common mathematical basis: Topics by Science.gov

Sample records for common mathematical basis

The role of prediction in the teaching and learning of mathematics

NASA Astrophysics Data System (ADS)

Lim, Kien H.; Buendía, Gabriela; Kim, Ok-Kyeong; Cordero, Francisco; Kasmer, Lisa

2010-07-01

The prevalence of prediction in grade-level expectations in mathematics curriculum standards signifies the importance of the role prediction plays in the teaching and learning of mathematics. In this article, we discuss benefits of using prediction in mathematics classrooms: (1) students' prediction can reveal their conceptions, (2) prediction plays an important role in reasoning and (3) prediction fosters mathematical learning. To support research on prediction in the context of mathematics education, we present three perspectives on prediction: (1) prediction as a mental act highlights the cognitive aspect and the conceptual basis of one's prediction, (2) prediction as a mathematical activity highlights the spectrum of prediction tasks that are common in mathematics curricula and (3) prediction as a socio-epistemological practice highlights the construction of mathematical knowledge in classrooms. Each perspective supports the claim that prediction when used effectively can foster mathematical learning. Considerations for supporting the use of prediction in mathematics classrooms are offered.
Traffic flow theory and chaotic behavior

DOT National Transportation Integrated Search

1989-03-01

Many commonly occurring natural systems are modeled with mathematical experessions and exhibit a certain stability. The inherent stability of these equations allows them to serve as the basis for engineering predictions. More complex models, such as ...
UnCommon Knowledge: Projects That Help Middle-School-Age Youth Discover the Science and Mathematics in Everyday Life. Volume Two: Hands-On Math Projects.

ERIC Educational Resources Information Center

Carter, Carolyn S.; Cohen, Sara; Keyes, Marian; Kusimo, Patricia S.; Lunsford, Crystal

This guide contains hands-on mathematics activities to connect middle-school students to the traditional knowledge of their grandparents and elders. Because girls often lose interest in math at the middle-school level, and because women in some communities (especially in rural areas) are seldom involved in work with an obvious math basis, the…
Simulation of hardwood log sawing

Treesearch

D.B. Richards; W.K. Adkins; H. Hallock; E.H. Bulgrin

1979-01-01

Mathematical modeling computer programs for several hardwood sawing systems have been developed and are described. One has judgment capabilities. Several of the subroutines are common to all of the models. These models are the basis for further research which examines the question of best-grade sawing method in terms of lumber value yield.
[Differential diagnosis of primary and secondary mathematical learning disability – indications from the dyscalculia test Basis-Math 4–8].

PubMed

Krinzinger, Helga

2016-09-01

Studies in children with AD(H)D without mathematical learning disability (MLD) as well as studies on the effects of methylphenidate on arithmetic have shown that most deficits in mathematics and most error types commonly described as specific to developmental dyscalculia (e. g., finger-counting, fact-retrieval deficit, complex counting, difficulties with carry/borrow procedures, self-corrections) cannot be classified as such and should thus not be used for the differential diagnosis of primary dyscalculia and secondary MLD. This article proposes using the overall score in the dyscalculia test Basis-Math 4-8 (Moser Opitz et al., 2010) as well as implausible subtraction errors as a marker for dyscalculia and the number of self-corrections made during the test as a cognitive marker for attention deficits. Hierarchical cluster analyses were calculated in a sample of 51 clinically referred children with normal IQ and suspicion of MLD, using IQ, years of schooling, overall score of the Basis-Math 4–8 and number of self-corrections in this test as variables. The results revealed a subgroup with primary dyscalculia as well as three subgroups with secondary MLD (two with attention deficit hyperactivity disorder, one with depression and one small subgroup with high IQ). In conclusion, the Basis-Math 4–8 (Moser Opitz et al., 2010) can offer substantial information for the differential diagnosis of dyscalculia and secondary deficits in mathematics due to attention problems and enable optimization of treatment decisions for the different groups.
Time estimation predicts mathematical intelligence.

PubMed

Kramer, Peter; Bressan, Paola; Grassi, Massimo

2011-01-01

Performing mental subtractions affects time (duration) estimates, and making time estimates disrupts mental subtractions. This interaction has been attributed to the concurrent involvement of time estimation and arithmetic with general intelligence and working memory. Given the extant evidence of a relationship between time and number, here we test the stronger hypothesis that time estimation correlates specifically with mathematical intelligence, and not with general intelligence or working-memory capacity. Participants performed a (prospective) time estimation experiment, completed several subtests of the WAIS intelligence test, and self-rated their mathematical skill. For five different durations, we found that time estimation correlated with both arithmetic ability and self-rated mathematical skill. Controlling for non-mathematical intelligence (including working memory capacity) did not change the results. Conversely, correlations between time estimation and non-mathematical intelligence either were nonsignificant, or disappeared after controlling for mathematical intelligence. We conclude that time estimation specifically predicts mathematical intelligence. On the basis of the relevant literature, we furthermore conclude that the relationship between time estimation and mathematical intelligence is likely due to a common reliance on spatial ability.
STATISTICAL ESTIMATES OF VARIANCE FOR 15N ISOTOPE DILUTION MEASUREMENTS OF GROSS RATES OF NITROGEN CYCLE PROCESSES

EPA Science Inventory

It has been fifty years since Kirkham and Bartholmew (1954) presented the conceptual framework and derived the mathematical equations that formed the basis of the now commonly employed method of 15N isotope dilution. Although many advances in methodology and analysis have been ma...
Aligning Practice to Policies: Changing the Culture to Recognize and Reward Teaching at Research Universities

ERIC Educational Resources Information Center

Dennin, Michael; Schultz, Zachary D.; Feig, Andrew; Finkelstein, Noah; Greenhoot, Andrea Follmer; Hildreth, Michael; Leibovich, Adam K.; Martin, James D.; Moldwin, Mark B.; O'Dowd, Diane K.; Posey, Lynmarie A.; Smith, Tobin L.; Miller, Emily R.

2017-01-01

Recent calls for improvement in undergraduate education within STEM (science, technology, engineering, and mathematics) disciplines are hampered by the methods used to evaluate teaching effectiveness. Faculty members at research universities are commonly assessed and promoted mainly on the basis of research success. To improve the quality of…
Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon's data plot then specify a unique differential equation for it.

PubMed

Kepner, Gordon R

2014-08-27

This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.
Reducible or irreducible? Mathematical reasoning and the ontological method.

PubMed

Fisher, William P

2010-01-01

Science is often described as nothing but the practice of measurement. This perspective follows from longstanding respect for the roles mathematics and quantification have played as media through which alternative hypotheses are evaluated and experience becomes better managed. Many figures in the history of science and psychology have contributed to what has been called the "quantitative imperative," the demand that fields of study employ number and mathematics even when they do not constitute the language in which investigators think together. But what makes an area of study scientific is, of course, not the mere use of number, but communities of investigators who share common mathematical languages for exchanging quantitative and quantitative value. Such languages require rigorous theoretical underpinning, a basis in data sufficient to the task, and instruments traceable to reference standard quantitative metrics. The values shared and exchanged by such communities typically involve the application of mathematical models that specify the sufficient and invariant relationships necessary for rigorous theorizing and instrument equating. The mathematical metaphysics of science are explored with the aim of connecting principles of quantitative measurement with the structures of sufficient reason.
Orthogonal Reflections on Computer Microworlds, Constructivism, Play and Mathematical Understanding.

ERIC Educational Resources Information Center

Kieren, Thomas E.

1994-01-01

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…
An Investigation of the Effectiveness of Reform Mathematics Curricula Analyzed by Ethnicity, Socio-Economic Status, and Limited English Proficiency

ERIC Educational Resources Information Center

Vega, Tina; Travis, Betty

2011-01-01

Progress in secondary education today is measured primarily through high stakes testing administered on a state-by-state basis. While states may require a common assessment instrument, how the objectives are to be taught, however, is generally up to the schools. This results in debates among educators as to the best curricula for all students.…
Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.
UnCommon Knowledge: Projects That Help Middle-School-Age Youth Discover the Science and Mathematics in Everyday Life. Volume One: Hands-On Science Projects.

ERIC Educational Resources Information Center

Carter, Carolyn S.; Keyes, Marian; Kusimo, Patricia S.; Lunsford, Crystal

This guide contains hands-on science activities to connect middle-school students to the traditional knowledge of their grandparents and elders. Because girls often lose interest in science at the middle-school level, and because women in some communities (especially in rural areas) are seldom involved in work with an obvious science basis, the…
The principle of acoustic time reversal and holography

NASA Astrophysics Data System (ADS)

Zverev, V. A.

2004-11-01

On the basis of earlier results (V. A. Zverev, Radiooptics (1975)), the principle of the time reversal of waves (TRW) with the use of a time-reversed signal is considered (M. Fink et al., Time-Reversed Acoustics, Rep. Prog. Phys. 63 (2000)). Both the common mathematical basis and the difference between the TRW and holography are revealed. The following conclusions are drawn: (i) to implement the TRW, it is necessary that the spatial and time coordinates be separated in the initial signal; (ii) two methods of implementing the TRW are possible, namely, the time reversal and the use of an inverse filter; (iii) certain differences exist in the spatial focusing by the TRW and holography; and (iv) on the basis of the theory developed, a numerical modeling of the TRW becomes possible.
What Is the Basis for Self-Assessment of Comprehension When Reading Mathematical Expository Texts?

ERIC Educational Resources Information Center

Österholm, Magnus

2015-01-01

The purpose of this study was to characterize students' self-assessments when reading mathematical texts, in particular regarding what students use as a basis for evaluations of their own reading comprehension. A total of 91 students read two mathematical texts, and for each text, they performed a self-assessment of their comprehension and…
A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms

PubMed Central

Ponnapalli, Sri Priya; Saunders, Michael A.; Van Loan, Charles F.; Alter, Orly

2011-01-01

The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N≥2 matrices , each with full column rank. Each matrix is exactly factored as Di = UiΣiVT, where V, identical in all factorizations, is obtained from the eigensystem SV = VΛ of the arithmetic mean S of all pairwise quotients of the matrices , i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λk≥1. Equality holds if and only if the corresponding eigenvector vk is a right basis vector of equal significance in all matrices Di and Dj, that is σi,k/σj,k = 1 for all i and j, and the corresponding left basis vector ui,k is orthogonal to all other vectors in Ui for all i. The eigenvalues λk = 1, therefore, define the “common HO GSVD subspace.” We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell-cycle peak times are correctly classified. PMID:22216090
Schema building profiles among elementary school students in solving problems related to operations of addition to fractions on the basis of mathematic abilities

NASA Astrophysics Data System (ADS)

Gembong, S.; Suwarsono, S. T.; Prabowo

2018-03-01

Schema in the current study refers to a set of action, process, object and other schemas already possessed to build an individual’s ways of thinking to solve a given problem. The current study aims to investigate the schemas built among elementary school students in solving problems related to operations of addition to fractions. The analyses of the schema building were done qualitatively on the basis of the analytical framework of the APOS theory (Action, Process, Object, and Schema). Findings show that the schemas built on students of high and middle ability indicate the following. In the action stage, students were able to add two fractions by way of drawing a picture or procedural way. In the Stage of process, they could add two and three fractions. In the stage of object, they could explain the steps of adding two fractions and change a fraction into addition of fractions. In the last stage, schema, they could add fractions by relating them to another schema they have possessed i.e. the least common multiple. Those of high and middle mathematic abilities showed that their schema building in solving problems related to operations odd addition to fractions worked in line with the framework of the APOS theory. Those of low mathematic ability, however, showed that their schema on each stage did not work properly.
Reaching the Mountaintop: Addressing the Common Core Standards in Mathematics for Students with Mathematics Difficulties

ERIC Educational Resources Information Center

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

2013-01-01

The Common Core State Standards provide teachers with a framework of necessary mathematics skills across grades K-12, which vary considerably from previous mathematics standards. In this article, we discuss concerns about the implications of the Common Core for students with mathematics difficulties (MD), given that students with MD, by…
Physiological pharmacokinetic modeling

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

Menzel, D.B.

1987-10-01

Risk assessment often defines the approach and the degree of regulation, decisions in risk assessment often have major regulatory impacts. Chemicals that have economic value or that were byproducts of the chemical industry are common subjects of such decisions. Regrettably, decisions related to risk assessment, science, or regulatory matters will frequently be made with incomplete information and on the basis of intuitive reasoning. Statistical fits to experimental data have been used to estimate risks in humans from experimental data in animals. These treatments have not taken into account the obvious differences in physiology, biochemistry, and size between aniamals and humans.more » In this article the use of mathematical models based on continuous relationships, rather than quantal events, are discussed. The mathematical models can be used to adjust the dose in the quantal response model, but the emphasis will be on how these mathematical models are conceived and what implications their use holds for risk assessment. Experiments with humans that produce toxic effects cannot be done. Data for human toxicity will always be lacking.« less

Familial aggregation patterns in mathematical ability.

PubMed

Wijsman, Ellen M; Robinson, Nancy M; Ainsworth, Kathryn H; Rosenthal, Elisabeth A; Holzman, Ted; Raskind, Wendy H

2004-01-01

Mathematical talent is an asset in modern society both at an individual and a societal level. Environmental factors such as quality of mathematics education undoubtedly affect an individual's performance, and there is some evidence that genetic factors also may play a role. The current study was performed to investigate the feasibility of undertaking genetics studies on mathematical ability. Because the etiology of low ability in mathematics is likely to be multifactorial and heterogeneous, we evaluated families ascertained through a proband with high mathematical performance in grade 7 on the SAT to eliminate, to some degree, adverse environmental factors. Families of sex-matched probands, selected for high verbal performance on the SAT, served as the comparison group. We evaluated a number of proxy measures for their usefulness in the study of clustering of mathematical talent. Given the difficulty of testing mathematics performance across developmental ages, especially with the added complexity of decreasing exposure to formal mathematics concepts post schooling, we also devised a semiquantitative scale that incorporated educational, occupational, and avocational information as a surrogate for an academic mathematics measure. Whereas several proxy measures showed no evidence of a genetic basis, we found that the semiquantitative scale of mathematical talent showed strong evidence of a genetic basis, with a differential response as a function of the performance measure used to select the proband. This observation suggests that there may be a genetic basis to specific mathematical talent, and that specific, as opposed to proxy, investigative measures that are designed to measure such talent in family members could be of benefit for this purpose.
Whole-coal versus ash basis in coal geochemistry: a mathematical approach to consistent interpretations

USGS Publications Warehouse

Geboy, Nicholas J.; Engle, Mark A.; Hower, James C.

