriculum in a self-contained classroom. A multiple probe single-subject research design (Horner & Baer, 1978) was used to evaluate the effectiveness of computer-based graphic organizers to solving mathematical one-step word problems. During the baseline phase, the students completed a teacher-generated worksheet that consisted of nine functional word problems in a traditional format using a pencil, paper, and a calculator. In the intervention and maintenance phases, the students were instructed to complete the word problems using a computer-based graphic organizer. Results indicated that all three of the students improved in their ability to solve the one-step word problems using computer-based graphic organizers compared to traditional instructional practices. Limitations of the study and recommendations for future research directions are discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Special relativity from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

The Mathematics of Sex and Marriage

DTIC Science & Technology

1972-01-01

the sense in which the one-sex problem is solved. A given and fixed set of birth and death rates , specific by age, say for females, determines the...and the second a weighted arithmetic mean of the given death rates ,UM and AF, the weights being the reciprocals of the birth rates. The... death rates . An example will suffice to present the problem and the proposed solution. Let us try to decide whether marriage among single persons 20 to

Developmental dissociation in the neural responses to simple multiplication and subtraction problems

PubMed Central

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 cross-sectional design to measure the neural activity associated with single-digit subtraction and multiplication in 34 children from 2nd to 7th grade. The neural correlates of language and numerical processing were also identified in each child via localizer scans. Although multiplication and subtraction were undistinguishable in terms of behavior, we found a striking developmental dissociation in their neural correlates. First, we observed grade-related increases of activity for multiplication, but not for subtraction, in a language-related region of the left temporal cortex. Second, we found grade-related increases of activity for subtraction, but not for multiplication, in a region of the right parietal cortex involved in the procedural manipulation of numerical quantities. The present results suggest that fluency in simple arithmetic in children may be achieved by both increasing reliance on verbal retrieval and by greater use of efficient quantity-based procedures, depending on the operation. PMID:25089323

Bounds for the price of discrete arithmetic Asian options

NASA Astrophysics Data System (ADS)

Vanmaele, M.; Deelstra, G.; Liinev, J.; Dhaene, J.; Goovaerts, M. J.

2006-01-01

In this paper the pricing of European-style discrete arithmetic Asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds. In our approach we use a general technique for deriving upper (and lower) bounds for stop-loss premiums of sums of dependent random variables, as explained in Kaas et al. (Ins. Math. Econom. 27 (2000) 151-168), and additionally, the ideas of Rogers and Shi (J. Appl. Probab. 32 (1995) 1077-1088) and of Nielsen and Sandmann (J. Financial Quant. Anal. 38(2) (2003) 449-473). We are able to create a unifying framework for European-style discrete arithmetic Asian options through these bounds, that generalizes several approaches in the literature as well as improves the existing results. We obtain analytical and easily computable bounds. The aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters, investigate the effect of different conditioning variables and compare their efficiency numerically. Several sets of numerical results are included. We also discuss hedging using these bounds. Moreover, our methods are applicable to a wide range of (pricing) problems involving a sum of dependent random variables.

Fast Fuzzy Arithmetic Operations

NASA Technical Reports Server (NTRS)

Hampton, Michael; Kosheleva, Olga

1997-01-01

In engineering applications of fuzzy logic, the main goal is not to simulate the way the experts really think, but to come up with a good engineering solution that would (ideally) be better than the expert's control, In such applications, it makes perfect sense to restrict ourselves to simplified approximate expressions for membership functions. If we need to perform arithmetic operations with the resulting fuzzy numbers, then we can use simple and fast algorithms that are known for operations with simple membership functions. In other applications, especially the ones that are related to humanities, simulating experts is one of the main goals. In such applications, we must use membership functions that capture every nuance of the expert's opinion; these functions are therefore complicated, and fuzzy arithmetic operations with the corresponding fuzzy numbers become a computational problem. In this paper, we design a new algorithm for performing such operations. This algorithm is applicable in the case when negative logarithms - log(u(x)) of membership functions u(x) are convex, and reduces computation time from O(n(exp 2))to O(n log(n)) (where n is the number of points x at which we know the membership functions u(x)).

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.

Processes in arithmetic strategy selection: a fMRI study.

PubMed

Taillan, Julien; Ardiale, Eléonore; Anton, Jean-Luc; Nazarian, Bruno; Félician, Olivier; Lemaire, Patrick

2015-01-01

This neuroimaging (functional magnetic resonance imaging) study investigated neural correlates of strategy selection. Young adults performed an arithmetic task in two different conditions. In both conditions, participants had to provide estimates of two-digit multiplication problems like 54 × 78. In the choice condition, participants had to select the better of two available rounding strategies, rounding-up (RU) strategy (i.e., doing 60 × 80 = 4,800) or rounding-down (RD) strategy (i.e., doing 50 × 70 = 3,500 to estimate product of 54 × 78). In the no-choice condition, participants did not have to select strategy on each problem but were told which strategy to use; they executed RU and RD strategies each on a series of problems. Participants also had a control task (i.e., providing correct products of multiplication problems like 40 × 50). Brain activations and performance were analyzed as a function of these conditions. Participants were able to frequently choose the better strategy in the choice condition; they were also slower when they executed the difficult RU than the easier RD. Neuroimaging data showed greater brain activations in right anterior cingulate cortex (ACC), dorso-lateral prefrontal cortex (DLPFC), and angular gyrus (ANG), when selecting (relative to executing) the better strategy on each problem. Moreover, RU was associated with more parietal cortex activation than RD. These results suggest an important role of fronto-parietal network in strategy selection and have important implications for our further understanding and modeling cognitive processes underlying strategy selection.