2013-01-01

Several standard methods require coal to be ashed prior to geochemical analysis. Researchers, however, are commonly interested in the compositional nature of the whole-coal, not its ash. Coal geochemical data for any given sample can, therefore, be reported in the ash basis on which it is analyzed or the whole-coal basis to which the ash basis data are back calculated. Basic univariate (mean, variance, distribution, etc.) and bivariate (correlation coefficients, etc.) measures of the same suite of samples can be very different depending which reporting basis the researcher uses. These differences are not real, but an artifact resulting from the compositional nature of most geochemical data. The technical term for this artifact is subcompositional incoherence. Since compositional data are forced to a constant sum, such as 100% or 1,000,000 ppm, they possess curvilinear properties which make the Euclidean principles on which most statistical tests rely inappropriate, leading to erroneous results. Applying the isometric logratio (ilr) transformation to compositional data allows them to be represented in Euclidean space and evaluated using traditional tests without fear of producing mathematically inconsistent results. When applied to coal geochemical data, the issues related to differences between the two reporting bases are resolved as demonstrated in this paper using major oxide and trace metal data from the Pennsylvanian-age Pond Creek coal of eastern Kentucky, USA. Following ilr transformation, univariate statistics, such as mean and variance, still differ between the ash basis and whole-coal basis, but in predictable and calculated manners. Further, the stability between two different components, a bivariate measure, is identical, regardless of the reporting basis. The application of ilr transformations addresses both the erroneous results of Euclidean-based measurements on compositional data as well as the inconsistencies observed on coal geochemical data reported on different bases.
DEVELOPMENT OF A MATHEMATICAL BASIS FOR RELATING SLUDGE PROPERTIES TO FGD-SCRUBBER OPERATING VARIABLES

EPA Science Inventory

The report gives results of research to investigate prospects for increasing the size of calcium sulfite sludge particles in flue gas desulfurization systems. The approach included four work packages: a literature survey and development of a mathematical basis for predicting calc...
Transfer of Algebraic and Graphical Thinking between Mathematics and Chemistry

ERIC Educational Resources Information Center

Potgieter, Marietjie; Harding, Ansie; Engelbrecht, Johann

2008-01-01

Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…
Summative and Formative Assessments in Mathematics Supporting the Goals of the Common Core Standards

ERIC Educational Resources Information Center

Schoenfeld, Alan H.

2015-01-01

Being proficient in mathematics involves having rich and connected mathematical knowledge, being a strategic and reflective thinker and problem solver, and having productive mathematical beliefs and dispositions. This broad set of mathematics goals is central to the Common Core State Standards for Mathematics. High-stakes testing often drives…
Use of open-ended problems as the basis for the mathematical creativity growth disclosure of student

NASA Astrophysics Data System (ADS)

Suyitno, A.; Suyitno, H.; Rochmad; Dwijanto

2018-03-01

Mathematical creativity is the essence of learning in mathematics. However, mathematical creativity had not yet grown among students. Means there was a gap between needs and reality. This gap must be bridged through by scientific studies, and there were novelty findings, namely the discovery of stages to cultivate of Mathematical Creativity. The problem formulation: How to use of open-ended problems as the basis for the mathematical creativity growth disclosure of student? The goal was to use of open issues as the basis for the mathematical creativity growth disclosure of student. Research method with a qualitative approach. After data was collected then activity in data analysis, include data reduction, data presentation, data interpretation, and conclusion/verification. The results of the research: After the learning by applying the modification of RTTW learning model, then the students were trained to do the open-ended problems and by looking at the UTS and UAS values then qualitatively the results: (1) There was a significant increase of the student's final score. (2) The category of the growth of mathematical creativity of students, the Very Good there were three students, the Good there were six students, There were 17 students, and there were six students. The validation of these results was reinforced by interviews and triangulation. (3) Stage to cultivate mathematical creativity: lecturers should need to provide inputs on student work; Apply an appropriate learning model, and train students to work on the continuing problems.
Literacy in Language and Mathematics: More in Common Than You Think

ERIC Educational Resources Information Center

Thompson, Denisse R.; Rubenstein, Rheta N.

2014-01-01

This paper shares perspectives on literacy in mathematics, particularly highlighting commonalities with literacy in language arts. We discuss levels of language development appropriate for the mathematics classroom, issues related to mathematical definitions, implied meanings in many mathematics concepts, and the importance of justification. We…
Preservice Secondary Teachers Perceptions of College-Level Mathematics Content Connections with the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Olson, Travis A.

2016-01-01

Preservice Secondary Mathematics Teachers (PSMTs) were surveyed to identify if they could connect early-secondary mathematics content (Grades 7-9) in the Common Core State Standards for Mathematics (CCSSM) with mathematics content studied in content courses for certification in secondary teacher preparation programs. Respondents were asked to…
Mathematical Writing Errors in Expository Writings of College Mathematics Students

ERIC Educational Resources Information Center

Guce, Ivee K.

2017-01-01

Despite the efforts to confirm the effectiveness of writing in learning mathematics, analysis on common errors in mathematical writings has not received sufficient attention. This study aimed to provide an account of the students' procedural explanations in terms of their commonly committed errors in mathematical writing. Nine errors in…
Biological Basis For Computer Vision: Some Perspectives

NASA Astrophysics Data System (ADS)

Gupta, Madan M.

1990-03-01

Using biology as a basis for the development of sensors, devices and computer vision systems is a challenge to systems and vision scientists. It is also a field of promising research for engineering applications. Biological sensory systems, such as vision, touch and hearing, sense different physical phenomena from our environment, yet they possess some common mathematical functions. These mathematical functions are cast into the neural layers which are distributed throughout our sensory regions, sensory information transmission channels and in the cortex, the centre of perception. In this paper, we are concerned with the study of the biological vision system and the emulation of some of its mathematical functions, both retinal and visual cortex, for the development of a robust computer vision system. This field of research is not only intriguing, but offers a great challenge to systems scientists in the development of functional algorithms. These functional algorithms can be generalized for further studies in such fields as signal processing, control systems and image processing. Our studies are heavily dependent on the the use of fuzzy - neural layers and generalized receptive fields. Building blocks of such neural layers and receptive fields may lead to the design of better sensors and better computer vision systems. It is hoped that these studies will lead to the development of better artificial vision systems with various applications to vision prosthesis for the blind, robotic vision, medical imaging, medical sensors, industrial automation, remote sensing, space stations and ocean exploration.
Neuronal periodicity detection as a basis for the perception of consonance: a mathematical model of tonal fusion.

PubMed

Ebeling, Martin

2008-10-01

A mathematical model is presented here to explain the sensation of consonance and dissonance on the basis of neuronal coding and the properties of a neuronal periodicity detection mechanism. This mathematical model makes use of physiological data from a neuronal model of periodicity analysis in the midbrain, whose operation can be described mathematically by autocorrelation functions with regard to time windows. Musical intervals produce regular firing patterns in the auditory nerve that depend on the vibration ratio of the two tones. The mathematical model makes it possible to define a measure for the degree of these regularities for each vibration ratio. It turns out that this measure value is in line with the degree of tonal fusion as described by Stumpf [Tonpsychologie (Psychology of Tones) (Knuf, Hilversum), reprinted 1965]. This finding makes it probable that tonal fusion is a consequence of certain properties of the neuronal periodicity detection mechanism. Together with strong roughness resulting from interval tones with fundamentals close together or close to the octave, this neuronal mechanism may be regarded as the basis of consonance and dissonance.
On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions

DTIC Science & Technology

1994-01-01

torque general nature. We then provide in section 3 a precise at a particular joint of a robot arm , and x the set of an- statement of a specific...sampling Y according to first need to introduce some terminology and to define P(ylx). In the robot arm example described above, it a number of...mathematical objects. A summary of the would mean that one could move the robot arm into most common notations and definitions used in this pa- ’Note that
Software For Fault-Tree Diagnosis Of A System

NASA Technical Reports Server (NTRS)

Iverson, Dave; Patterson-Hine, Ann; Liao, Jack

1993-01-01

Fault Tree Diagnosis System (FTDS) computer program is automated-diagnostic-system program identifying likely causes of specified failure on basis of information represented in system-reliability mathematical models known as fault trees. Is modified implementation of failure-cause-identification phase of Narayanan's and Viswanadham's methodology for acquisition of knowledge and reasoning in analyzing failures of systems. Knowledge base of if/then rules replaced with object-oriented fault-tree representation. Enhancement yields more-efficient identification of causes of failures and enables dynamic updating of knowledge base. Written in C language, C++, and Common LISP.
Public Conceptions of Algorithms and Representations in the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Nanna, Robert J.

2016-01-01

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…
Determination of power distribution in the VVER-440 core on the basis of data from in-core monitors by means of a metric analysis

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

Kryanev, A. V.; Udumyan, D. K.; Kurchenkov, A. Yu., E-mail: s327@vver.kiae.ru

2014-12-15

Problems associated with determining the power distribution in the VVER-440 core on the basis of a neutron-physics calculation and data from in-core monitors are considered. A new mathematical scheme is proposed for this on the basis of a metric analysis. In relation to the existing mathematical schemes, the scheme in question improves the accuracy and reliability of the resulting power distribution.
Working Memory and Language: Skill-Specific or Domain-General Relations to Mathematics?

ERIC Educational Resources Information Center

Purpura, David J.; Ganley, Colleen M.

2014-01-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the…
Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

Ferri, Rita Borromeo

2017-07-01

Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.
Comparison of Virginia's 2009 Mathematics Standards of Learning with the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Virginia Department of Education, 2011

2011-01-01

This first draft of the "Comparison of Virginia's 2009 Mathematics Standards of Learning (SOL) with the Common Core State Standards (CCSS) for Mathematics" provides a side-by-side overview demonstrating how the 2009 Mathematics SOL are aligned to the CCSS. The comparison was made using Virginia's complete standards program for supporting…
Comparison of Virginia's College and Career Ready Mathematics Performance Expectations with the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Virginia Department of Education, 2010

2010-01-01

This paper presents a comparison of Virginia's mathematics performance expectations with the common core state standards for mathematics. The comparison focuses on number and quantity, algebra, functions, geometry, and statistics and probability. (Contains 1 footnote.)
Relationships between autofocus methods for SAR and self-survey techniques for SONAR. [Synthetic Aperture Radar (SAR)

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

Wahl, D.E.; Jakowatz, C.V. Jr.; Ghiglia, D.C.

1991-01-01

Autofocus methods in SAR and self-survey techniques in SONAR have a common mathematical basis in that they both involve estimation and correction of phase errors introduced by sensor position uncertainties. Time delay estimation and correlation methods have been shown to be effective in solving the self-survey problem for towed SONAR arrays. Since it can be shown that platform motion errors introduce similar time-delay estimation problems in SAR imaging, the question arises as to whether such techniques could be effectively employed for autofocus of SAR imagery. With a simple mathematical model for motion errors in SAR, we will show why suchmore » correlation/time-delay techniques are not nearly as effective as established SAR autofocus algorithms such as phase gradient autofocus or sub-aperture based methods. This analysis forms an important bridge between signal processing methodologies for SAR and SONAR. 5 refs., 4 figs.« less

A beautiful sea: P. A. M. Dirac's epistemology and ontology of the vacuum.

PubMed

Wright, Aaron Sidney

2016-07-01

This paper charts P.A.M. Dirac's development of his theory of the electron, and its radical picture of empty space as an almost-full plenum. Dirac's Quantum Electrodynamics famously accomplished more than the unification of special relativity and quantum mechanics. It also accounted for the 'duplexity phenomena' of spectral line splitting that we now attribute to electron spin. But the extra mathematical terms that allowed for spin were not alone, and this paper charts Dirac's struggle to ignore or account for them as a sea of strange, negative-energy, particles with positive 'holes'. This work was not done in solitude, but rather in exchanges with Dirac's correspondence network. This social context for Dirac's work contests his image as a lone genius, and documents a community wrestling with the ontological consequences of their work. Unification, consistency, causality, and community are common factors in explanations in the history of physics. This paper argues on the basis of materials in Dirac's archive that --- in addition --- mathematical beauty was an epistemological factor in the development of the electron and hole theory. In fact, if we believe that Dirac's beautiful mathematics captures something of the world, then there is both an epistemology and an ontology of mathematical beauty.
Mathematical Discovery and "Affect": The "Effect" of Aha! Experiences on Undergraduate Mathematics Students

ERIC Educational Resources Information Center

Liljedahl, Peter G.

2005-01-01

The AHA! experience-the moment of illumination on the heels of lengthy, and seemingly fruitless, intentional effort-has long been the basis for lore in mathematics. Unfortunately, such lore is often restricted to the discussion of these phenomena in the context of great mathematicians and great mathematical advancement. But are such experiences…
Structurally Sound Statistics Instruction

ERIC Educational Resources Information Center

Casey, Stephanie A.; Bostic, Jonathan D.

2016-01-01

The Common Core's Standards for Mathematical Practice (SMP) call for all K-grade 12 students to develop expertise in the processes and proficiencies of doing mathematics. However, the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) as a whole addresses students' learning of not only mathematics but also statistics. This situation…
Attitude Determination Error Analysis System (ADEAS) mathematical specifications document

NASA Technical Reports Server (NTRS)

Nicholson, Mark; Markley, F.; Seidewitz, E.

1988-01-01

The mathematical specifications of Release 4.0 of the Attitude Determination Error Analysis System (ADEAS), which provides a general-purpose linear error analysis capability for various spacecraft attitude geometries and determination processes, are presented. The analytical basis of the system is presented. The analytical basis of the system is presented, and detailed equations are provided for both three-axis-stabilized and spin-stabilized attitude sensor models.
The Evolution of Random Number Generation in MUVES

DTIC Science & Technology

2017-01-01

mathematical basis and statistical justification for algorithms used in the code. The working code provided produces results identical to the current...MUVES, includ- ing the mathematical basis and statistical justification for algorithms used in the code. The working code provided produces results...questionable numerical and statistical properties. The development of the modern system is traced through software change requests, resulting in a random number
Mathematics-Literacy Checklists: A Pedagogical Innovation to Support Teachers as They Implement the Common Core

ERIC Educational Resources Information Center

del Prado Hill, Pixita; Friedland, Ellen S.; McMillen, Susan

2016-01-01

This article presents two innovative tools--the Mathematics-Literacy Planning Framework and Mathematics-Literacy Implementation Checklist--which are designed to help instructional coaches and specialists support teachers to meet the challenges of the mathematics-literacy integration goals of the Common Core. Developed with teacher input, these…
Using Short Video Lectures to Enhance Mathematics Learning--Experiences on Differential and Integral Calculus Course for Engineering Students

ERIC Educational Resources Information Center

Kinnari-Korpela, Hanna

2015-01-01

Mathematics' skills and knowledge lay the basis for engineering studies. However, the resources targeted to mathematics' teaching are in many cases very limited. During the past years in our university the reduction of mathematics' contact hours has been significant while at the same time the study groups have grown. However, the mathematical…
The Common Core Mathematics Companion: The Standards Decoded, High School

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2017

2017-01-01

When it comes to mathematics, standards aligned is achievement aligned… In the short time since "The Common Core Mathematics Companions" for grades K-2, 3-5 and 6-8 burst on the scene, they have been lauded as the best resources for making critical mathematics ideas easy to teach. With this brand-new volume, high school mathematics…
Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

2015-01-01

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…
Incorporating the Common Core's Problem Solving Standard for Mathematical Practice into an Early Elementary Inclusive Classroom

ERIC Educational Resources Information Center

Fletcher, Nicole

2014-01-01

Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…
Promoting Access to Common Core Mathematics for Students with Severe Disabilities through Mathematical Problem Solving

ERIC Educational Resources Information Center

Spooner, Fred; Saunders, Alicia; Root, Jenny; Brosh, Chelsi

2017-01-01

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…
Public-Key Cryptography: A Hardware Implementation and Novel Neural Network-Based Approach

DTIC Science & Technology

1992-09-01

FUNDINGISPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION (if applicable ) 8c. ADDRESS (City, State, and ZIP Code) 10...8217....... ......... 4. .. . . iii TABLE OF CONTENTS I. INTRODUCTION ............................. 1 II. MATHEMATICAL BASIS FOR THE DEVELOPMENT OF PUBLIC-KEY...in the spirit of this future that this thesis is presented. It is an in-depth study of the public-key cryptosystem. First, the mathematical basis
Mathematics Teachers' Criteria of Dimension

ERIC Educational Resources Information Center

Ural, Alattin

2014-01-01

The aim of the study is to determine mathematics teachers' decisions about dimensions of the geometric figures, criteria of dimension and consistency of decision-criteria. The research is a qualitative research and the model applied in the study is descriptive method on the basis of general scanning model. 15 mathematics teachers attended the…
Issues in Teaching Mathematics

ERIC Educational Resources Information Center

Ediger, Marlow

2013-01-01

In this article, the author states that there are selected issues in mathematics instruction that educators should be well aware of when planning lessons and units of study. These issues provide a basis for thought and discussion when assisting pupils to attain more optimally. Purposeful studying of issues guides mathematics teachers in…
Student Achievement in College Calculus, Louisiana State University 1967-1968.

ERIC Educational Resources Information Center

Scannicchio, Thomas Henry

An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…
Slovenian Pre-Service Teachers' Prototype Biography

ERIC Educational Resources Information Center

Lipovec, Alenka; Antolin, Darja

2014-01-01

In this article we apply narrative methodology to the study of pre-service elementary teachers' school-time memories connected to mathematics education. In the first phase of our empirical study we asked 214 Slovenian pre-service teachers to write their mathematical autobiographies. On the basis of the mathematical autobiographies we constructed a…
GOALS FOR SCHOOL MATHEMATICS, THE REPORT OF THE CONFERENCE ON SCHOOL MATHEMATICS (CAMBRIDGE, MASSACHUSETTS, 1963).

ERIC Educational Resources Information Center

Educational Services, Inc., Watertown, MA.

REPORTED ARE THE TENTATIVE VIEWS OF A GROUP OF MATHEMATICIANS ON THE CONTENT OF A PRE-COLLEGE MATHEMATICS CURRICULUM THAT MIGHT CONCEIVABLY REPRESENT THE TYPE OF PROGRAM WHICH WILL BE OPERATING IN A FEW DECADES. THE COMMITTEE PRESENTS ITS VIEWS, NOT AS A CURRICULUM GUIDE FOR ADMINISTRATORS AND MATHEMATICS EDUCATORS, BUT AS A BASIS FOR DISCUSSION,…
Learning Mathematics or Losing Money--Betting as a Topic for Mathematical Education

ERIC Educational Resources Information Center

Siller, Hans-Stefan; MaaB, Jurgen

2012-01-01

No risk, no fun--betting on sports events costs the gamblers a lot of money and brings excellent profits to those who offer the bets. Among the people who bet on a regular basis, the proportion of young adults is frighteningly high. We now suggest a concept (as part of a basic mathematics course) for acquiring the necessary mathematical knowledge…
The Philosophical and Mathematical Context of two Gerbert's Musical Letters to Constantine

NASA Astrophysics Data System (ADS)

Otisk, Marek

2015-04-01

The paper deals with two letters written by Gerbert of Aurillac to Constantine of Fleury. In these letters Gerbert points out some passages from Boethius’s Introduction to Music (II, 10; respectively IV, 2 and II, 21) concerning mathematical operations (multiplication and subtraction) with superparticular ratios i.e. ratios of the type (n+1) : n. The musical harmonies rule the Cosmos and the Celestial Spheres according to Martianus Capella De nuptiis Philologiae et Mercurii; Music is the basis for understanting Astronomy. This paper follows two main aims: philosophical importance of music as liberal art and mathematical basis of the Pythagorean tuning.
The Implementation of APIQ Creative Mathematics Game Method in the Subject Matter of Greatest Common Factor and Least Common Multiple in Elementary School

NASA Astrophysics Data System (ADS)

Rahman, Abdul; Saleh Ahmar, Ansari; Arifin, A. Nurani M.; Upu, Hamzah; Mulbar, Usman; Alimuddin; Arsyad, Nurdin; Ruslan; Rusli; Djadir; Sutamrin; Hamda; Minggi, Ilham; Awi; Zaki, Ahmad; Ahmad, Asdar; Ihsan, Hisyam

2018-01-01

One of causal factors for uninterested feeling of the students in learning mathematics is a monotonous learning method, like in traditional learning method. One of the ways for motivating students to learn mathematics is by implementing APIQ (Aritmetika Plus Intelegensi Quantum) creative mathematics game method. The purposes of this research are (1) to describe students’ responses toward the implementation of APIQ creative mathematics game method on the subject matter of Greatest Common Factor (GCF) and Least Common Multiple (LCM) and (2) to find out whether by implementing this method, the student’s learning completeness will improve or not. Based on the results of this research, it is shown that the responses of the students toward the implementation of APIQ creative mathematics game method in the subject matters of GCF and LCM were good. It is seen in the percentage of the responses were between 76-100%. (2) The implementation of APIQ creative mathematics game method on the subject matters of GCF and LCM improved the students’ learning.

Mathematical Content of Curricula and Beginning Salaries of Graduating Students

ERIC Educational Resources Information Center

Lee, B. Brian; Lee, Jungsun

2009-01-01

The authors examined an association between mathematical content in college-level curricula and beginning salaries of graduating students on the basis of data collected from a public university in the southern region of the United States. The authors classified the mathematical content requirements of the curricula into the following 5 groups…
Using Spreadsheets to Teach Aspects of Biology Involving Mathematical Models

ERIC Educational Resources Information Center

Carlton, Kevin; Nicholls, Mike; Ponsonby, David

2004-01-01

Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…
The Framing Discussion: Connecting Student Experience with Mathematical Knowledge

ERIC Educational Resources Information Center

Henning, John E.; Balong, Megan

2011-01-01

This article introduces the framing discussion, an informal discussion of a mathematical problem that takes place at the beginning of a lesson or unit. The purpose of the framing discussion is to assess student knowledge, motivate student interest, and to serve as a basis for guiding students to more formal mathematical knowledge. The article…
History, Applications, and Philosophy in Mathematics Education: HAPh--A Use of Primary Sources

ERIC Educational Resources Information Center

Jankvist, Uffe Thomas

2013-01-01

The article first investigates the basis for designing teaching activities dealing with aspects of history, applications, and philosophy of mathematics in unison by discussing and analyzing the different "whys" and "hows" of including these three dimensions in mathematics education. Based on the observation that a use of history, applications, and…
Developing and Piloting the Planning for Facilitating Mathematical Processes and Strategies for Preschool Learners

ERIC Educational Resources Information Center

Botha, M.; Maree, J. G.; de Witt, M. W.

2005-01-01

From an early age young children actively engage informally in acquiring fundamental concepts and process skills that form a basis for mathematical understanding. Quite logically, questions will arise during planning when young children first encounter a more formal learning environment: what strategy should one use to develop mathematical …
A bio-physical basis of mathematics in synaptic function of the nervous system: a theory.

PubMed

Dempsher, J

1980-01-01

The purpose of this paper is to present a bio-physical basis of mathematics. The essence of the theory is that function in the nervous system is mathematical. The mathematics arises as a result of the interaction of energy (a wave with a precise curvature in space and time) and matter (a molecular or ionic structure with a precise form in space and time). In this interaction, both energy and matter play an active role. That is, the interaction results in a change in form of both energy and matter. There are at least six mathematical operations in a simple synaptic region. It is believed the form of both energy and matter are specific, and their interaction is specific, that is, function in most of the 'mind' and placed where it belongs - in nature and the synaptic regions of the nervous system; it results in both places from a precise interaction between energy (in a precise form) and matter ( in a precise structure).
Zernike-like systems in polygons and polygonal facets.

PubMed

Ferreira, Chelo; López, José L; Navarro, Rafael; Sinusía, Ester Pérez

2015-07-20

Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit disk. In [Opt. Lett.32, 74 (2007)10.1364/OL.32.000074OPLEDP0146-9592] we introduced a new Zernike basis for elliptic and annular optical apertures based on an appropriate diffeomorphism between the unit disk and the ellipse and the annulus. Here, we present a generalization of this Zernike basis for a variety of important optical apertures, paying special attention to polygons and the polygonal facets present in segmented mirror telescopes. On the contrary to ad hoc solutions, most of them based on the Gram-Smith orthonormalization method, here we consider a piecewise diffeomorphism that transforms the unit disk into the polygon under consideration. We use this mapping to define a Zernike-like orthonormal system over the polygon. We also consider ensembles of polygonal facets that are essential in the design of segmented mirror telescopes. This generalization, based on in-plane warping of the basis functions, provides a unique solution, and what is more important, it guarantees a reasonable level of invariance of the mathematical properties and the physical meaning of the initial basis functions. Both the general form and the explicit expressions for a typical example of telescope optical aperture are provided.
Basic statistics with Microsoft Excel: a review.

PubMed

Divisi, Duilio; Di Leonardo, Gabriella; Zaccagna, Gino; Crisci, Roberto

2017-06-01

The scientific world is enriched daily with new knowledge, due to new technologies and continuous discoveries. The mathematical functions explain the statistical concepts particularly those of mean, median and mode along with those of frequency and frequency distribution associated to histograms and graphical representations, determining elaborative processes on the basis of the spreadsheet operations. The aim of the study is to highlight the mathematical basis of statistical models that regulate the operation of spreadsheets in Microsoft Excel.
Basic statistics with Microsoft Excel: a review

PubMed Central

Di Leonardo, Gabriella; Zaccagna, Gino; Crisci, Roberto

2017-01-01

The scientific world is enriched daily with new knowledge, due to new technologies and continuous discoveries. The mathematical functions explain the statistical concepts particularly those of mean, median and mode along with those of frequency and frequency distribution associated to histograms and graphical representations, determining elaborative processes on the basis of the spreadsheet operations. The aim of the study is to highlight the mathematical basis of statistical models that regulate the operation of spreadsheets in Microsoft Excel. PMID:28740690
The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-04-01

This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.
The conceptual basis of mathematics in cardiology III: linear systems theory and integral transforms.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-05-01

This is the third in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas.This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.
The conceptual basis of mathematics in cardiology IV: statistics and model fitting.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-06-01

This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.
The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.
The Alberta K-9 Mathematics Program of Studies with Achievement Indicators

ERIC Educational Resources Information Center

Alberta Education, 2007

2007-01-01

The "Alberta K-9 Mathematics Program of Studies with Achievement Indicators" has been derived from "The Common Curriculum Framework for K-9 Mathematics: Western and Northern Canadian Protocol," May 2006 (the Common Curriculum Framework). The program of studies incorporates the conceptual framework for Kindergarten to Grade 9…
The Influences of Middle School Mathematics Teachers' Practical Rationality on Instructional Decision Making Regarding the Common Core State Standards for Mathematical Practices

ERIC Educational Resources Information Center

Sobolewski-McMahon, Lauren M.

2017-01-01

The purpose of this study was to examine the influences of various facets of middle school mathematics teachers' practical rationality on their instructional decision making as they plan to enact the Common Core State Standards for Mathematical Practice, CCSS-MP1 (perseverance in problem solving) and CCSS-MP3 (communicating and critiquing). The…
Promoting Mathematical Argumentation

ERIC Educational Resources Information Center

Rumsey, Chepina; Langrall, Cynthia W.

2016-01-01

The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…
Inequalities and Real Numbers as a Basis for School Mathematics, Cambridge Conference on School Mathematics Feasibility Study No. 38.

ERIC Educational Resources Information Center

Lomon, Earle

These materials were developed as a practical response to some of the recommendations of the 1963 Cambridge Conference on School Mathematics (CCSM). Experimental sessions are described in detail in this report. In the Estabrook Elementary School, Lexington, Massachusetts, first grade children (1964-65 Academic Year) concentrated on material…
Motivational Classroom Climate for Learning Mathematics: A Reversal Theory Perspective

ERIC Educational Resources Information Center

Lewis, Gareth

2015-01-01

In this article, a case is made that affect is central in determining students' experience of learning or not learning mathematics. I show how reversal theory (Apter, 2001), and particularly its taxonomy of motivations and emotions, provides a basis for a thick description of students' experiences of learning in a mathematics classroom. Using data…
Biomedical Mathematics, Unit I: Measurement, Linear Functions and Dimensional Algebra. Student Text. Revised Version, 1975.

ERIC Educational Resources Information Center

Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.

This text presents lessons relating specific mathematical concepts to the ideas, skills, and tasks pertinent to the health care field. Among other concepts covered are linear functions, vectors, trigonometry, and statistics. Many of the lessons use data acquired during science experiments as the basis for exercises in mathematics. Lessons present…
A Conceptual Analysis of the Knowledge of Prospective Mathematics Teachers about Degree and Radian

ERIC Educational Resources Information Center

Tuna, Abdulkadir

2013-01-01

This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

Mathematics Education ITE Students Examining the Value of Digital Learning Objects

ERIC Educational Resources Information Center

Hawera Ngarewa; Wright, Noeline; Sharma, Sashi

2017-01-01

One issue in mathematics initial teacher education (ITE) is how to best support students to use digital technologies (DTs) to enhance their teaching of mathematics. While most ITE students are probably using DTs on a daily basis for personal use, they are often unfamiliar with using them for educative purposes in New Zealand primary school…
The Contribution of Ernst Mach to Embodied Cognition and Mathematics Education

ERIC Educational Resources Information Center

Zudini, Verena; Zuccheri, Luciana

2016-01-01

A study of the interactions between mathematics and cognitive science, carried out within a historical perspective, is important for a better understanding of mathematics education in the present. This is evident when analysing the contribution made by the epistemological theories of Ernst Mach. On the basis of such theories, a didactic method was…
Vehicular headways on signalized intersections: theory, models, and reality

NASA Astrophysics Data System (ADS)

Krbálek, Milan; Šleis, Jiří

2015-01-01

We discuss statistical properties of vehicular headways measured on signalized crossroads. On the basis of mathematical approaches, we formulate theoretical and empirically inspired criteria for the acceptability of theoretical headway distributions. Sequentially, the multifarious families of statistical distributions (commonly used to fit real-road headway statistics) are confronted with these criteria, and with original empirical time clearances gauged among neighboring vehicles leaving signal-controlled crossroads after a green signal appears. Using three different numerical schemes, we demonstrate that an arrangement of vehicles on an intersection is a consequence of the general stochastic nature of queueing systems, rather than a consequence of traffic rules, driver estimation processes, or decision-making procedures.
Applied Mathematics for agronomical engineers in Spain at UPM

NASA Astrophysics Data System (ADS)

Anton, J. M.; Grau, J. B.; Tarquis, A. M.; Fabregat, J.; Sanchez, M. E.

2009-04-01

Mathematics, created or discovered, are a global human conceptual endowment, containing large systems of knowledge, and varied skills to use definite parts of them, in creation or discovery, or for applications, e.g. in Physics, or notably in engineering behaviour. When getting upper intellectual levels in the 19th century, the agronomical science and praxis was noticeably or mainly organised in Spain in agronomical engineering schools and also in institutes, together with technician schools, also with different lower lever centres, and they have evolved with progress and they are much changing at present to a EEES schema (Bolonia process). They work in different lines that need some basis or skills from mathematics. The vocation to start such careers, that have varied curriculums, contains only some mathematics, and the number of credits for mathematics is restrained because time is necessary for other initial sciences such as applied chemistry, biology, ecology and soil sciences, but some basis and skill of maths are needed, also with Physics, at least for electricity, machines, construction, economics at initial ground levels, and also for Statistics that are here considered part of Applied Mathematics. The ways of teaching mathematical basis and skills are especial, and are different from the practical ways needed e. g. for Soil Sciences, and they involve especial efforts from students, and especial controls or exams that guide much learning. The mathematics have a very large accepted content that uses mostly a standard logic, and that is remarkably stable and international, rather similar notation and expressions being used with different main languages. For engineering the logical basis is really often not taught, but the use of it is transferred, especially for calculus that requires both adapted somehow simplified schemas and the learning of a specific skill to use it, and also for linear algebra. The basic forms of differential calculus in several variables are an example, maybe since Leibnitz, of the difficulty of balance rigor and usefulness in limited hours of teaching. In part engineers use of mathematics with manuals and now with computers that use packages, general (MAPLE, MATLAB, may be MATHCAD, et. C. ) or specific, such as for Statistics, Topography, Structural design, Hydraulics, specific Machines,…, and mostly the details of the algorithms are hidden, but the engineer must have in mind the basic mathematical schemas justifying what he is constructing with these tools, the PC being also used for organisation and drawing. The engineers must adapt to the evolution of these packages and computers that get much changed and improved in five or ten years, quicker than the specific engineering environment, and a clear idea of the much more stable mathematical structures behind gives a solid mental ground for that. An initiation to using computers also with a mathematical structure behind is necessary, to be followed in professional life. A specific actualisation of mathematical knowledge is often necessary for some new applications.
IDEAS.