Processes in arithmetic strategy selection: a fMRI study

PubMed Central

Taillan, Julien; Ardiale, Eléonore; Anton, Jean-Luc; Nazarian, Bruno; Félician, Olivier; Lemaire, Patrick

2015-01-01

This neuroimaging (functional magnetic resonance imaging) study investigated neural correlates of strategy selection. Young adults performed an arithmetic task in two different conditions. In both conditions, participants had to provide estimates of two-digit multiplication problems like 54 × 78. In the choice condition, participants had to select the better of two available rounding strategies, rounding-up (RU) strategy (i.e., doing 60 × 80 = 4,800) or rounding-down (RD) strategy (i.e., doing 50 × 70 = 3,500 to estimate product of 54 × 78). In the no-choice condition, participants did not have to select strategy on each problem but were told which strategy to use; they executed RU and RD strategies each on a series of problems. Participants also had a control task (i.e., providing correct products of multiplication problems like 40 × 50). Brain activations and performance were analyzed as a function of these conditions. Participants were able to frequently choose the better strategy in the choice condition; they were also slower when they executed the difficult RU than the easier RD. Neuroimaging data showed greater brain activations in right anterior cingulate cortex (ACC), dorso-lateral prefrontal cortex (DLPFC), and angular gyrus (ANG), when selecting (relative to executing) the better strategy on each problem. Moreover, RU was associated with more parietal cortex activation than RD. These results suggest an important role of fronto-parietal network in strategy selection and have important implications for our further understanding and modeling cognitive processes underlying strategy selection. PMID:25698995

Modelling with Difference Equations Supported by GeoGebra: Exploring the Kepler Problem

ERIC Educational Resources Information Center

Kovacs, Zoltan

2010-01-01

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

Contextualizing Arithmetic into Developmental Elementary Algebra Using Guided Problem Solving

ERIC Educational Resources Information Center

Guy, G. Michael; Cornick, Jonathan; Puri, Karan

2016-01-01

Many colleges are finding that the use of acceleration in developmental education is a promising direction for improved student progress toward a degree or certificate. Acceleration has been defined in the literature as the reorganization of curricula and instruction in ways that facilitate the completion of educational requirements in an…

Algebraic Functions, Computer Programming, and the Challenge of Transfer

ERIC Educational Resources Information Center

Schanzer, Emmanuel Tanenbaum

2015-01-01

Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

Staff Development Project--Mathematics. Grades K-6. Revision.

ERIC Educational Resources Information Center

Shaw, Jean M.; And Others

This manual was designed for use in conducting staff development sessions for elementary teachers of mathematics in Mississippi in grades K-6. The four topical areas treated in the document are: (1) measurement and geometry; (2) fractions; (3) procedural errors in arithmetic; and (4) problem solving. The number of instructional hours necessary for…

Identities for Generalized Fibonacci Numbers: A Combinatorial Approach

ERIC Educational Resources Information Center

Plaza, A.; Falcon, S.

2008-01-01

This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. (Contains…

Rounding Technique for High-Speed Digital Signal Processing

NASA Technical Reports Server (NTRS)

Wechsler, E. R.

1983-01-01

Arithmetic technique facilitates high-speed rounding of 2's complement binary data. Conventional rounding of 2's complement numbers presents problems in high-speed digital circuits. Proposed technique consists of truncating K + 1 bits then attaching bit in least significant position. Mean output error is zero, eliminating introducing voltage offset at input.

Business and Technology Concepts--Business Computations. Teacher's Guide.

ERIC Educational Resources Information Center

Illinois State Board of Education, Springfield. Dept. of Adult, Vocational and Technical Education.

This Illinois State Board of Education teacher's guide on business computations is for students enrolled in the 9th or 10th grade. The course provides a foundation in arithmetic skills and their applications to common business problems for the senior high school vocational business courses. The curriculum guide includes teacher and student…

Eating breakfast enhances the efficiency of neural networks engaged during mental arithmetic in school-aged children

USDA-ARS?s Scientific Manuscript database

To determine the influence of a morning meal on complex mental functions in children (8-11 y), time-frequency analyses were applied to electroencephalographic (EEG) activity recorded while children solved simple addition problems after an overnight fast and again after having either eaten or skipped...

Eating breakfast enhances the efficiency of neural networks engaged during mental arithmetic in school-aged children

USDA-ARS?s Scientific Manuscript database

Are there effects of morning nutrition on brain functions important for learning and performance in children? We used time-frequency analyses of EEG activity recorded while children solved simple math problems to study how brain processes were influenced by eating or skipping breakfast. Participants...

Systems Engineering of Education V: Quantitative Concepts for Education Systems.

ERIC Educational Resources Information Center

Silvern, Leonard C.

The fifth (of 14) volume of the Education and Training Consultant's (ETC) series on systems engineering of education is designed for readers who have completed others in the series. It reviews arithmetic and algebraic procedures and applies these to simple education and training systems. Flowchart models of example problems are developed and…

Self-Regulated Learning of Basic Arithmetic Skills: A Longitudinal Study

ERIC Educational Resources Information Center

Throndsen, Inger

2011-01-01

Background: Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other…

Longitudinal Comparison of Place-Value and Arithmetic Knowledge in Montessori and Non-Montessori Students

ERIC Educational Resources Information Center

Laski, Elida V.; Vasilyeva, Marina; Schiffman, Joanna

2016-01-01

Understanding of base 10 and place value are important foundational math concepts that are associated with higher use of decomposition strategies and higher accuracy on addition problems (Laski, Ermakova, & Vasilyeva, 2014; Fuson, 1990; Fuson & Briars, 1990; National Research Council, 2001). The current study examined base-10 knowledge,…

Operator Priming and Generalization of Practice in Adults' Simple Arithmetic

ERIC Educational Resources Information Center

Chen, Yalin; Campbell, Jamie I. D.

2016-01-01

There is a renewed debate about whether educated adults solve simple addition problems (e.g., 2 + 3) by direct fact retrieval or by fast, automatic counting-based procedures. Recent research testing adults' simple addition and multiplication showed that a 150-ms preview of the operator (+ or ×) facilitated addition, but not multiplication,…

Gender Differences in Mathematical Achievement at the Norwegian Elementary-School Level.