ERIC Educational Resources Information Center

Young, Sharon L.

1991-01-01

Presented are activities that focus on gathering, using, and interpreting data about fingerprints as a basis for integrating mathematics and science. Patterns, classification, logical reasoning, and mathematical relationships are explored by making graphs, classifying fingerprints, and matching identical fingerprints. A parent-involvement activity…
Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

NASA Astrophysics Data System (ADS)

Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

2018-03-01

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.
REASON: A Self-Instruction Strategy for Twice-Exceptional Learners Struggling With Common Core Mathematics

ERIC Educational Resources Information Center

Van Boxtel, Joanne M.

2016-01-01

Educators across the nation are now well under way in implementing the Common Core State Standards (CCSS; National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA & CCSSO], 2010) for mathematics. The emerging literature regarding CCSS mathematics instruction for students with disabilities urges…
Solving Common Mathematical Problems

NASA Technical Reports Server (NTRS)

Luz, Paul L.

2005-01-01

Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
Modeling in the Common Core State Standards

ERIC Educational Resources Information Center

Tam, Kai Chung

2011-01-01

The inclusion of modeling and applications into the mathematics curriculum has proven to be a challenging task over the last fifty years. The Common Core State Standards (CCSS) has made mathematical modeling both one of its Standards for Mathematical Practice and one of its Conceptual Categories. This article discusses the need for mathematical…
Mathematical Rigor in the Common Core

ERIC Educational Resources Information Center

Hull, Ted H.; Balka, Don S.; Miles, Ruth Harbin

2013-01-01

A whirlwind of activity surrounds the topic of teaching and learning mathematics. The driving forces are a combination of changes in assessment and advances in technology that are being spurred on by the introduction of content in the Common Core State Standards for Mathematical Practice. Although the issues are certainly complex, the same forces…
Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.
Document Set Differentiability Analyzer v. 0.1

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

Osborn, Thor D.

Software is a JMP Scripting Language (JSL) script designed to evaluate the differentiability of a set of documents that exhibit some conceptual commonalities but are expected to describe substantially different – thus differentiable – categories. The script imports the document set, a subset of which may be partitioned into an additions pool. The bulk of the documents form a basis pool. Text analysis is applied to the basis pool to extract a mathematical representation of its conceptual content, referred to as the document concept space. A bootstrapping approach is applied to that mathematical representation in order to generate a representationmore » of a large population of randomly designed documents that could be written within the concept space, notably without actually writing the text of those documents.The Kolmogorov-Smirnov test is applied to determine whether the basis pool document set exhibits superior differentiation relative to the randomly designed virtual documents produced by bootstrapping. If an additions pool exists, the documents are incrementally added to the basis pool, choosing the best differentiated remaining document at each step. In this manner the impact of additional categories to overall document set differentiability may be assessed.The software was developed to assess the differentiability of job description document sets. Differentiability is key to meaningful categorization. Poor job differentiation may have economic, ethical, and/or legal implications for an organization. Job categories are used in the assignment of market-based salaries; consequently, poor differentiation of job duties may set the stage for legal challenges if very similar jobs pay differently depending on title, a circumstance that also invites economic waste.The software can be applied to ensure job description set differentiability, reducing legal, economic, and ethical risks to an organization and its people. The extraction of the conceptual space to a mathematical representation enables identification of exceedingly similar documents. In the event of redundancy, two jobs may be collapsed into one. If in the judgment of the subject matter experts the jobs are truly different, the conceptual similarities are highlighted, inviting inclusion of appropriate descriptive content to explicitly characterize those differences. When additional job categories may be needed as the organization changes, the software enables evaluation of proposed additions to ensure that the resulting document set remains adequately differentiated.« less
Mathematical thinking styles of undergraduate students and their achievement in mathematics

NASA Astrophysics Data System (ADS)

Risnanosanti

2017-08-01

The main purpose of this study is to analyze the role of mathematical thinking styles in students' achievement in mathematics. On the basis of this study, it is also to generate recommendation for classroom instruction. The two specific aims are; first to observe students' mathematical thinking styles during problem solving, the second to asses students' achievement in mathematics. The data were collected by using Mathematical Thinking Styles questionnaires and test of students' achievement in mathematics. The subject in this study was 35 students from third year at mathematics study program of Muhammadiyah University of Bengkulu in academic year 2016/2017. The result of this study was that the students have three mathematical thinking styles (analytic, visual, and integrated), and the students who have analytic styles have better achievement than those who have visual styles in mathematics.
Level of Students' Achievement in Mathematics at the End of Elementary Education in Yemen

ERIC Educational Resources Information Center

Khair, Tarig Mohamed Ali Mohamed; Khairani, Ahmad Zamri; Elrofai, Tahra Aisa

2012-01-01

The main purpose of this study was to investigate the level of student's achievement in mathematics in Yemen. This study use a sample of 200 male students and 200 female students, chosen from eight government schools on the basis of diversified sampling techniques. A mathematics test which composed of seventy five items that covered geometrical…
Spoon-Feeding to Tongue-Biting and Beyond: Factors That Contributed to Changes in Irish Primary School Teachers' Mathematics Practice

ERIC Educational Resources Information Center

Treacy, Mia

2017-01-01

Research that aimed to examine teachers' experiences whilst implementing a reform approach to mathematics teaching in an Irish primary school forms the basis of this paper. In particular, factors that contributed to changing mathematics practice in this case study school are outlined. The school engaged in professional development (PD) that…
Some aspects of mathematical and chemical modeling of complex chemical processes

NASA Technical Reports Server (NTRS)

Nemes, I.; Botar, L.; Danoczy, E.; Vidoczy, T.; Gal, D.

1983-01-01

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.
The Secondary-Tertiary Transition Viewed as a Change in Mathematical Cultures: An Exploration Concerning Symbolism and Its Use

ERIC Educational Resources Information Center

Corriveau, Claudia; Bednarz, Nadine

2017-01-01

Secondary-tertiary transition issues are explored from the perspective of ways of doing mathematics that are constituted in the implicit aspects of teachers' action. Theories of culture (Hall, 1959) and ethnomethodology (Garfinkel, 1967) provide us with a basis for describing and explicating the ways of doing mathematics specific to each teaching…
Implications of Informal Education Experiences for Mathematics Teachers' Ability to Make Connections beyond Formal Classroom

ERIC Educational Resources Information Center

Popovic, Gorjana; Lederman, Judith S.

2015-01-01

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and…
Curricular Coherence and the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Schmidt, William H.; Houang, Richard T.

2012-01-01

In this work, we explored the relationship of the Common Core State Standards in Mathematics (CCSSM) to student achievement. Building on techniques developed for the Third International Mathematics and Science Study (TIMSS), we found a very high degree of similarity between CCSSM and the standards of the highest-achieving nations on the 1995…
Mathematical Modeling, Sense Making, and the Common Core State Standards

ERIC Educational Resources Information Center

Schoenfeld, Alan H.

2013-01-01

On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…

Teacher Concerns and the Enacted Curriculum of the Common Core State Standards in High School Mathematics

ERIC Educational Resources Information Center

Diletti, Jeri S.

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) highlight the importance of students' conceptual understanding, mathematical reasoning, and problem solving in order to prepare students for college and careers. However, the success of this reform effort largely depends on how teachers actually design and implement instruction based on the…
Slope across the Curriculum: Principles and Standards for School Mathematics and Common Core State Standards

ERIC Educational Resources Information Center

Nagle, Courtney; Moore-Russo, Deborah

2014-01-01

This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property,…
Linking Literacy and Mathematics: The Support for Common Core Standards for Mathematical Practice

ERIC Educational Resources Information Center

Swanson, Mary; Parrott, Martha

2013-01-01

In a new era of Common Core State Standards (CCSS), teachers are expected to provide more rigorous, coherent, and focused curriculum at every grade level. To respond to the call for higher expectations across the curriculum and certainly within reading, writing, and mathematics, educators should work closely together to create mathematically…
Transitioning to the Common Core State Standards for Mathematics: A Mixed Methods Study of Elementary Teachers' Experiences and Perspectives

ERIC Educational Resources Information Center

Swars, Susan Lee; Chestnutt, Cliff

2016-01-01

This mixed methods study explored elementary teachers' (n = 73) experiences with and perspectives on the recently implemented Common Core State Standards for Mathematics (CCSS-Mathematics) at a high-needs, urban school. Analysis of the survey, questionnaire, and interview data reveals the findings cluster around: familiarity with and preparation…
Assessing the Quality of the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Cobb, Paul; Jackson, Kara

2011-01-01

The authors comment on Porter, McMaken, Hwang, and Yang's recent analysis of the Common Core State Standards for Mathematics by critiquing their measures of the focus of the standards and the absence of an assessment of coherence. The authors then consider whether the standards are an improvement over most state mathematics standards by discussing…
Impacts of Professional Development on High School Mathematics Teachers as They Implement Common Core State Standards

ERIC Educational Resources Information Center

Saucedo, Ana A.

2017-01-01

The purpose of this qualitative study was to understand the perceptions of high school mathematics teachers regarding the support provided through professional development (PD) as they engage in the implementation of the Common Core State Standards (CCSS). By means of a qualitative instrumental case study, eight high school mathematics teachers…
Using Covariation Reasoning to Support Mathematical Modeling

ERIC Educational Resources Information Center

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…
Storytelling Adds Meaning

ERIC Educational Resources Information Center

Selby, Victor M.

2009-01-01

This article describes several enrichment activities that connect mathematics to science in an algebra 1 curriculum. It provides a basis and suggestions for teachers to include student-produced essays about the role of mathematics in the history of civilization. (Contains 6 figures and 1 table.)
Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

ERIC Educational Resources Information Center

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…
Basis And Application Of The CARES/LIFE Computer Program

NASA Technical Reports Server (NTRS)

Nemeth, Noel N.; Janosik, Lesley A.; Gyekenyesi, John P.; Powers, Lynn M.

1996-01-01

Report discusses physical and mathematical basis of Ceramics Analysis and Reliability Evaluation of Structures LIFE prediction (CARES/LIFE) computer program, described in "Program for Evaluation of Reliability of Ceramic Parts" (LEW-16018).
Accomplishment in Science, Technology, Engineering, and Mathematics (STEM) and Its Relation to STEM Educational Dose: A 25-Year Longitudinal Study

ERIC Educational Resources Information Center

Wai, Jonathan; Lubinski, David; Benbow, Camilla P.; Steiger, James H.

2010-01-01

Two studies examined the relationship between precollegiate advanced/enriched educational experiences and adult accomplishments in science, technology, engineering, and mathematics (STEM). In Study 1, 1,467 13-year-olds were identified as mathematically talented on the basis of scores [greater than or equal to] 500 (top 0.5%) on the math section…
Preliminary Investigation of Profiling Tools and Methods

DTIC Science & Technology

2011-06-01

1 Jaccard coefficient is a unique mathematical way to measure behaviour co-occurancesrd’s coefficient (measure similarity) 4 DRDC Toronto TM...a few heuristics (that are the basis for the mathematical algorithms used in GP systems) these individuals perform just as well as the system...route that GP is a holistic method of data interpretation with unsystematic methodologies, practices and varying mathematical principles, then anecdotes
Selected Topics in the Teaching of Mathematics. National Council of Teachers of Mathematics, Yearbook 3 [1928].

ERIC Educational Resources Information Center

Clark, John R., Ed.; Reeve, W. D., Ed.

This yearbook is a collection of 14 articles covering a wide range of topics. The first argues that arithmetic is "a general mode of thinking," not a "tool subject." The need and use of mathematics for the average citizen is the basis for the second chapter, and the following chapter continues in this vein by attempting to show…
An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…
Phoenix Rising: Bringing the Common Core State Mathematics Standards to Life

ERIC Educational Resources Information Center

Wu, Hung-Hsi

2011-01-01

Many sets of state and national mathematics standards have come and gone in the past two decades. The Common Core State Mathematics Standards (CCSMS), which were released in June of 2010, have been adopted by almost all states and will be phased in across the nation in 2014. The main difference between these standards and most of the others is…
Solving the Common Core Equation: Teaching Mathematics CCSS to Students with Moderate and Severe Disabilities

ERIC Educational Resources Information Center

Saunders, Alicia F.; Bethune, Keri S.; Spooner, Fred; Browder, Diane

2013-01-01

The Common Core State Standards (CCSS) in mathematics were created to help all students become prepared for the demands of future careers and life in an age of technology. Similarly, students with moderate and severe disability will need these skills to meet these changing expectations. Although mathematics instruction could focus on a few of the…
"Better to Be a Pessimist": A Narrative Inquiry into Mathematics Teachers' Experience of the Transition to the Common Core

ERIC Educational Resources Information Center

Martinie, Sherri L.; Kim, Jeong-Hee; Abernathy, Deborah

2016-01-01

The Common Core State Standards (CCSS) are a focus of state education policy today influencing curriculum implementation and assessment in public schools. The purpose of this narrative inquiry is to understand how high school mathematics teachers experience the transition period. Based on interviews with mathematics teachers in a high school in…
Mathematics Formative Assessment System--Common Core State Standards: A Randomized Field Trial in Kindergarten and First Grade

ERIC Educational Resources Information Center

Lang, Laura B.; Schoen, Robert R.; LaVenia, Mark; Oberlin, Maureen

2014-01-01

The Florida Center for Research in Science, Technology, Engineering and Mathematics (FCR-STEM) was awarded a grant by the Florida Department of Education to develop a Mathematics Formative Assessment System (MFAS) aligned with the Common Core State Standards (CCSS). Intended for both teachers and students, formative assessment is a process that…
76 FR 37158 - Agency Information Collection Activities: Comment Request

Federal Register 2010, 2011, 2012, 2013, 2014

2011-06-24

... Presidential Awards for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM) program. In 2003... representative scientific or engineering organization.'' On the basis of these recommendations, the Committee was... individual's work on the current state of physical, biological, mathematical, engineering or social and...
Comparing the Common Core State Standards in Mathematics and NCTM's "Curriculum Focal Points". Achieving the Common Core

ERIC Educational Resources Information Center

Achieve, Inc., 2010

2010-01-01

Through the Common Core State Standards (CCSS) Initiative, states and territories have collaborated in the development of a common core of standards in English Language Arts and mathematics for grades kindergarten through twelve that are now being adopted by states. Designed not only for the purpose of providing strong, shared expectations, the…

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Launching a Discourse-Rich Mathematics Lesson

ERIC Educational Resources Information Center

Trocki, Aaron; Taylor, Christine; Starling, Tina; Sztajn, Paola; Heck, Daniel

2014-01-01

The idea of elementary school students working together on mathematical tasks is not new, but recent attention to creating purposeful discourse in mathematics classrooms prompts teachers to revisit discourse-promoting strategies for mathematics lessons. The Common Core's Standards for Mathematical Practice (CCSSI 2010) encourage teachers to…
Does Time Matter in Improving Mathematical Discussions? The Influence of Mathematical Autonomy

ERIC Educational Resources Information Center

Kosko, Karl W.; Wilkins, Jesse L. M.