ERIC Educational Resources Information Center

Manger, Terje

1995-01-01

The relationship between gender and mathematical achievement was investigated in 440 female and 480 male Norwegian third graders. Boys had higher test scores, but the effect size was small. Boys performed better in numeracy, mental arithmetic, and measurement problems. Marked gender differences were found at extreme tails of the distribution.…

Young Children "Solve for X" Using the Approximate Number System

ERIC Educational Resources Information Center

Kibbe, Melissa M.; Feigenson, Lisa

2015-01-01

The Approximate Number System (ANS) supports basic arithmetic computation in early childhood, but it is unclear whether the ANS also supports the more complex computations introduced later in formal education. "Solving for x" in addend-unknown problems is notoriously difficult for children, who often struggle with these types of problems…

The Role of Gesture in Supporting Mental Representations: The Case of Mental Abacus Arithmetic

ERIC Educational Resources Information Center

Brooks, Neon B.; Barner, David; Frank, Michael; Goldin-Meadow, Susan

2018-01-01

People frequently gesture when problem-solving, particularly on tasks that require spatial transformation. Gesture often facilitates task performance by interacting with internal mental representations, but how this process works is not well understood. We investigated this question by exploring the case of mental abacus (MA), a technique in which…

Using Disks as Models for Proofs of Series

ERIC Educational Resources Information Center

Somchaipeng, Tongta; Kruatong, Tussatrin; Panijpan, Bhinyo

2012-01-01

Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…

Behavioral Assessment of Impulsivity: A Comparison of Children with and without Attention Deficit Hyperactivity Disorder

ERIC Educational Resources Information Center

Neef, Nancy A.; Marckel, Julie; Ferreri, Summer J.; Bicard, David F.; Endo, Sayaka; Aman, Michael G.; Miller, Kelly M.; Jung, Sunhwa; Nist, Lindsay; Armstrong, Nancy

2005-01-01

We conducted a brief computer-based assessment involving choices of concurrently presented arithmetic problems associated with competing reinforcer dimensions to assess impulsivity (choices controlled primarily by reinforcer immediacy) as well as the relative influence of other dimensions (reinforcer rate, quality, and response effort), with 58…

Children's Understanding of Addition and Subtraction Concepts

ERIC Educational Resources Information Center

Robinson, Katherine M.; Dube, Adam K.

2009-01-01

After the onset of formal schooling, little is known about the development of children's understanding of the arithmetic concepts of inversion and associativity. On problems of the form a+b-b (e.g., 3+26-26), if children understand the inversion concept (i.e., that addition and subtraction are inverse operations), then no calculations are needed…

Quantum mechanics problems in observer's mathematics

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

Khots, Boris; Khots, Dmitriy; iMath Consulting LLC, Omaha, Nebraska

2012-11-06

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, andmore » {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.« less

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.

Passive hand movements disrupt adults' counting strategies.

PubMed

Imbo, Ineke; Vandierendonck, André; Fias, Wim

2011-01-01

In the present study, we experimentally tested the role of hand motor circuits in simple-arithmetic strategies. Educated adults solved simple additions (e.g., 8 + 3) or simple subtractions (e.g., 11 - 3) while they were required to retrieve the answer from long-term memory (e.g., knowing that 8 + 3 = 11), to transform the problem by making an intermediate step (e.g., 8 + 3 = 8 + 2 + 1 = 10 + 1 = 11) or to count one-by-one (e.g., 8 + 3 = 8…9…10…11). During the process of solving the arithmetic problems, the experimenter did or did not move the participants' hand on a four-point matrix. The results show that passive hand movements disrupted the counting strategy while leaving the other strategies unaffected. This pattern of results is in agreement with a procedural account, showing that the involvement of hand motor circuits in adults' mathematical abilities is reminiscent of finger counting during childhood.

Adolescents’ Functional Numeracy Is Predicted by Their School Entry Number System Knowledge

PubMed Central

Geary, David C.; Hoard, Mary K.; Nugent, Lara; Bailey, Drew H.

2013-01-01

One in five adults in the United States is functionally innumerate; they do not possess the mathematical competencies needed for many modern jobs. We administered functional numeracy measures used in studies of young adults’ employability and wages to 180 thirteen-year-olds. The adolescents began the study in kindergarten and participated in multiple assessments of intelligence, working memory, mathematical cognition, achievement, and in-class attentive behavior. Their number system knowledge at the beginning of first grade was defined by measures that assessed knowledge of the systematic relations among Arabic numerals and skill at using this knowledge to solve arithmetic problems. Early number system knowledge predicted functional numeracy more than six years later (ß = 0.195, p = .0014) controlling for intelligence, working memory, in-class attentive behavior, mathematical achievement, demographic and other factors, but skill at using counting procedures to solve arithmetic problems did not. In all, we identified specific beginning of schooling numerical knowledge that contributes to individual differences in adolescents’ functional numeracy and demonstrated that performance on mathematical achievement tests underestimates the importance of this early knowledge. PMID:23382934

Towards a system-paced near-infrared spectroscopy brain-computer interface: differentiating prefrontal activity due to mental arithmetic and mental singing from the no-control state.

PubMed

Power, Sarah D; Kushki, Azadeh; Chau, Tom

2011-12-01

Near-infrared spectroscopy (NIRS) has recently been investigated as a non-invasive brain-computer interface (BCI) for individuals with severe motor impairments. For the most part, previous research has investigated the development of NIRS-BCIs operating under synchronous control paradigms, which require the user to exert conscious control over their mental activity whenever the system is vigilant. Though functional, this is mentally demanding and an unnatural way to communicate. An attractive alternative to the synchronous control paradigm is system-paced control, in which users are required to consciously modify their brain activity only when they wish to affect the BCI output, and can remain in a more natural, 'no-control' state at all other times. In this study, we investigated the feasibility of a system-paced NIRS-BCI with one intentional control (IC) state corresponding to the performance of either mental arithmetic or mental singing. In particular, this involved determining if these tasks could be distinguished, individually, from the unconstrained 'no-control' state. Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations (International 10-20 System) while eight able-bodied adults performed mental arithmetic and mental singing to answer multiple-choice questions within a system-paced paradigm. With a linear classifier trained on a six-dimensional feature set, an overall classification accuracy of 71.2% across participants was achieved for the mental arithmetic versus no-control classification problem. While the mental singing versus no-control classification was less successful across participants (62.7% on average), four participants did attain accuracies well in excess of chance, three of which were above 70%. Analyses were performed offline. Collectively, these results are encouraging, and demonstrate the potential of a system-paced NIRS-BCI with one IC state corresponding to either mental arithmetic or mental singing.

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.

Towards a system-paced near-infrared spectroscopy brain-computer interface: differentiating prefrontal activity due to mental arithmetic and mental singing from the no-control state

NASA Astrophysics Data System (ADS)

Power, Sarah D.; Kushki, Azadeh; Chau, Tom

2011-10-01

Near-infrared spectroscopy (NIRS) has recently been investigated as a non-invasive brain-computer interface (BCI) for individuals with severe motor impairments. For the most part, previous research has investigated the development of NIRS-BCIs operating under synchronous control paradigms, which require the user to exert conscious control over their mental activity whenever the system is vigilant. Though functional, this is mentally demanding and an unnatural way to communicate. An attractive alternative to the synchronous control paradigm is system-paced control, in which users are required to consciously modify their brain activity only when they wish to affect the BCI output, and can remain in a more natural, 'no-control' state at all other times. In this study, we investigated the feasibility of a system-paced NIRS-BCI with one intentional control (IC) state corresponding to the performance of either mental arithmetic or mental singing. In particular, this involved determining if these tasks could be distinguished, individually, from the unconstrained 'no-control' state. Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations (International 10-20 System) while eight able-bodied adults performed mental arithmetic and mental singing to answer multiple-choice questions within a system-paced paradigm. With a linear classifier trained on a six-dimensional feature set, an overall classification accuracy of 71.2% across participants was achieved for the mental arithmetic versus no-control classification problem. While the mental singing versus no-control classification was less successful across participants (62.7% on average), four participants did attain accuracies well in excess of chance, three of which were above 70%. Analyses were performed offline. Collectively, these results are encouraging, and demonstrate the potential of a system-paced NIRS-BCI with one IC state corresponding to either mental arithmetic or mental singing.

An Exploratory Study Contrasting High- and Low-Achieving Students' Percent Word Problem Solving

ERIC Educational Resources Information Center

Jitendra, Asha K.; Star, Jon R.

2012-01-01

This study evaluated whether schema-based instruction (SBI), a promising method for teaching students to represent and solve mathematical word problems, impacted the learning of percent word problems. Of particular interest was the extent that SBI improved high- and low-achieving students' learning and to a lesser degree on the indirect effect of…

Tense and Aspect in Word Problems about Motion: Diagram, Gesture, and the Felt Experience of Time

ERIC Educational Resources Information Center

de Freitas, Elizabeth; Zolkower, Betina

2015-01-01

Word problems about motion contain various conjugated verb forms. As students and teachers grapple with such word problems, they jointly operationalize diagrams, gestures, and language. Drawing on findings from a 3-year research project examining the social semiotics of classroom interaction, we show how teachers and students use gesture and…

Redefining the Whole: Common Errors in Elementary Preservice Teachers' Self-Authored Word Problems for Fraction Subtraction

ERIC Educational Resources Information Center

Dixon, Juli K.; Andreasen, Janet B.; Avila, Cheryl L.; Bawatneh, Zyad; Deichert, Deana L.; Howse, Tashana D.; Turner, Mercedes Sotillo

2014-01-01

A goal of this study was to examine elementary preservice teachers' (PSTs) ability to contextualize and decontextualize fraction subtraction by asking them to write word problems to represent fraction subtraction expressions and to choose prewritten word problems to support given fraction subtraction expressions. Three themes emerged from the…

Assessing the Effect of Language Demand in Bundles of Math Word Problems

ERIC Educational Resources Information Center

Banks, Kathleen; Jeddeeni, Ahmad; Walker, Cindy M.

2016-01-01

Differential bundle functioning (DBF) analyses were conducted to determine whether seventh and eighth grade second language learners (SLLs) had lower probabilities of answering bundles of math word problems correctly that had heavy language demands, when compared to non-SLLs of equal math proficiency. Math word problems on each of four test forms…

When Best Intentions Go Awry: The Failures of Concrete Representations to Help Solve Probability Word Problems

ERIC Educational Resources Information Center

Beitzel, Brian D.; Staley, Richard K.; DuBois, Nelson F.

2011-01-01

Previous research has cast doubt on the efficacy of utilizing external representations as an aid to solving word problems. The present study replicates previous findings that concrete representations hinder college students' ability to solve probability word problems, and extends those findings to apply to a multimedia instructional context. Our…

Word Frequency, Function Words and the Second Gavagai Problem

ERIC Educational Resources Information Center

Hochmann, Jean-Remy

2013-01-01

The classic gavagai problem exemplifies the difficulty to identify the referent of a novel word uttered in a foreign language. Here, we consider the reverse problem: identifying the referential part of a label. Assuming "gavagai" indicates a rabbit in a foreign language, it may very well mean ""a" rabbit" or ""that" rabbit". How can a learner know…

The Motivation of Secondary School Students in Mathematical Word Problem Solving

ERIC Educational Resources Information Center

Gasco, Javier; Villarroel, Jose-Domingo

2014-01-01

Introduction: Motivation is an important factor in the learning of mathematics. Within this area of education, word problem solving is central in most mathematics curricula of Secondary School. The objective of this research is to detect the differences in motivation in terms of the strategies used to solve word problems. Method: It analyzed the…

Model Drawing Strategy for Fraction Word Problem Solving of Fourth-Grade Students with Learning Disabilities

ERIC Educational Resources Information Center

Sharp, Emily; Shih Dennis, Minyi

2017-01-01

This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…

Additive Relations Word Problems in the South African Curriculum and Assessment Policy Standard at Foundation Phase

ERIC Educational Resources Information Center

Roberts, Nicky

2016-01-01

Drawing on a literature review of classifications developed by each of Riley, Verschaffel and Carpenter and their respective research groups, a refined typology of additive relations word problems is proposed and then used as analytical tool to classify the additive relations word problems in South African Curriculum and Assessment Policy Standard…

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

Ego depletion in color priming research: self-control strength moderates the detrimental effect of red on cognitive test performance.

PubMed

Bertrams, Alex; Baumeister, Roy F; Englert, Chris; Furley, Philip

2015-03-01

Colors have been found to affect psychological functioning. Empirical evidence suggests that, in test situations, brief perceptions of the color red or even the word "red" printed in black ink prime implicit anxious responses and consequently impair cognitive performance. However, we propose that this red effect depends on people's momentary capacity to exert control over their prepotent responses (i.e., self-control). In three experiments (Ns = 66, 78, and 130), first participants' self-control strength was manipulated. Participants were then primed with the color or word red versus gray prior to completing an arithmetic test or an intelligence test. As expected, self-control strength moderated the red effect. While red had a detrimental effect on performance of participants with depleted self-control strength (ego depletion), it did not affect performance of participants with intact self-control strength. We discuss implications of the present findings within the current debate on the robustness of priming results. © 2015 by the Society for Personality and Social Psychology, Inc.