2015-01-01

Facilitating students' transition from less to more mathematically productive engagement in discussions is an important area of investigation. Research on mathematical whole-class discussions has consistently identified facilitating students' mathematical autonomy as a central component of this transition. Additionally, research commonly infers…
44 CFR 67.6 - Basis of appeal.

Code of Federal Regulations, 2010 CFR

2010-10-01

... absolute (except where mathematical or measurement error or changed physical conditions can be demonstrated... a mathematical or measurement error or changed physical conditions, then the specific source of the... registered professional engineer or licensed land surveyor, of the new data necessary for FEMA to conduct a...
Learning to Assess and Assessing to Learn: A Descriptive Study of a District-Wide Mathematics Assessment Implementation

ERIC Educational Resources Information Center

Ringer, Catharina W.

2013-01-01

In today's mathematics education, there is an increasing emphasis on students' understanding of the mathematics set forth in standards documents such as the "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics, 2000) and, most recently, the "Common Core State Standards for Mathematics"…
A Data Set of Human Body Movements for Physical Rehabilitation Exercises.

PubMed

Vakanski, Aleksandar; Jun, Hyung-Pil; Paul, David; Baker, Russell

2018-03-01

The article presents University of Idaho - Physical Rehabilitation Movement Data (UI-PRMD) - a publically available data set of movements related to common exercises performed by patients in physical rehabilitation programs. For the data collection, 10 healthy subjects performed 10 repetitions of different physical therapy movements, with a Vicon optical tracker and a Microsoft Kinect sensor used for the motion capturing. The data are in a format that includes positions and angles of full-body joints. The objective of the data set is to provide a basis for mathematical modeling of therapy movements, as well as for establishing performance metrics for evaluation of patient consistency in executing the prescribed rehabilitation exercises.
Common Core State Standards in the Middle Grades: What's New in the Geometry Domain and How Can Teachers Support Student Learning?

ERIC Educational Resources Information Center

Teuscher, Dawn; Tran, Dung; Reys, Barbara J.

2015-01-01

The Common Core State Standards for Mathematics (CCSSM) is a primary focus of attention for many stakeholders' (e.g., teachers, district mathematics leaders, and curriculum developers) intent on improving mathematics education. This article reports on specific content shifts related to the geometry domain in the middle grades (6-8)…
Teachers' Evaluations and Use of Web-Based Curriculum Resources in Relation to the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Webel, Corey; Krupa, Erin E.; McManus, Jason

2015-01-01

This study examines patterns in how a group of fifth- and sixth-grade teachers evaluated and reported using different types of curriculum resources to support their teaching in relation to the mathematical concepts outlined in the Common Core State Standards for Mathematics. In particular, it explores the use of resources that were available to…
Making Sense of Mathematics

ERIC Educational Resources Information Center

Umphrey, Jan

2011-01-01

The National Council of Teachers of Mathematics (NCTM) is a voice and advocate for mathematics educators, working to ensure that all students receive equitable mathematics learning of the highest quality. To help teachers and school leaders understand the Common Core State Standards for Mathematics (CCSSM) and to point out how the CCSSM can be…
Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Pre-Service Teachers' Mathematics Content Knowledge: Implications for How Mathematics Is Taught in Higher Education

ERIC Educational Resources Information Center

Lowrie, Tom; Jorgensen, Robyn

2016-01-01

This investigation explored pre-service teachers' mathematics content knowledge (MCK) and beliefs associated with mathematics education practices. An Exploratory Factor Analysis, conducted on a beliefs and attitudes questionnaire, produced three common attitude factors associated with (1) inquiry-based teaching; (2) how mathematics knowledge is…
The Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Akkus, Murat

2016-01-01

The Common Core State Standards for Mathematics (CCSSM) was published in 2010 and includes a complete collection of standards that are published and reviewed as a "common core" in which math skills have been extensively adopted. The recommendations provided have been entirely or partially adapted by more than 47 states of the US.…
Remembering the hindu festivities mathematically by the balinese using integer operations and least common multiple

NASA Astrophysics Data System (ADS)

Budi Darmayasa, Jero; Wahyudin; Mulyana, Tatang; Subali Noto, Muchamad

2018-04-01

Ethnomathematicsis considered as a new study in mathematic education. As a study, numerous regions in this world starts to explore through ethnomathematics, including Indonesia. As the intersection between mathematics and mathematical modelling and culture, ethnomathematics exists in various society’s cultural elements, including in the Balinese Hindus’ festivities. To find the mathematical concept used in determining the festivity days, the researcher(s) conducted ethnographic research in Bali Mula society in Kintamani District, Bali. Participation observation, in-depth interview, and literature and documentation were used in collecting the data. As the result, the researcher(s) revealed that the mathematical concept used is integer operations, least common multiple, mixed fraction, and number sequences. Since it contains mathematical concept used in junior high, thus ethnomathematics of “4-hindu’s festivities” may be used as context in mathematics learning. By using ethnomathematics as the context, the researcher(s) expect that it will help teachers in motivation their students to learn mathematics.
Consequences, Characteristics, and Causes of Mathematical Learning Disabilities and Persistent Low Achievement in Mathematics

PubMed Central

Geary, David C.

2011-01-01

Objective The goals of the review are threefold; a) to highlight the educational and employment consequences of poorly developed mathematical competencies; b) overview the characteristics of the children with persistently low achievement in mathematics; and c) provide a primer on cognitive science research that is aimed at identifying the cognitive mechanisms underlying these learning disabilities and associated cognitive interventions. Method Literatures on the educational and economic consequences of poor mathematics achievement were reviewed and integrated with reviews of epidemiological, behavioral genetic, and cognitive science studies of poor mathematics achievement. Results Poor mathematical competencies are common among adults and result in employment difficulties and difficulties in many common day-to-day activities. Among students, about 7% of children and adolescents have a mathematical learning disability (MLD) and another 10% show persistent low achievement (LA) in mathematics despite average abilities in most other areas. Children with MLD and their LA peers have deficits in understanding and representing numerical magnitude, difficulties retrieving basic arithmetic facts from long-term memory, and delays in learning mathematical procedures. These deficits and delays cannot be attributed to intelligence, but are related to working memory deficits for children with MLD, but not LA children. Interventions that target these cognitive deficits are in development and preliminary results are promising. Conclusion Mathematical learning disabilities and learning difficulties associated with persistent low achievement in mathematics are common and not attributable to intelligence. These individuals have identifiable number and memory delays and deficits that appear to be specific to mathematics learning. The most promising interventions are those that target these specific deficits and, in addition, for children with MLD interventions that target their low working memory capacity. PMID:21285895
Mathematical and information maintenance of biometric systems

NASA Astrophysics Data System (ADS)

Boriev, Z.; Sokolov, S.; Nyrkov, A.; Nekrasova, A.

2016-04-01

This article describes the different mathematical methods for processing biometric data. A brief overview of methods for personality recognition by means of a signature is conducted. Mathematical solutions of a dynamic authentication method are considered. Recommendations on use of certain mathematical methods, depending on specific tasks, are provided. Based on the conducted analysis of software and the choice made in favor of the wavelet analysis, a brief basis for its use in the course of software development for biometric personal identification is given for the purpose of its practical application.
Teaching Integer Operations Using Ring Theory

ERIC Educational Resources Information Center

Hirsch, Jenna

2012-01-01

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…
Listening Responsively

ERIC Educational Resources Information Center

Callahan, Kadian M.

2011-01-01

Standards documents, such as the Common Core State Standards for Mathematics and "Principles and Standards for School Mathematics", expect teachers to foster mathematics learning by engaging students in meaningful mathematical discourse to expose students to different ways of thinking about and solving problems and positively influence their…
The Use of Applets for Developing Understanding in Mathematics: A Case Study Using Maplets for Calculus with Continuity Concepts

ERIC Educational Resources Information Center

Patenaude, Raymond E.

2013-01-01

The Common Core State Standards for Mathematics (CCSSM) are founded on a long history of mathematics education research emphasizing the importance of teaching mathematics for understanding. The CCSSM along with the National Council of Teachers of Mathematics (NCTM) recommend the use of technology in the teaching of mathematics. New mobile…
Math in Common. Taking Stock of Common Core Math Implementation: Supporting Teachers to Shift Instruction. Insights from the Math in Common 2015 Baseline Survey of Teachers and Administrators. Formative Evaluation Cycle Report for the Math in Common Initiative: Volume 3

ERIC Educational Resources Information Center

Perry, Rebecca R.; Finkelstein, Neal D.; Seago, Nanette; Heredia, Alberto; Sobolew-Shubin, Sandy; Carroll, Cathy

2015-01-01

Math in Common® (MiC) is a five-year initiative that supports a formal network of 10 California school districts as they implement the Common Core State Standards in Mathematics (CCSS-M) across grades K-8. In spring 2015, WestEd administered surveys to understand the perspectives on Common Core State Standards-Mathematics (CCSS-M) implementation…

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…
Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

Sword, Sarah; Matsuura, Ryota; Cuoco, Al; Kang, Jane; Gates, Miriam

2018-01-01

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…
Working memory and language: skill-specific or domain-general relations to mathematics?

PubMed

Purpura, David J; Ganley, Colleen M

2014-06-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the specific relations of these two non-mathematical factors to individual aspects of early mathematics. Thus, the focus of this study was to determine whether working memory and language were related to only individual aspects of early mathematics or related to many components of early mathematics skills. A total of 199 4- to 6-year-old preschool and kindergarten children were assessed on a battery of early mathematics tasks as well as measures of working memory and language. Results indicated that working memory has a specific relation to only a few-but critically important-early mathematics skills and language has a broad relation to nearly all early mathematics skills. Copyright © 2014 Elsevier Inc. All rights reserved.
STEM Gives Meaning to Mathematics

ERIC Educational Resources Information Center

Hefty, Lukas J.

2015-01-01

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…
Professional Noticing: Developing Responsive Mathematics Teaching

ERIC Educational Resources Information Center

Thomas, Jonathan N.; Eisenhardt, Sara; Fisher, Molly H.; Schack, Edna O.; Tassell, Janet; Yoder, Margaret

2014-01-01

Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult.…
Ethical Concerns: Negotiating Truth and Trust

ERIC Educational Resources Information Center

McGarvey, Lynn M.; Sterenberg, Gladys

2009-01-01

Few studies in mathematics education explicitly address ethical issues arising from student interactions. The ethical concerns held by students are expressed in their words, actions, and interactions. The purpose of this article is to explore the ethical nature of copying as it arises in a mathematics classroom. We investigate the basis for…
Taiwanese Preservice Teachers' Science, Technology, Engineering, and Mathematics Teaching Intention

ERIC Educational Resources Information Center

Lin, Kuen-Yi; Williams, P. John

2016-01-01

This study applies the theory of planned behavior as a basis for exploring the impact of knowledge, values, subjective norms, perceived behavioral controls, and attitudes on the behavioral intention toward science, technology, engineering, and mathematics (STEM) education among Taiwanese preservice science teachers. Questionnaires (N = 139)…
Hungry for Early Spatial and Algebraic Reasoning

ERIC Educational Resources Information Center

Cross, Dionne I.; Adefope, Olufunke; Lee, Mi Yeon; Perez, Arnulfo

2012-01-01

Tasks that develop spatial and algebraic reasoning are crucial for learning and applying advanced mathematical ideas. In this article, the authors describe how two early childhood teachers used stories as the basis for a unit that supports spatial reasoning in kindergartners and first graders. Having mathematical experiences that go beyond…
Task Analysis in Instructional Design: Some Cases from Mathematics.

ERIC Educational Resources Information Center

Resnick, Lauren B.

Task analysis as a tool in the design of instruction is the subject of this paper. Some of the major historical approaches (associationist/behaviorist, gestalt, and Piagetian) are described using examples from mathematics. The usefulness of these approaches to instructional design is evaluated on the basis of four criteria: instructional…
Mathematical modeling of aeroelastic systems

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.

2017-12-01

In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.
Indigenous teachers' experiences of the implementation of culture-based mathematics activities in Sámi school

NASA Astrophysics Data System (ADS)

Nutti, Ylva Jannok

2013-03-01

The goal of Indigenous education is that it should be approached on the basis of the Indigenous language and culture; this is also the case with Sámi education. The Sámi School Board has stated that all teaching in Sámi schools should be culturally based, despite the fact that Sámi culture-based teaching is not specifically defined. Therefore, teachers themselves must adapt the teaching and as a result, usually no Sámi culture-based mathematics teaching takes place. The aim of this article is to discuss Indigenous teachers' experiences with designing and implementing culture-based mathematics activities in Sámi preschool and primary school. The teachers' work with culture-based mathematics activities took the form of Sámi cultural thematic work with ethnomathematical content, Multicultural school mathematics with Sámi cultural elements, and Sámi intercultural mathematics teaching. Culture-based mathematics activities took place within an action research study in the Swedish part of Sápmi. Sápmi comprises northern Norway, Sweden, and Finland, as well as the Kola Peninsula in Russia. In the action research study, six teachers conducted culture-based mathematics activities in preschool and primary school on the basis of the action research loop "plan-act-observe-reflect." During the study the teachers changed from a problem-focused perspective to a possibility-focused culture-based teaching perspective characterised by a self-empowered Indigenous teacher role, as a result of which they started to act as agents for Indigenous school change. The concept of "decolonisation" was visible in the teachers' narratives. The teachers' newly developed knowledge about the ethnomathematical research field seemed to enhance their work with Indigenous culture-based mathematics teaching.
Oki-Doku: Number Puzzles

ERIC Educational Resources Information Center

Gomez, Cristina; Novak, Dani

2014-01-01

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) emphasize the Standards for Mathematical Practice (SMP) that describe processes and proficiencies included in the NCTM Process Standards (NCTM 2000) and in the Strands for Mathematical Proficiency (NRC 2001). The development of these mathematical practices should happen in…
Exploring Yellowstone National Park with Mathematical Modeling

ERIC Educational Resources Information Center

Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

2017-01-01

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…
System principles, mathematical models and methods to ensure high reliability of safety systems

NASA Astrophysics Data System (ADS)

Zaslavskyi, V.

2017-04-01

Modern safety and security systems are composed of a large number of various components designed for detection, localization, tracking, collecting, and processing of information from the systems of monitoring, telemetry, control, etc. They are required to be highly reliable in a view to correctly perform data aggregation, processing and analysis for subsequent decision making support. On design and construction phases of the manufacturing of such systems a various types of components (elements, devices, and subsystems) are considered and used to ensure high reliability of signals detection, noise isolation, and erroneous commands reduction. When generating design solutions for highly reliable systems a number of restrictions and conditions such as types of components and various constrains on resources should be considered. Various types of components perform identical functions; however, they are implemented using diverse principles, approaches and have distinct technical and economic indicators such as cost or power consumption. The systematic use of different component types increases the probability of tasks performing and eliminates the common cause failure. We consider type-variety principle as an engineering principle of system analysis, mathematical models based on this principle, and algorithms for solving optimization problems of highly reliable safety and security systems design. Mathematical models are formalized in a class of two-level discrete optimization problems of large dimension. The proposed approach, mathematical models, algorithms can be used for problem solving of optimal redundancy on the basis of a variety of methods and control devices for fault and defects detection in technical systems, telecommunication networks, and energy systems.
Empowering Mathematical Practices

ERIC Educational Resources Information Center

Coomes, Jacqueline; Lee, Hyung Sook

2017-01-01

Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…
Mathematics and General Education. Stirling Seminar Papers No. 2.

ERIC Educational Resources Information Center

Ruthven, Kenneth

1979-01-01

Despite the development of a common mathematics course, and the raising of the school leaving age, Scotland's mathematics curriculum is still designed for specialization. A general education perspective suggests that the curriculum should enable students to relate mathematics to everyday life (f=fiche number). (Author/CP)
Technology Focus: Enhancing Conceptual Knowledge of Linear Programming with a Flash Tool

ERIC Educational Resources Information Center

Garofalo, Joe; Cory, Beth

2007-01-01

Mathematical knowledge can be categorized in different ways. One commonly used way is to distinguish between procedural mathematical knowledge and conceptual mathematical knowledge. Procedural knowledge of mathematics refers to formal language, symbols, algorithms, and rules. Conceptual knowledge is essential for meaningful understanding of…
Early Mathematics Fluency with CCSSM

ERIC Educational Resources Information Center

Matney, Gabriel T.

2014-01-01

To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…
Equity and Access: All Students Are Mathematical Problem Solvers

ERIC Educational Resources Information Center

Franz, Dana Pompkyl; Ivy, Jessica; McKissick, Bethany R.

2016-01-01

Often mathematical instruction for students with disabilities, especially those with learning disabilities, includes an overabundance of instruction on mathematical computation and does not include high-quality instruction on mathematical reasoning and problem solving. In fact, it is a common misconception that students with learning disabilities…
Impact of excipient interactions on solid dosage form stability.

PubMed

Narang, Ajit S; Desai, Divyakant; Badawy, Sherif

2012-10-01

Drug-excipient interactions in solid dosage forms can affect drug product stability in physical aspects such as organoleptic changes and dissolution slowdown, or chemically by causing drug degradation. Recent research has allowed the distinction in chemical instability resulting from direct drug-excipient interactions and from drug interactions with excipient impurities. A review of chemical instability in solid dosage forms highlights common mechanistic themes applicable to multiple degradation pathways. These common themes include the role of water and microenvironmental pH. In addition, special aspects of solid-state reactions with excipients and/or excipient impurities add to the complexity in understanding and modeling reaction pathways. This paper discusses mechanistic basis of known drug-excipient interactions with case studies and provides an overview of common underlying themes. Recent developments in the understanding of degradation pathways further impact methodologies used in the pharmaceutical industry for prospective stability assessment. This paper discusses these emerging aspects in terms of limitations of drug-excipient compatibility studies, emerging paradigms in accelerated stability testing, and application of mathematical modeling for prediction of drug product stability.

A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor

NASA Technical Reports Server (NTRS)

Sayyah, Rana; Hunt, Mitchell; MacLeod, Todd C.; Ho, Fat D.

2009-01-01

This paper presents a mathematical model characterizing the behavior of a simple amplifier using a FeFET. The model is based on empirical data and incorporates several variables that affect the output, including frequency, load resistance, and gate-to-source voltage. Since the amplifier is the basis of many circuit configurations, a mathematical model that describes the behavior of a FeFET-based amplifier will help in the integration of FeFETs into many other circuits.
What Should Common Core Assessments Measure?

ERIC Educational Resources Information Center

Chandler, Kayla; Fortune, Nicholas; Lovett, Jennifer N.; Scherrer, Jimmy

2016-01-01

The Common Core State Standards for mathematics promote ideals about learning mathematics by providing specific standards focused on conceptual understanding and incorporating practices in which students must participate to develop conceptual understanding. Thus, how we define learning is pivotal because our current definition isn't aligned with…
Development of Row of Vibration Insulators and its Mathematical Models on a Base of Common Multi-parameter Scheme of Element Axial Line

NASA Astrophysics Data System (ADS)

Ponomarev, Yury K.

2018-01-01

The mathematical model of deformation of a cable (rope) vibration insulator consisting of two identical clips connected by means of elastic elements of a complex axial line is developed in detail. The axial line of the element is symmetric relatively to the horizontal axis of the shape and is made up of five rectilinear sections of arbitrary length a, b, c, conjugated to four radius sections with parameters R1 and R2 with angular extent 90°. On the basis of linear representations of the theory of bending and torsion of mechanics of materials, applied mechanics and linear algebra, a mathematical model of loading of an element and a vibration insulator as a whole in the direction of the vertical Y axis has been developed. Generalized characteristics of the friction and elastic forces for an elastic element with a complete set of the listed sections are obtained. Further, with the help of nullification in the generalized model of the characteristics of certain parameters, special cases of friction and elastic forces are obtained without taking into account the nullified parameters. Simultaneously, on the basis of the 3D computer-aided design system, volumetric models of simplified structures were created, given in the work. It is shown that, with the help of a variation of the five parameters of the axial scheme of the element, in combination with the variation of the moment of inertia of the rope section and the number of elements entering the ensemble, the load characteristics and stiffness of the vibration insulators can be changed tens and hundreds of times. This opens up unlimited possibilities for the optimal design of vibration protection systems in terms of weight characteristics, in cost, in terms of vibration intensity, in overall dimensions in different directions, which is very important for aerospace and transport engineering.
Understanding synergy.

PubMed

Geary, Nori

2013-02-01

Analysis of the interactive effects of combinations of hormones or other manipulations with qualitatively similar individual effects is an important topic in basic and clinical endocrinology as well as other branches of basic and clinical research related to integrative physiology. Functional, as opposed to mechanistic, analyses of interactions rely on the concept of synergy, which can be defined qualitatively as a cooperative action or quantitatively as a supra-additive effect according to some metric for the addition of different dose-effect curves. Unfortunately, dose-effect curve addition is far from straightforward; rather, it requires the development of an axiomatic mathematical theory. I review the mathematical soundness, face validity, and utility of the most frequently used approaches to supra-additive synergy. These criteria highlight serious problems in the two most common synergy approaches, response additivity and Loewe additivity, which is the basis of the isobole and related response surface approaches. I conclude that there is no adequate, generally applicable, supra-additive synergy metric appropriate for endocrinology or any other field of basic and clinical integrative physiology. I recommend that these metrics be abandoned in favor of the simpler definition of synergy as a cooperative, i.e., nonantagonistic, effect. This simple definition avoids mathematical difficulties, is easily applicable, meets regulatory requirements for combination therapy development, and suffices to advance phenomenological basic research to mechanistic studies of interactions and clinical combination therapy research.
Mathematics Education in Europe: Common Challenges and National Policies

ERIC Educational Resources Information Center

Parveva, Teodora; Noorani, Sogol; Ranguelov, Stanislav; Motiejunaite, Akvile; Kerpanova, Viera

2011-01-01

Competence in mathematics is integral to a wide range of disciplines, professions and areas of life. This Eurydice report reveals crucial elements of the policies and practices that shape mathematics instruction in European education systems, focusing on reforms of mathematics curricula, teaching and assessment methods, as well as teacher…
Core-Plus Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

"Core-Plus Mathematics" is a four-year curriculum that replaces the traditional sequence with courses that each feature interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. The first three courses in the series provide a common core of broadly useful mathematics,…
Second-Graders' Mathematical Practices for Solving Fraction Tasks

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Bolyard, Johnna J.; Tucker, Stephen I.

2014-01-01

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…
A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
Ways That Preservice Teachers Integrate Children's Literature into Mathematics Lessons

ERIC Educational Resources Information Center

Rogers, Rachelle Meyer; Cooper, Sandi; Nesmith, Suzanne M.; Purdum-Cassidy, Barbara

2015-01-01

Children's literature involving mathematics provides a common, natural context for the sharing of mathematics. To learn more about how preservice teachers included children's literature in their mathematics lessons, a study was conducted over two semesters during a required field experience component of an undergraduate teacher education program.…
Fostering Student Engagement with the Flip

ERIC Educational Resources Information Center

Moore, Amanda J.; Gillett, Matthew R.; Steele, Michael D.

2014-01-01

The Common Core Standards for Mathematical Practice (CCSSI 2010) and NCTM's "Focus in High School Mathematics: Reasoning and Sense Making" (2009) present a vision of high school classrooms in which the majority of the activity involves students working on rich mathematical problems and engaging in mathematical discourse. This model…
Missing the Promise of Mathematical Modeling

ERIC Educational Resources Information Center

Meyer, Dan

2015-01-01

The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…
An Investigation of the Relative Effectiveness of the Basic Mathematics Review Program at Essex Community College.

ERIC Educational Resources Information Center

Bloomberg, Jerome

Basic Mathematics Review (BMR) is a remedial non-credit course at Essex Community College (Maryland) being taught on an individualized basis. Following diagnostic testing and placement, instruction utilizes programmed materials, tutors, and self-tests. Evaluation of the new individualized BMR and comparison with the traditional remedial course…
A Teacher Pair Approach to Adopting Effective Numeracy Teaching Practice

ERIC Educational Resources Information Center

Lamb, Janeen; Geiger, Vince

2010-01-01

While the notion of numeracy as the capacity to make use of mathematics within contexts associated with personal and public life, as distinct from basis mathematical competence, is broadly accepted, forms of professional teacher learning that lead to the effective teaching of numeracy are still the subject of ongoing research. This paper reports…
Undergraduate Students' Preference for Procedural to Conceptual Solutions to Mathematical Problems

ERIC Educational Resources Information Center

Engelbrecht, Johann; Bergsten, Christer; Kagesten, Owe

2009-01-01

This article reports on a collaboration project between South Africa and Sweden, in which we want to investigate whether the emphasis in undergraduate mathematics courses for engineering students should be more conceptual than the current traditional way of teaching. On the basis of a review of the distinction between conceptual and procedural…
Strategy Use and Strategy Choice in Fraction Magnitude Comparison

ERIC Educational Resources Information Center

Fazio, Lisa K.; DeWolf, Melissa; Siegler, Robert S.

2016-01-01

We examined, on a trial-by-trial basis, fraction magnitude comparison strategies of adults with more and less mathematical knowledge. College students with high mathematical proficiency used a large variety of strategies that were well tailored to the characteristics of the problems and that were guaranteed to yield correct performance if executed…
Middle School Mathematics Teachers' Experiences with School-Based and District-Based Support and Its Relationship to Integrating Technology

ERIC Educational Resources Information Center

Hampshire, Onequa N.

2014-01-01

Technological advances play a major role in educating students' in mathematics. Research indicates that technology could create learning environments that support innovativeness and assist teachers in developing a positive attitude toward integrating technology. Unfortunately, teachers are not utilizing technology on a regular basis in mathematics…
Career Education--An Idea Book for Mathematics Teachers.

ERIC Educational Resources Information Center

Soper, Joan, Ed.

The book contains a series of career-oriented ideas for mathematics teachers, contributed by teachers in the East Providence Career Education Project. The ideas are the basis of the interdisciplinary contracting system for grades 7-12 in three pilot schools. They are classified by occupational clusters, which the teachers can use to incorporate…
Once, Sometimes, or Always in Special Education: Mathematics Growth and Achievement Gaps

ERIC Educational Resources Information Center

Schulte, Ann C.; Stevens, Joseph J.

2015-01-01

This study used a statewide longitudinal sample to examine mathematics achievement gaps and growth in students with and without disabilities and to examine the impact of different methods of determining disability group membership on achievement gaps and growth. When disability status was determined on the basis of special education placement each…
U.S. Middle School Mathematics Teachers' Perceptions of the Standards for Mathematical Practice by Textbook Type

ERIC Educational Resources Information Center

Davis, Jon D.; Choppin, Jeffrey; Drake, Corey; Roth McDuffie, Amy; Carson, Cynthia

2018-01-01

An important component of the Common Core State Standards for Mathematics (CCSSM), used by the majority of states in the U.S., has the eight standards for mathematical practice (SMPs). While surveys have investigated teachers' perceptions of the CCSSM few have investigated middle school mathematics teachers' (MSMTs') (grades 6-8) perceptions of…
Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion

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

Yükçü, Niyazi

Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical propertiesmore » of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.« less

Moving in Parallel Toward a Modern Modeling Epistemology: Bayes Factors and Frequentist Modeling Methods.

PubMed

Rodgers, Joseph Lee

2016-01-01

The Bayesian-frequentist debate typically portrays these statistical perspectives as opposing views. However, both Bayesian and frequentist statisticians have expanded their epistemological basis away from a singular focus on the null hypothesis, to a broader perspective involving the development and comparison of competing statistical/mathematical models. For frequentists, statistical developments such as structural equation modeling and multilevel modeling have facilitated this transition. For Bayesians, the Bayes factor has facilitated this transition. The Bayes factor is treated in articles within this issue of Multivariate Behavioral Research. The current presentation provides brief commentary on those articles and more extended discussion of the transition toward a modern modeling epistemology. In certain respects, Bayesians and frequentists share common goals.
A RUTCOR Project on Discrete Applied Mathematics

DTIC Science & Technology

1989-01-30

the more important results of this work is the possibility that Groebner basis methods of computational commutative algebra might lead to effective...Billera, L.J., " Groebner Basis Methods for Multivariate Splines," prepared for the Proceedings of the Oslo Conference on Computer-aided Geometric Design
Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.
Automated Scoring of Mathematics Tasks in the Common Core Era: Enhancements to M-Rater in Support of "CBAL"™ Mathematics and the Common Core Assessments. Research Reports. ETS RR-13-26

ERIC Educational Resources Information Center

Fife, James H.

2013-01-01

The m-rater scoring engine has been used successfully for the past several years to score "CBAL"™ mathematics tasks, for the most part without the need for human scoring. During this time, various improvements to m-rater and its scoring keys have been implemented in response to specific CBAL needs. In 2012, with the general move toward…
The Common Core and Inverse Functions

ERIC Educational Resources Information Center

Edenfield, Kelly W.

2012-01-01

The widespread adoption of the Common Core State Standards for Mathematics (CCSSI 2010) shows a commitment to changing mathematics teaching and learning in pursuit of increasing student achievement. CCSSM should not be viewed as just another list of content standards for publishers and assessment groups to design their products around. Many…
Behind the Numbers: The Preliminary Findings of a Mixed Methods Study Investigating the Existence of Mathematics Anxiety among Mature Students

ERIC Educational Resources Information Center

Ryan, Maria; Fitzmaurice, Olivia

2017-01-01

Admitting that one is "no good at mathematics" or "hates mathematics" is a common admission among student cohorts. For mature students who harbour a strong dislike of mathematics, these feelings can be exacerbated when they are faced with having to do an obligatory service mathematics module as part of a programme of study. For…
Mathematics and Comprehensive Ideals

ERIC Educational Resources Information Center

Watson, Anne

2011-01-01

This article revisits methods and debates about teaching mathematics that were common in the 1980s and early 1990s, and then moves up to date with the findings from three mathematics departments that set out to make a difference for their lowest attaining students. The methods they used were distinctly focused on core mathematical ideas, and how…
Mathematics and Numeracy--Is There a Difference?

ERIC Educational Resources Information Center

Australian Mathematics Teacher, 2012

2012-01-01

The term "numeracy" seems to be commonly used in discussions about school mathematics education these days. It is not altogether clear what various school systems intend "numeracy" to mean and whether or not it is meant to replace the term "mathematics", whether it is just one part of mathematics or whether it is…
Definitions of Mathematical Knowledge for Teaching: Using These Constructs in Research on Secondary and College Mathematics Teachers

ERIC Educational Resources Information Center

Speer, Natasha M.; King, Karen D.; Howell, Heather

2015-01-01

The construct "mathematical knowledge for teaching" (MKT) has received considerable attention in the mathematics education community in recent years. The development and refinement of the MKT construct, including the components of common content knowledge (CCK) and specialized content knowledge (SCK), came from research into elementary…
A Study of Prospective Secondary Mathematics Teachers' Evolving Understanding of Reasoning-and-Proving

ERIC Educational Resources Information Center

Boyle, Justin D.