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

Exploring the Feasibility of a DNA Computer: Design of an ALU Using Sticker-Based DNA Model.

PubMed

Sarkar, Mayukh; Ghosal, Prasun; Mohanty, Saraju P

2017-09-01

Since its inception, DNA computing has advanced to offer an extremely powerful, energy-efficient emerging technology for solving hard computational problems with its inherent massive parallelism and extremely high data density. This would be much more powerful and general purpose when combined with other existing well-known algorithmic solutions that exist for conventional computing architectures using a suitable ALU. Thus, a specifically designed DNA Arithmetic and Logic Unit (ALU) that can address operations suitable for both domains can mitigate the gap between these two. An ALU must be able to perform all possible logic operations, including NOT, OR, AND, XOR, NOR, NAND, and XNOR; compare, shift etc., integer and floating point arithmetic operations (addition, subtraction, multiplication, and division). In this paper, design of an ALU has been proposed using sticker-based DNA model with experimental feasibility analysis. Novelties of this paper may be in manifold. First, the integer arithmetic operations performed here are 2s complement arithmetic, and the floating point operations follow the IEEE 754 floating point format, resembling closely to a conventional ALU. Also, the output of each operation can be reused for any next operation. So any algorithm or program logic that users can think of can be implemented directly on the DNA computer without any modification. Second, once the basic operations of sticker model can be automated, the implementations proposed in this paper become highly suitable to design a fully automated ALU. Third, proposed approaches are easy to implement. Finally, these approaches can work on sufficiently large binary numbers.

A Comparative Analysis of Word Problems in Selected United States and Russian First Grade Textbooks

ERIC Educational Resources Information Center

Grishchenko, Svetlana

2009-01-01

The purpose of this study was to explore word problems as a subject matter in mathematics textbook curricula. The motivation for the study derived from the following evidence: (a) American students find some word problems are more difficult than others (Garcia, Jimenez, & Hess, 2006; Riley & Green, 1988; Stern, 2001), and (b) one of the…

Mathematical Word Problem Solving Ability of Children with Autism Spectrum Disorder and Their Typically Developing Peers

ERIC Educational Resources Information Center

Bae, Young Seh; Chiang, Hsu-Min; Hickson, Linda

2015-01-01

This study examined the difference between children with autism spectrum disorders (ASD) and children with typical development (TD) in mathematical word problem solving ability and the factors associated with these children's word problem-solving ability. A total of 20 children with ASD and 20 children with TD participated in this study.…

The Effects of Using Diagramming as a Representational Technique on High School Students' Achievement in Solving Math Word Problems

ERIC Educational Resources Information Center

Banerjee, Banmali

2010-01-01

Methods and procedures for successfully solving math word problems have been, and continue to be a mystery to many U.S. high school students. Previous studies suggest that the contextual and mathematical understanding of a word problem, along with the development of schemas and their related external representations, positively contribute to…

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

Invariant Tori in the Secular Motions of the Three-body Planetary Systems

NASA Astrophysics Data System (ADS)

Locatelli, Ugo; Giorgilli, Antonio

We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun-Jupiter-Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.

A variant of nested dissection for solving n by n grid problems

NASA Technical Reports Server (NTRS)

George, A.; Poole, W. G., Jr.; Voigt, R. G.

1976-01-01

Nested dissection orderings are known to be very effective for solving the sparse positive definite linear systems which arise from n by n grid problems. In this paper nested dissection is shown to be the final step of incomplete nested dissection, an ordering which corresponds to the premature termination of dissection. Analyses of the arithmetic and storage requirements for incomplete nested dissection are given, and the ordering is shown to be competitive with nested dissection under certain conditions.

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.

Polynomial time blackbox identity testers for depth-3 circuits : the field doesn't matter.

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

Seshadhri, Comandur; Saxena, Nitin

Let C be a depth-3 circuit with n variables, degree d and top fanin k (called {Sigma}{Pi}{Sigma}(k, d, n) circuits) over base field F. It is a major open problem to design a deterministic polynomial time blackbox algorithm that tests if C is identically zero. Klivans & Spielman (STOC 2001) observed that the problem is open even when k is a constant. This case has been subjected to a serious study over the past few years, starting from the work of Dvir & Shpilka (STOC 2005). We give the first polynomial time blackbox algorithm for this problem. Our algorithm runsmore » in time poly(n)d{sup k}, regardless of the base field. The only field for which polynomial time algorithms were previously known is F = Q (Kayal & Saraf, FOCS 2009, and Saxena & Seshadhri, FOCS 2010). This is the first blackbox algorithm for depth-3 circuits that does not use the rank based approaches of Karnin & Shpilka (CCC 2008). We prove an important tool for the study of depth-3 identities. We design a blackbox polynomial time transformation that reduces the number of variables in a {Sigma}{Pi}{Sigma}(k, d, n) circuit to k variables, but preserves the identity structure. Polynomial identity testing (PIT) is a major open problem in theoretical computer science. The input is an arithmetic circuit that computes a polynomial p(x{sub 1}, x{sub 2},..., x{sub n}) over a base field F. We wish to check if p is the zero polynomial, or in other words, is identically zero. We may be provided with an explicit circuit, or may only have blackbox access. In the latter case, we can only evaluate the polynomial p at various domain points. The main goal is to devise a deterministic blackbox polynomial time algorithm for PIT.« less

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…

Pupils' Error on the Concept of Reversibility in Solving Arithmetic Problems

ERIC Educational Resources Information Center

Maf'ulah, Syarifatul; Juniati, Dwi; Siswono, Tatag Yuli Eko

2016-01-01

The fact that there is no much study on reversibility is one of reason this study was conducted. Others, the importance of reversibility is also being researcher's motivation for focusing pupils' reversibility. On the other hand, the concern on pupils' reversibility is a major concern. The objective of this research is to identify errors done by…

An Exploration of the Relationships among Cattell-Horn-Carroll (CHC) Theory-Aligned Cognitive Abilities and Math Fluency

ERIC Educational Resources Information Center

Piselli, Katherine D.

2017-01-01

Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links…

An Electro-Physiological Temporal Principal Component Analysis of Processing Stages of Number Comparison in Developmental Dyscalculia

ERIC Educational Resources Information Center

Soltesz, Fruzsina; Szucs, Denes

2009-01-01

Developmental dyscalculia (DD) still lacks a generally accepted definition. A major problem is that the cognitive component processes contributing to arithmetic performance are still poorly defined. By a reanalysis of our previous event-related brain potential (ERP) data (Soltesz et al., 2007) here our objective was to identify and compare…

A Critical Approach to Social Emotional Learning Instruction through Community-Based Service Learning

ERIC Educational Resources Information Center

McKay-Jackson, Cassandra

2014-01-01

The traditional teaching of reading, writing, and arithmetic alone will not fully prepare students to lead with integrity, govern fairly, analyze problems, and work collectively with people different from themselves. Social emotional learning (SEL) has been described as one of the missing links in academic education, but a restrictive approach to…

The Procedural Learning Deficit Hypothesis of Language Learning Disorders: We See Some Problems

ERIC Educational Resources Information Center

West, Gillian; Vadillo, Miguel A.; Shanks, David R.; Hulme, Charles

2018-01-01

Impaired procedural learning has been suggested as a possible cause of developmental dyslexia (DD) and specific language impairment (SLI). This study examined the relationship between measures of verbal and non-verbal implicit and explicit learning and measures of language, literacy and arithmetic attainment in a large sample of 7 to 8-year-old…

Conceptual Integration of Arithmetic Operations with Real-World Knowledge: Evidence from Event-Related Potentials

ERIC Educational Resources Information Center

Guthormsen, Amy M.; Fisher, Kristie J.; Bassok, Miriam; Osterhout, Lee; DeWolf, Melissa; Holyoak, Keith J.

2016-01-01

Research on language processing has shown that the disruption of conceptual integration gives rise to specific patterns of event-related brain potentials (ERPs)--N400 and P600 effects. Here, we report similar ERP effects when adults performed cross-domain conceptual integration of analogous semantic and mathematical relations. In a problem-solving…

Compound Interest Is As Easy As Pi. Teacher's Guide [and] Student Manual.

ERIC Educational Resources Information Center

Auman, L. Charles

This document provides teaching guidelines and student material for a unit intended for use in 12th grade algebra classes. Time allotment is from four to six hours of classroom time. The objective of this capsule is to teach students how to solve compound interest problems using arithmetic, logorithms, and calculators. Prerequisites for the unit…

Strategy Repetition in Young and Older Adults: A Study in Arithmetic

ERIC Educational Resources Information Center

Lemaire, Patrick; Leclère, Mariel

2014-01-01

We investigated a new phenomenon that sheds light on age-related differences in strategy selection: the strategy repetition phenomenon (i.e., tendency to repeat the same strategy over consecutive items). Young and older adults had to provide the best estimates of multiplication problems like 47 × 86. They had to select the best of 2 rounding…

How Does a Child Solve 7 + 8? Decoding Brain Activity Patterns Associated with Counting and Retrieval Strategies

ERIC Educational Resources Information Center

Cho, Soohyun; Ryali, Srikanth; Geary, David C.; Menon, Vinod

2011-01-01

Cognitive development and learning are characterized by diminished reliance on effortful procedures and increased use of memory-based problem solving. Here we identify the neural correlates of this strategy shift in 7-9-year-old children at an important developmental period for arithmetic skill acquisition. Univariate and multivariate approaches…

The Inequality of Arithmetic and Geometric Means from Multiple Perspectives

ERIC Educational Resources Information Center

Askey, Richard; Matsuura, Ryota; Sword, Sarah

2015-01-01

NCTM's Connections Standard recommends that students in grades 9-12 "develop an increased capacity to link mathematical ideas and a deeper understanding of how more than one approach to the same problem can lead to equivalent results, even though the approaches might look quite different" (NCTM 2000, p. 354). In this article, the authors…

Children's Additive Concepts: Promoting Understanding and the Role of Inhibition

ERIC Educational Resources Information Center

Robinson, Katherine M.; Dube, Adam K.

2013-01-01

This study investigated the promotion of children's understanding and acquisition of arithmetic concepts and the effects of inhibitory skills. Children in Grades 3, 4, and 5 solved two sets of three-term addition and subtraction problems (e.g., 3 + 24 - 24, 3 + 24 - 22) and completed an inhibition task. Half of the participants received a…

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.

The Effects of Using Drawings in Developing Young Children's Mathematical Word Problem Solving: A Design Experiment with Third-Grade Hungarian Students

ERIC Educational Resources Information Center

Csikos, Csaba; Szitanyi, Judit; Kelemen, Rita

2012-01-01

The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students' knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment…

A process for reaching standardization of word processing software for Sandia National Laboratories (Albuquerque) secretaries

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

Hudson, S.R.

1989-04-01

In the summer of 1986, a number of problems being experienced by Sandia secretaries due to multiple word processing packages being used were brought to the attention of Sandia's upper management. This report discusses how these problems evolved, how management chose to correct the problem, and how standardization of word processing for Sandia secretaries was achieved. 11 refs.

The Effects of Differing Presentations of Mathematical Word Problems Upon the Achievement of Tenth Grade Students.

ERIC Educational Resources Information Center

Sherrill, James M.

Described is a study concerned with the mode of presentation of printed mathematical word problems. Tenth grade students were given twenty word problems to solve, presented in one of three ways: (1) prose only, (2) prose with an accurate picture included, or (3) prose with a distorted picture. Experimental results showed that the group with an…

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…

Research and Implementation of Tibetan Word Segmentation Based on Syllable Methods

NASA Astrophysics Data System (ADS)

Jiang, Jing; Li, Yachao; Jiang, Tao; Yu, Hongzhi

2018-03-01

Tibetan word segmentation (TWS) is an important problem in Tibetan information processing, while abbreviated word recognition is one of the key and most difficult problems in TWS. Most of the existing methods of Tibetan abbreviated word recognition are rule-based approaches, which need vocabulary support. In this paper, we propose a method based on sequence tagging model for abbreviated word recognition, and then implement in TWS systems with sequence labeling models. The experimental results show that our abbreviated word recognition method is fast and effective and can be combined easily with the segmentation model. This significantly increases the effect of the Tibetan word segmentation.