2012-01-01

Proof is a foundational mathematical activity that has been underrepresented in school mathematics. The recently adopted Common Core State Standards in Mathematics includes eight process standards, several of which promote the inclusion of reasoning and proof across all grades, courses, and students. If students are to reach the expectations…
Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…
Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…
Discourse-Based Instructional Strategies to Engage Middle School Students with Standards for Mathematical

ERIC Educational Resources Information Center

Cookson, Sandra

2017-01-01

Student achievement in mathematics is correlated with factors related to student engagement. Improving engagement has the potential to improve student achievement at the middle school level. The Common Core State Standards for Mathematics explicate eight specific Standards for Mathematical Practice (SMPs) that clarify the types of skills and…
Mathematically Rich, Investigative Tasks for Teaching Algebra

ERIC Educational Resources Information Center

Day, Lorraine

2015-01-01

A challenge for teachers is to incorporate the Standards for Mathematical Practice (CCSSI 2010) throughout their teaching of mathematics so that the Common Core Standards do not revert back to a purely content-driven curriculum. One way to achieve this is through the use of mathematically rich, investigative tasks. These tasks encourage students…
Establishing and Sustaining an Effective Pre-Kindergarten Math Intervention at Scale

ERIC Educational Resources Information Center

Klein, Alice; Starkey, Prentice; DeFlorio, Lydia; Brown, E. Todd

2012-01-01

Educators are increasingly concerned about the low level of mathematics performance of U.S. students on the TIMSS and other international assessments of mathematics (National Mathematics Advisory Panel, 2008) as well as their insufficient preparation for mathematics standards, such as the Common Core State Standards. Students from low-income and…
Reflections on a Technology-Rich Mathematics Classroom

ERIC Educational Resources Information Center

Hodges, Thomas E.; Conner, Elizabeth

2011-01-01

Integrating technology into the mathematics classroom means more than just new teaching tools--it is an opportunity to redefine what it means to teach and learn mathematics. Yet deciding when a particular form of technology may be appropriate for a specific mathematics topic can be difficult. Such decisions center on what is commonly being…
Curricular Orientations to Real-World Contexts in Mathematics

ERIC Educational Resources Information Center

Smith, Cathy; Morgan, Candia

2016-01-01

A common claim about mathematics education is that it should equip students to use mathematics in the "real world". In this paper, we examine how relationships between mathematics education and the real world are materialised in the curriculum across a sample of eleven jurisdictions. In particular, we address the orientation of the…
Fracking: Drilling into Math and Social Justice

ERIC Educational Resources Information Center

Hendrickson, Katie A.

2015-01-01

Mathematical modeling, a focus of the Common Core State Standards for School Mathematics (CCSSI 2010) and one of the Standards for Mathematical Practice, is generally considered to be the process of exploring a real-world situation and making sense of it using mathematics (Lesh and Zawojewski 2007). Teachers need to create opportunities for…
Inquiry based learning: a student centered learning to develop mathematical habits of mind

NASA Astrophysics Data System (ADS)

Handayani, A. D.; Herman, T.; Fatimah, S.; Setyowidodo, I.; Katminingsih, Y.

2018-05-01

Inquiry based learning is learning that based on understanding constructivist mathematics learning. Learning based on constructivism is the Student centered learning. In constructivism, students are trained and guided to be able to construct their own knowledge on the basis of the initial knowledge that they have before. This paper explained that inquiry based learning can be used to developing student’s Mathematical habits of mind. There are sixteen criteria Mathematical Habits of mind, among which are diligent, able to manage time well, have metacognition ability, meticulous, etc. This research method is qualitative descriptive. The result of this research is that the instruments that have been developed to measure mathematical habits of mind are validated by the expert. The conclusion is the instrument of mathematical habits of mind are valid and it can be used to measure student’s mathematical habits of mind.
A Study of the Alignment between the NAEP Mathematics Framework and the Common Core State Standards for Mathematics (CCSS-M)

ERIC Educational Resources Information Center

Hughes, Gerunda B.; Daro, Phil; Holtzman, Deborah; Middleton, Kyndra

2013-01-01

Introduction: For decades, prior to the inception of the Common Core State Standards (CCSS), the National Assessment of Educational Progress (NAEP) was the only vehicle through which states could assess the progress of their students using a common metric. Now, 45 states, 4 U.S. territories, and the District of Columbia have adopted the CCSS to…

Transition from Model to Proof: Example of Water Treatment Plant

ERIC Educational Resources Information Center

Güler, Gürsel

2016-01-01

The aim of this study was to research the prospective mathematics teachers' ability to construct a mathematical model for a real life problem and to prove these models by generalizing them to use in similar situations. The study was conducted with 129 prospective teachers determined on a volunteering basis. The data were obtained with the help of…
The Social Basis of Math Teaching and Learning. Final Report.

ERIC Educational Resources Information Center

Orvik, James M.; Van Veldhuizen, Philip A.

This study was designed to identify a set of research questions and testable hypothesis to aid in planning long-range research. Five mathematics teachers were selected. These instructors enrolled in a special project-related seminar, video-taped sessions of their own mathematics classes, and kept field journals. The group met once a week to…
Supporting High Quality Teacher-Child Interactions in Pre-K Mathematics

ERIC Educational Resources Information Center

McGuire, Patrick

2010-01-01

The purpose of this three-paper manuscript dissertation is to add value to the limited knowledge base of research surrounding the quality of teacher-child interactions in pre-k mathematics contexts. The first paper, based on an extensive review of literature, presents a theoretical basis for using five-frames to support children's development of…
Advanced Mathematics Online: Assessing Particularities in the Online Delivery of a Second Linear Algebra Course

ERIC Educational Resources Information Center

Montiel, Mariana; Bhatti, Uzma

2010-01-01

This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…
Identification of Prospective Science Teachers' Mathematical-Logical Structures in Reference to Magnetism

ERIC Educational Resources Information Center

Yilmaz, Ismail

2014-01-01

This paper is a qualitative case study designed to identify prospective science teachers' mathematical-logical structures on the basis of their knowledge and achievement levels in magnetism. The study also made an attempt to reveal the effects of knowledge-level variables and procedural variables, which were considered to be potential…
Topical Modules in Secondary Mathematics. Final Project Report.

ERIC Educational Resources Information Center

Fresno City Unified School District, CA.

Summative evaluation of an ESEA Title III project designed to raise the mathematics achievement scores of low achievers in grades 10 and 11 is reported. In a summer writing project, teachers developed 21 arithmetic modules and 11 algebra modules for use by students on an individual basis. Students used the modules at their own pace and stayed with…
Equilibrium liquid free-surface configurations: Mathematical theory and space experiments

NASA Technical Reports Server (NTRS)

Concus, P.; Finn, R.

1996-01-01

Small changes in container shape or in contact angle can give rise to large shifts of liquid in a microgravity environment. We describe some of our mathematical results that predict such behavior and that form the basis for physical experiments in space. The results include cases of discontinuous dependence on data and symmetry-breaking type of behavior.
A "Great Way to Get On"? The Early Career Destinations of Science, Technology, Engineering and Mathematics Graduates

ERIC Educational Resources Information Center

Smith, Emma; White, Patrick

2017-01-01

Concerns about a shortage of highly skilled workers in the science, technology, engineering and mathematics (STEM) sector have been expressed frequently since the late 1940s. Although these claims have been challenged as being insufficiently grounded in evidence, they have formed the basis of policies directing considerable resources to STEM…
Early-Years Swimming: Creating Opportunities for Adding Mathematical Capital to Under 5s

ERIC Educational Resources Information Center

Jorgensen, Robyn

2013-01-01

Drawing on survey data from over 2000 parents, this paper explores the possibility of early-years swimming to add mathematical capital to young children. Using developmental milestones as the basis, it was found that parents reported significantly earlier achievement on many of these milestones. Such data suggest that the early years swim…
Survey of Adult Students with Mathematical Difficulties

ERIC Educational Resources Information Center

Jarlskog, Linda

2016-01-01

This paper relates to one of the test procedures being used in Sweden, used to establish if students need a more thorough investigation of their mathematical difficulties. This paper mainly describes the test process and the results from 10 test subjects. The paper also refers to parts of the research forming the basis for the test process. The…
Fluoroscopy guided percutaneous renal access in prone position

PubMed Central

Sharma, Gyanendra R; Maheshwari, Pankaj N; Sharma, Anshu G; Maheshwari, Reeta P; Heda, Ritwik S; Maheshwari, Sakshi P

2015-01-01

Percutaneous nephrolithotomy is a very commonly done procedure for management of renal calculus disease. Establishing a good access is the first and probably the most crucial step of this procedure. A proper access is the gateway to success. However, this crucial step has the steepest learning curve for, in a fluoroscopy guided access, it involves visualizing a three dimensional anatomy on a two dimensional fluoroscopy screen. This review describes the anatomical basis of the renal access. It provides a literature review of all aspects of percutaneous renal access along with the advances that have taken place in this field over the years. The article describes a technique to determine the site of skin puncture, the angle and depth of puncture using a simple mathematical principle. It also reviews the common problems faced during the process of puncture and dilatation and describes the ways to overcome them. The aim of this article is to provide the reader a step by step guide for percutaneous renal access. PMID:25789297
Aerodynamics and mathematics in National Socialist Germany and Fascist Italy: a comparison of research institutes.

PubMed

Epple, Moritz; Karachalios, Andreas; Remmert, Volker R

2005-01-01

The article is concerned with the mathematical sciences in National Socialist Germany and Fascist Italy, with special attention to research important to the war effort. It focuses on three institutional developments: the expansion of the Kaiser Wilhelm Institute for Fluid Dynamics in Göttingen, the foundation of the Reich Institute for Mathematics in Oberwolfach (Black Forest), and the work of the Istituto Nazionale per le Applicazioni del Calcolo in Rome. All three developments are embedded in the general political background, thus providing a basis for comparative conclusions about the conditions of the mathematical sciences and military-related research in Germany and Italy. It turns out that in both countries, the increasing demand for mathematical knowledge in modern warfare led to the establishment of "extra-university" national institutions specifically devoted to mathematical research.
Topology of an intracellular transduction chain (phototropism of Phycomyces): 1. Joint review of functional, temporal, and spatial aspects.

PubMed

Wenzler, D; Reinhardt, M; Fukshansky, L

2001-08-21

Two light-induced growth reactions in a unicellular cylindrical sporangiophore of Phycomyces blakesleeanus-vertical growth acceleration under symmetrical irradiation (photomecism) and directional growth under unilateral irradiation (phototropism)-share common input light perception as well as common output growth mechanism but have strongly divergent dynamics and other distinctive features. This divergence culminates in the phototropic paradoxes the main of which states that photomecism shows total adaptation, while phototropism does not adapt. The basis for this contradiction is that the phototropic transduction chain, unlike that of photomecism, faces a spatially non-uniform stimulus and processes a series of spatial patterns (light and absorption profiles, adaptation profile, etc.). The only way to resolve the paradoxes and correlate features of both responses within a single transduction chain is to assume non-local signal transduction, e.g. a cross-talk between different azimuthal locations within the cylindrical cell. On the other hand, to establish the presence of an appropriate cross-talk is equivalent of gaining insight into the topology of the transduction chain. This series of two papers contains a review reconsidering the entire field from this viewpoint (Paper 1) and a mathematical model of pattern transduction which unifies features of phototropism and resolves the paradoxes (Paper 2). At the same time, this is the first "proof of concept" for the "activity/pooling (a/p) networks"-a specific mathematical apparatus designed to analyse systemic properties and control in metabolic pathways. Copyright 2001 Academic Press.
Using Integer Manipulatives: Representational Determinism

ERIC Educational Resources Information Center

Bossé, Michael J.; Lynch-Davis, Kathleen; Adu-Gyamfi, Kwaku; Chandler, Kayla

2016-01-01

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…
An Examination of the Statistical Problem-Solving Process as a Potential Means for Developing an Understanding of Argumentation

ERIC Educational Resources Information Center

Smith Baum, Brittany Deshae

2017-01-01

As part of the recent history of the mathematics curriculum, reasoning and argument have been emphasized throughout mathematics curriculum standards. Specifically, as part of the Common Core State Standards for Mathematics, the Standards for Mathematical Practice were presented, which included the expectation that students develop arguments and…
Unpacking Teachers' Moves in the Classroom: Navigating Micro- and Macro-Levels of Mathematical Complexity

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2015-01-01

The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. ("Journal for Research in Mathematics Education"…
Early Childhood Teachers' Misconceptions about Mathematics Education for Young Children in the United States

ERIC Educational Resources Information Center

Lee, Joon Sun; Ginsburg, Herbert P.

2009-01-01

In this article we discuss nine common misconceptions about learning and teaching mathematics for young children that are widespread among prospective and practicing early childhood teachers in the United States. These misconceptions include: 1. Young children are not ready for mathematics education; 2. Mathematics is for some bright kids with…
A RUTCOR Project in Discrete Applied Mathematics

DTIC Science & Technology

1990-02-20

representations of smooth piecewise polynomial functions over triangulated regions have led in particular to the conclusion that Groebner basis methods of...Reversing Number of a Digraph," in preparation. 4. Billera, L.J., and Rose, L.L., " Groebner Basis Methods for Multivariate Splines," RRR 1-89, January
Addressing the Standards for Mathematical Practice in a Calculus Class

ERIC Educational Resources Information Center

Pilgrim, Mary E.

2014-01-01

The Common Core State Standards (CCSS) provide teachers with the expectations and requirements that are meant to prepare K-12 students for college and the workforce (CCSSI 2010b). The Common Core State Standards for Mathematical Practice (SMPs) emphasize the development of skills and conceptual understanding for students to become proficient in…
Common Grounds for Modelling Mathematics in Educational Software

ERIC Educational Resources Information Center

Neuper, Walther

2010-01-01

Two kinds of software, CAS and DGS, are starting to work towards mutual integration. This paper envisages common grounds for such integration based on principles of computer theorem proving (CTP). Presently, the CTP community seems to lack awareness as to which of their products' features might serve mathematics education from high-school to…

Making It Happen: Common Core Standards

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2011

2011-01-01

This one-of-a-kind guide identifies and highlights the ways in which NCTM (National Council of Teachers of Mathematics) resources can support teachers as they implement and supplement the Common Core State Standards for Mathematics (CCSSM) in their states. The guide and accompanying charts are tools to help educators as they continue to make…
Leadership through Professional Collaborations

ERIC Educational Resources Information Center

Pfeil, Jessica; Hirsch, Jenna

2013-01-01

Leaders in mathematics are responsible for implementing positive change within their school districts and motivating teachers of mathematics to improve their practices. One way mathematics leaders can achieve this goal is by establishing professional collaborations. We analyzed the research and summarized the common attributes found in successful…
Preschoolers' Thinking during Block Play

ERIC Educational Resources Information Center

Piccolo, Diana L.; Test, Joan

2010-01-01

Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…
Imaging Freeform Optical Systems Designed with NURBS Surfaces

DTIC Science & Technology

2015-12-01

reflective, anastigmat 1 Introduction The imaging freeform optical systems described here are designed using non-uniform rational basis -spline (NURBS...from piecewise splines. Figure 1 shows a third degree NURBS surface which is formed from cubic basis splines. The surface is defined by the set of...with mathematical details covered by Piegl and Tiller7. Compare this with Gaussian basis functions8 where it is challenging to provide smooth
National Youth Sports Program: Math/Science. Final report, [June 1, 1992--November 30, 1992

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

Not Available

1992-12-31

NYSP, a partnership of NCAA, HHS, and colleges and universities, is aimed at sports instruction and physical activity for disadvantaged youth. In 1992, DOE joined in to add a mathematics/science component. Federal funds were used to conduct mathematics and science education components on a limited pilot basis at 16 sites. Recommendations for future improvements are given.
Equilibrium Fluid Interface Behavior Under Low- and Zero-Gravity Conditions. 2

NASA Technical Reports Server (NTRS)

Concus, Paul; Finn, Robert

1996-01-01

The mathematical basis for the forthcoming Angular Liquid Bridge investigation on board Mir is described. Our mathematical work is based on the classical Young-Laplace-Gauss formulation for an equilibrium free surface of liquid partly filling a container or otherwise in contact with solid support surfaces. The anticipated liquid behavior used in the apparatus design is also illustrated.
Evidence for the Effectiveness of Inquiry-Based, Particulate-Level Instruction on Conceptions of the Particulate Nature of Matter

ERIC Educational Resources Information Center

Bridle, Chad A.; Yezierski, Ellen J.