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.

Analysis of space telescope data collection system

NASA Technical Reports Server (NTRS)

Ingels, F. M.; Schoggen, W. O.

1982-01-01

An analysis of the expected performance for the Multiple Access (MA) system is provided. The analysis covers the expected bit error rate performance, the effects of synchronization loss, the problem of self-interference, and the problem of phase ambiguity. The problem of false acceptance of a command word due to data inversion is discussed. A mathematical determination of the probability of accepting an erroneous command word due to a data inversion is presented. The problem is examined for three cases: (1) a data inversion only, (2) a data inversion and a random error within the same command word, and a block (up to 256 48-bit words) containing both a data inversion and a random error.

The semantic Stroop effect: An ex-Gaussian analysis.

PubMed

White, Darcy; Risko, Evan F; Besner, Derek

2016-10-01

Previous analyses of the standard Stroop effect (which typically uses color words that form part of the response set) have documented effects on mean reaction times in hundreds of experiments in the literature. Less well known is the fact that ex-Gaussian analyses reveal that such effects are seen in (a) the mean of the normal distribution (mu), as well as in (b) the standard deviation of the normal distribution (sigma) and (c) the tail (tau). No ex-Gaussian analysis exists in the literature with respect to the semantically based Stroop effect (which contrasts incongruent color-associated words with, e.g., neutral controls). In the present experiments, we investigated whether the semantically based Stroop effect is also seen in the three ex-Gaussian parameters. Replicating previous reports, color naming was slower when the color was carried by an irrelevant (but incongruent) color-associated word (e.g., sky, tomato) than when the control items consisted of neutral words (e.g., keg, palace) in each of four experiments. An ex-Gaussian analysis revealed that this semantically based Stroop effect was restricted to the arithmetic mean and mu; no semantic Stroop effect was observed in tau. These data are consistent with the views (1) that there is a clear difference in the source of the semantic Stroop effect, as compared to the standard Stroop effect (evidenced by the presence vs. absence of an effect on tau), and (2) that interference associated with response competition on incongruent trials in tau is absent in the semantic Stroop effect.

The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

2016-01-01

The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

Working memory components that predict word problem solving: Is it merely a function of reading, calculation, and fluid intelligence?

PubMed

Fung, Wenson; Swanson, H Lee

2017-07-01

The purpose of this study was to assess whether the differential effects of working memory (WM) components (the central executive, phonological loop, and visual-spatial sketchpad) on math word problem-solving accuracy in children (N = 413, ages 6-10) are completely mediated by reading, calculation, and fluid intelligence. The results indicated that all three WM components predicted word problem solving in the nonmediated model, but only the storage component of WM yielded a significant direct path to word problem-solving accuracy in the fully mediated model. Fluid intelligence was found to moderate the relationship between WM and word problem solving, whereas reading, calculation, and related skills (naming speed, domain-specific knowledge) completely mediated the influence of the executive system on problem-solving accuracy. Our results are consistent with findings suggesting that storage eliminates the predictive contribution of executive WM to various measures Colom, Rebollo, Abad, & Shih (Memory & Cognition, 34: 158-171, 2006). The findings suggest that the storage component of WM, rather than the executive component, has a direct path to higher-order processing in children.

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.

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

Automatic Item Generation of Probability Word Problems

ERIC Educational Resources Information Center

Holling, Heinz; Bertling, Jonas P.; Zeuch, Nina

2009-01-01

Mathematical word problems represent a common item format for assessing student competencies. Automatic item generation (AIG) is an effective way of constructing many items with predictable difficulties, based on a set of predefined task parameters. The current study presents a framework for the automatic generation of probability word problems…

Serial-order learning impairment and hypersensitivity-to-interference in dyscalculia.

PubMed

De Visscher, Alice; Szmalec, Arnaud; Van Der Linden, Lize; Noël, Marie-Pascale

2015-11-01

In the context of heterogeneity, the different profiles of dyscalculia are still hypothetical. This study aims to link features of mathematical difficulties to certain potential etiologies. First, we wanted to test the hypothesis of a serial-order learning deficit in adults with dyscalculia. For this purpose we used a Hebb repetition learning task. Second, we wanted to explore a recent hypothesis according to which hypersensitivity-to-interference hampers the storage of arithmetic facts and leads to a particular profile of dyscalculia. We therefore used interfering and non-interfering repeated sequences in the Hebb paradigm. A final test was used to assess the memory trace of the non-interfering sequence and the capacity to manipulate it. In line with our predictions, we observed that people with dyscalculia who show good conceptual knowledge in mathematics but impaired arithmetic fluency suffer from increased sensitivity-to-interference compared to controls. Secondly, people with dyscalculia who show a deficit in a global mathematical test suffer from a serial-order learning deficit characterized by a slow learning and a quick degradation of the memory trace of the repeated sequence. A serial-order learning impairment could be one of the explanations for a basic numerical deficit, since it is necessary for the number-word sequence acquisition. Among the different profiles of dyscalculia, this study provides new evidence and refinement for two particular profiles. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Word Problem Wizardry.

ERIC Educational Resources Information Center

Cassidy, Jack

1991-01-01

Presents suggestions for teaching math word problems to elementary students. The strategies take into consideration differences between reading in math and reading in other areas. A problem-prediction game and four self-checking activities are included along with a magic password challenge. (SM)

Math and Humane Education.

ERIC Educational Resources Information Center

DeRosa, Bill

1986-01-01

Describes an activity designed to improve students' skills at solving mathematical word problems through an awareness of the pet overpopulation problem. Uses the concept of cumulative female offspring as a focal point in assisting students to analyze and work through word problems. (ML)

Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: A cytoarchitectonic mapping study

PubMed Central

Rosenberg-Lee, Miriam; Chang, Ting Ting; Young, Christina B; Wu, Sarah; Menon, Vinod

2011-01-01

Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically-defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division vs. multiplication and subtraction vs. addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distributed representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings. PMID:21616086

Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: a cytoarchitectonic mapping study.

PubMed

Rosenberg-Lee, Miriam; Chang, Ting Ting; Young, Christina B; Wu, Sarah; Menon, Vinod

2011-07-01

Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division versus multiplication and subtraction versus addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distribute representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings. Copyright © 2011 Elsevier Ltd. All rights reserved.

Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension

ERIC Educational Resources Information Center

Fuchs, Lynn S.; Gilbert, Jennifer K.; Fuchs, Douglas; Seethaler, Pamela M.; N. Martin, BrittanyLee

2018-01-01

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory,…

Fuzzy approaches to supplier selection problem

NASA Astrophysics Data System (ADS)

Ozkok, Beyza Ahlatcioglu; Kocken, Hale Gonce

2013-09-01

Supplier selection problem is a multi-criteria decision making problem which includes both qualitative and quantitative factors. In the selection process many criteria may conflict with each other, therefore decision-making process becomes complicated. In this study, we handled the supplier selection problem under uncertainty. In this context; we used minimum criterion, arithmetic mean criterion, regret criterion, optimistic criterion, geometric mean and harmonic mean. The membership functions created with the help of the characteristics of used criteria, and we tried to provide consistent supplier selection decisions by using these memberships for evaluating alternative suppliers. During the analysis, no need to use expert opinion is a strong aspect of the methodology used in the decision-making.

Tense and aspect in word problems about motion: diagram, gesture, and the felt experience of time

NASA Astrophysics Data System (ADS)

de Freitas, Elizabeth; Zolkower, Betina

2015-09-01

Word problems about motion contain various conjugated verb forms. As students and teachers grapple with such word problems, they jointly operationalize diagrams, gestures, and language. Drawing on findings from a 3-year research project examining the social semiotics of classroom interaction, we show how teachers and students use gesture and diagram to make sense of complex verb forms in such word problems. We focus on the grammatical category of "aspect" for how it broadens the concept of verb tense. Aspect conveys duration and completion or frequency of an event. The aspect of a verb defines its temporal flow (or lack thereof) and the location of a vantage point for making sense of this durational process.

Constructing a Coherent Problem Model to Facilitate Algebra Problem Solving in a Chemistry Context

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Yeung, Alexander Seeshing; Phan, Huy P.

2015-01-01

An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…

Differential Effects of Activity-Oriented vs. Textbook-Oriented Mathematics Instruction for Elementary School Children with Learning and Behavior Problems. Monograph No. 4.

ERIC Educational Resources Information Center

Dunlap, William; And Others

Compared were the effects of two experimental arithmetic treatments, called Laboratory and Textbook, upon achievement and attitude development of fourth grade children. Prior to the study, the experimenter employed task analysis procedures to develop hierarchies of skills for the four operations on whole numbers. During the instructional phase of…

Surface EEG Shows that Functional Segregation via Phase Coupling Contributes to the Neural Substrate of Mental Calculations

ERIC Educational Resources Information Center

Dimitriadis, Stavros I.; Kanatsouli, Kassiani; Laskaris, Nikolaos A.; Tsirka, Vasso; Vourkas, Michael; Micheloyannis, Sifis

2012-01-01

Multichannel EEG traces from healthy subjects are used to investigate the brain's self-organisation tendencies during two different mental arithmetic tasks. By making a comparison with a control-state in the form of a classification problem, we can detect and quantify the changes in coordinated brain activity in terms of functional connectivity.…

Rupture or Continuity: The Arithmetico-Algebraic Thinking as an Alternative in a Modelling Process in a Paper and Pencil and Technology Environment

ERIC Educational Resources Information Center

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

2017-01-01

Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…

Geometrical Meaning of Arithmetic Series [Image Omitted], [Image Omitted] and [Image Omitted] in Terms of the Elementary Combinatorics

ERIC Educational Resources Information Center

Kobayashi, Yukio

2011-01-01

The formula [image omitted] is closely related to combinatorics through an elementary geometric exercise. This approach can be expanded to the formulas [image omitted], [image omitted] and [image omitted]. These formulas are also nice examples of showing two approaches, one algebraic and one combinatoric, to a problem of counting. (Contains 6…

Functional roles of the cingulo-frontal network in performance on working memory.

PubMed

Kondo, Hirohito; Morishita, Masanao; Osaka, Naoyuki; Osaka, Mariko; Fukuyama, Hidenao; Shibasaki, Hiroshi

2004-01-01

We examined the relationship between brain activities and task performance on working memory. A large-scale study was initially administered to identify good and poor performers using the operation span and reading span tasks. On the basis of those span scores, we divided 20 consenting participants into high- and low-span groups. In an fMRI study, the participants performed verification of arithmetic problems and retention of target words either concurrently or separately. The behavioral results showed that performance was better in the high-span group than in the low-span group under a dual-task condition, but not under two single-task conditions. The anterior cingulate cortex (ACC), left prefrontal cortex (PFC), left inferior frontal cortex, and bilateral parietal cortex were primarily activated for both span groups. We found that signal changes in the ACC were greater in the high-span group than in the low-span group under the dual-task condition, but not under the single-task conditions. Structural equation modeling indicated that an estimate of effective connectivity from the ACC to the left PFC was positive for the high-span group and negative for the-low span group, suggesting that closer cooperation between the two brain regions was strongly related to working memory performance. We conclude that central executive functioning for attention shifting is modulated by the cingulo-frontal network.

A single-layer platform for Boolean logic and arithmetic through DNA excision in mammalian cells

PubMed Central

Weinberg, Benjamin H.; Hang Pham, N. T.; Caraballo, Leidy D.; Lozanoski, Thomas; Engel, Adrien; Bhatia, Swapnil; Wong, Wilson W.

2017-01-01

Genetic circuits engineered for mammalian cells often require extensive fine-tuning to perform their intended functions. To overcome this problem, we present a generalizable biocomputing platform that can engineer genetic circuits which function in human cells with minimal optimization. We used our Boolean Logic and Arithmetic through DNA Excision (BLADE) platform to build more than 100 multi-input-multi-output circuits. We devised a quantitative metric to evaluate the performance of the circuits in human embryonic kidney and Jurkat T cells. Of 113 circuits analysed, 109 functioned (96.5%) with the correct specified behavior without any optimization. We used our platform to build a three-input, two-output Full Adder and six-input, one-output Boolean Logic Look Up Table. We also used BLADE to design circuits with temporal small molecule-mediated inducible control and circuits that incorporate CRISPR/Cas9 to regulate endogenous mammalian genes. PMID:28346402