2012-01-01

Research has shown that students in traditional college-preparatory chemistry courses become masters of mathematical equations without an understanding of the conceptual basis for the mathematical relationships. This problem is rooted not only in what curriculum is presented to students, but also in how it is experienced by the students. Ample…
Comparing the Similarities and Differences of PISA 2003 and TIMSS. OECD Education Working Papers, No. 32

ERIC Educational Resources Information Center

Wu, Margaret

2010-01-01

This paper makes an in-depth comparison of the PISA (OECD) and TIMSS (IEA) mathematics assessments conducted in 2003. First, a comparison of survey methodologies is presented, followed by an examination of the mathematics frameworks in the two studies. The methodologies and the frameworks in the two studies form the basis for providing…
Testing the Theory of Successful Intelligence in Teaching Grade 4 Language Arts, Mathematics, and Science

ERIC Educational Resources Information Center

Sternberg, Robert J.; Jarvin, Linda; Birney, Damian P.; Naples, Adam; Stemler, Steven E.; Newman, Tina; Otterbach, Renate; Parish, Carolyn; Randi, Judy; Grigorenko, Elena L.

2014-01-01

This study addressed whether prior successes with educational interventions grounded in the theory of successful intelligence could be replicated on a larger scale as the primary basis for instruction in language arts, mathematics, and science. A total of 7,702 4th-grade students in the United States, drawn from 223 elementary school classrooms in…
Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

PubMed

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.
A Mathematical Basis for the Safety Analysis of Conflict Prevention Algorithms

NASA Technical Reports Server (NTRS)

Maddalon, Jeffrey M.; Butler, Ricky W.; Munoz, Cesar A.; Dowek, Gilles

2009-01-01

In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.
Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.
What Would the Mathematics Curriculum Look Like if Values Were the Focus?

ERIC Educational Resources Information Center

Seah, Wee Tiong; Andersson, Annica; Bishop, Alan; Clarkson, Philip

2016-01-01

The crucial reason for the common dislike, fear, and even hatred of mathematics by students and others is probably not the nature of mathematics itself, but the way the subject is portrayed and taught. We propose that instead of a mathematics curriculum that focuses on concepts and techniques (which is often seen), it might be more productive if…
An Exploration of the Common Content Knowledge of High School Mathematics Teachers

ERIC Educational Resources Information Center

Bansilal, Sarah; Brijlall, Deonarain; Mkhwanazi, Thokozani

2014-01-01

Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers' knowledge of the mathematics they are themselves teaching. Data was generated from the teachers' (n = 253) written responses to test that was a shortened form of a previous Grade 12…
Does the Apple Fall Far from the Tree? A Mixed Methods Study on the Intergenerational Transmission of Mathematics Attitudes

ERIC Educational Resources Information Center

Olivares, Vidal Elizabeth

2012-01-01

Cold sweats, head shakes, and memories of hardship are the common reactions when adults are introduced to a high school mathematics teacher. Observations show that few adults enjoyed mathematics in their youth. This study aimed to investigate the ways in which students internalize the mathematics attitudes of their parents. Additionally it…
Fuzzy Logic for Incidence Geometry

PubMed Central

2016-01-01

The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Mathematical Approaches to Understanding and Imaging Atrial Fibrillation: Significance for Mechanisms and Management

PubMed Central

Trayanova, Natalia A

2014-01-01

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This articles aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention. PMID:24763468
DOE Office of Scientific and Technical Information (OSTI.GOV)

Anthony, R.W.; Bodig, J.; Phillips, G.E.

This report describes the development of a nondestructive evaluation (NDE) methodology for assessing the bending strength of new wood utility poles. Fundamental concepts of stress wave propagation are presented. The development of a longitudinal stress wave methodology for predicting pole strength and the results of destructive tests on full-size poles are described. Mathematical correlations between stress wave parameters, geometric characteristics, and individual pole bending strengths form the basis of strength prediction models for western redcedar, Douglas-fir and southern pine poles. Models were developed for NDE in the whitewood stage and after preservative treatment of poles. For each species the twomore » most commonly used preservative types were evaluated. Excellent correlations were obtained for western redcedar and Douglas-fir poles, but high moisture content in the southern pine poles resulted in lower prediction accuracies for this species. Verification of the developed mathematical models demonstrates that improvement in classifying poles into the ANSI 05.1 tip-load capacities is technically feasible. The development and field trial of the prototype equipment for strength grading of new poles is also described. Research results can be used to benefit utilities by enabling the supply of strength graded poles with a higher accuracy than previously possible.« less
Shotgun Canceling.

ERIC Educational Resources Information Center

Szymanski, Theodore

1999-01-01

Discusses a common misunderstanding demonstrated by many students in basic mathematics courses: not knowing how to properly "cancel" factors in simplifying mathematical equations. Asserts that "crossing-out" or "canceling" is not a valid mathematical operation, and that instructors should be wary about using these terms because of the ease with…
Mathematical and Scientific Foundations for an Integrative Engineering Curriculum.

ERIC Educational Resources Information Center

Carr, Robin; And Others

1995-01-01

Describes the Mathematical and Scientific Foundations of Engineering curriculum which emphasizes the mathematical and scientific concepts common to all engineering fields. Scientists and engineers together devised topics and experiments that emphasize the relevance of theory to real-world applications. Presents material efficiently while building…

Exploration of Patterns in a Calendar

ERIC Educational Resources Information Center

Huang, Rongjin; Prince, Kyle M.; Schmidt, Teresa

2014-01-01

The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…
Online Mathematics Homework Increases Student Achievement

ERIC Educational Resources Information Center

Roschelle, Jeremy; Feng, Mingyu; Murphy, Robert F.; Mason, Craig A.

2016-01-01

In a randomized field trial with 2,850 seventh-grade mathematics students, we evaluated whether an educational technology intervention increased mathematics learning. Assigning homework is common yet sometimes controversial. Building on prior research on formative assessment and adaptive teaching, we predicted that combining an online homework…
Electromagnetic Concepts in Mathematical Representation of Physics.

ERIC Educational Resources Information Center

Albe, Virginie; Venturini, Patrice; Lascours, Jean

2001-01-01

Addresses the use of mathematics when studying the physics of electromagnetism. Focuses on common electromagnetic concepts and their associated mathematical representation and arithmetical tools. Concludes that most students do not understand the significant aspects of physical situations and have difficulty using relationships and models specific…
A High School Statistics Class Investigates the Death Penalty

ERIC Educational Resources Information Center

Brelias, Anastasia

2015-01-01

Recommendations for reforming high school mathematics curricula emphasize the importance of engaging students in mathematical investigations of societal issues (CCSSI [Common Core State Standards Initiative] 2010; NCTM [National Council of Teachers of Mathematics] 2000). Proponents argue that these investigations can positively influence students'…
The Common Core State Standards: Comparisons of Access and Quality

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2011-01-01

Last year the United States unveiled the Common Core State Standards (CCSS) in English and Mathematics for grades K-12. In particular, the authors included two possible sequences of 8-12 mathematics courses that would fulfill the standards. Most notably, the courses titled "3a" and "3b" in these two sequences have become…
Oakland and San Francisco Create Course Pathways through Common Core Mathematics. White Paper

ERIC Educational Resources Information Center

Daro, Phil

2014-01-01

The Common Core State Standards for Mathematics (CCSS-M) set rigorous standards for each of grades 6, 7 and 8. Strategic Education Research Partnership (SERP) has been working with two school districts, Oakland Unified School District and San Francisco Unified School District, to evaluate extant policies and practices and formulate new policies…
Quality Online Resources and Supports for Educators Teaching the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Walters, Kirk; Smith, Toni; Leinwand, Steve; Ford, Jennifer; Scheopner Torres, Aubrey

2015-01-01

This study was designed in response to a request from rural educators in the Northeast for support in identifying high-quality online resources to implement the Common Core State Standards for Mathematics (CCSSM). The process for identifying online resources included selecting resources that had an easily navigable CCSSM organizational structure…
From the Classroom: Implementing the Common Core in English Language Arts and in Mathematics: Practitioners' Perspectives

ERIC Educational Resources Information Center

VanTassel-Baska, Joyce; Johnsen, Susan K.

2016-01-01

At the 61st National Association for Gifted Children (NAGC) Annual Conference in Baltimore, Maryland, two practitioner panels responded to questions about implementing the Common Core in English language arts (ELA) and in mathematics. After listening to their responses, the authors felt that the "Gifted Child Today" readers would enjoy…
Teachers' Perceptions of Preparedness Related to National Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Brown, Tykier

2016-01-01

With the adoption of the National Common Core State Standards in Mathematics (CCSSM) in many states and the lack of understanding and strategies to implement the new standards by classroom teachers, implementing effective professional development is vital. The focus of this qualitative case study was to provide insight into elementary school…
Research Commentary: Educational Technology--An Equity Challenge to the Common Core

ERIC Educational Resources Information Center

Kitchen, Richard; Berk, Sarabeth

2016-01-01

The implementation of the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) has the potential to move forward key features of standards-based reforms in mathematics that have been promoted in the United States for more than 2 decades (e.g.,…
KSC Education Technology Research and Development Plan

NASA Technical Reports Server (NTRS)

Odell, Michael R. L.

2003-01-01

Educational technology is facilitating new approaches to teaching and learning science, technology, engineering, and mathematics (STEM) education. Cognitive research is beginning to inform educators about how students learn providing a basis for design of more effective learning environments incorporating technology. At the same time, access to computers, the Internet and other technology tools are becoming common features in K-20 classrooms. Encouraged by these developments, STEM educators are transforming traditional STEM education into active learning environments that hold the promise of enhancing learning. This document illustrates the use of technology in STEM education today, identifies possible areas of development, links this development to the NASA Strategic Plan, and makes recommendations for the Kennedy Space Center (KSC) Education Office for consideration in the research, development, and design of new educational technologies and applications.
Variable habitat conditions drive species covariation in the human microbiota

PubMed Central

Mora, Thierry; Walczak, Aleksandra M.

2017-01-01

Two species with similar resource requirements respond in a characteristic way to variations in their habitat—their abundances rise and fall in concert. We use this idea to learn how bacterial populations in the microbiota respond to habitat conditions that vary from person-to-person across the human population. Our mathematical framework shows that habitat fluctuations are sufficient for explaining intra-bodysite correlations in relative species abundances from the Human Microbiome Project. We explicitly show that the relative abundances of closely related species are positively correlated and can be predicted from taxonomic relationships. We identify a small set of functional pathways related to metabolism and maintenance of the cell wall that form the basis of a common resource sharing niche space of the human microbiota. PMID:28448493
Finding and defining the natural automata acting in living plants: Toward the synthetic biology for robotics and informatics in vivo.

PubMed

Kawano, Tomonori; Bouteau, François; Mancuso, Stefano

2012-11-01

The automata theory is the mathematical study of abstract machines commonly studied in the theoretical computer science and highly interdisciplinary fields that combine the natural sciences and the theoretical computer science. In the present review article, as the chemical and biological basis for natural computing or informatics, some plants, plant cells or plant-derived molecules involved in signaling are listed and classified as natural sequential machines (namely, the Mealy machines or Moore machines) or finite state automata. By defining the actions (states and transition functions) of these natural automata, the similarity between the computational data processing and plant decision-making processes became obvious. Finally, their putative roles as the parts for plant-based computing or robotic systems are discussed.
Finding and defining the natural automata acting in living plants: Toward the synthetic biology for robotics and informatics in vivo

PubMed Central

Kawano, Tomonori; Bouteau, François; Mancuso, Stefano

2012-01-01

The automata theory is the mathematical study of abstract machines commonly studied in the theoretical computer science and highly interdisciplinary fields that combine the natural sciences and the theoretical computer science. In the present review article, as the chemical and biological basis for natural computing or informatics, some plants, plant cells or plant-derived molecules involved in signaling are listed and classified as natural sequential machines (namely, the Mealy machines or Moore machines) or finite state automata. By defining the actions (states and transition functions) of these natural automata, the similarity between the computational data processing and plant decision-making processes became obvious. Finally, their putative roles as the parts for plant-based computing or robotic systems are discussed. PMID:23336016
Micro-Macro Duality and Space-Time Emergence

NASA Astrophysics Data System (ADS)

Ojima, Izumi

2011-03-01

The microscopic origin of space-time geometry is explained on the basis of an emergence process associated with the condensation of infinite number of microscopic quanta responsible for symmetry breakdown, which implements the basic essence of "Quantum-Classical Correspondence" and of the forcing method in physical and mathematical contexts, respectively. From this viewpoint, the space-time dependence of physical quantities arises from the "logical extension" [8] to change "constant objects" into "variable objects" by tagging the order parameters associated with the condensation onto "constant objects"; the logical direction here from a value y to a domain variable x (to materialize the basic mechanism behind the Gel'fand isomorphism) is just opposite to that common in the usual definition of a function ƒ : x⟼ƒ(x) from its domain variable x to a value y = ƒ(x).
Calculation of the change in corneal astigmatism following cataract extraction.

PubMed

Cravy, T V

1979-01-01

Obtaining a minimal amount of postoperative astigmatism following cataract surgery is becoming increasingly important. One aspect of the patient's surgery which should not be overlooked is the preoperative keratometry which provides a basis for preoperative planning of surgical technique to be used and a point of reference for determining the amount of change in astigmatism produced by the surgery. Analysis of the surgically induced change in astigmatism using the calculations described in this paper will allow the surgeon to evaluate his own techniques and to maximize his potential for obtaining consistently good postoperative astigmatic results without the need for suture removal. The method presented is based upon concepts in common use in surgical ophthalmology and requires only simple mathematical procedures, familiar to all with a background in algebra and trigonometry.
The Role of the Mathematics Supervisor in K-12 Education

ERIC Educational Resources Information Center

Greenes, Carole

2013-01-01

The implementation of "the Common Core Standards for Mathematics" and the assessments of those concepts, skills, reasoning methods, and mathematical practices that are in development necessitate the updating of teachers' knowledge of content, pedagogical techniques to enhance engagement and persistence, and strategies for responding to…
Anticipation Guides: Reading for Mathematics Understanding

ERIC Educational Resources Information Center

Adams, Anne E.; Pegg, Jerine; Case, Melissa

2015-01-01

With the acceptance by many states of the Common Core State Standards for Mathematics, new emphasis is being placed on students' ability to engage in mathematical practices such as understanding problems (including word problems), reading and critiquing arguments, and making explicit use of definitions (CCSSI 2010). Engaging students in…
Supporting Common Core Sense Making

ERIC Educational Resources Information Center

Keazer, Lindsay; Gerberry, Carla

2017-01-01

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…
Problem Solvers: Problem--Jesse's Train

ERIC Educational Resources Information Center

James, Julie; Steimle, Alice

2014-01-01

Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by…

Conceptualizing "Homework" in Flipped Mathematics Classes

ERIC Educational Resources Information Center

de Araujo, Zandra; Otten, Samuel; Birisci, Salih

2017-01-01

Flipped instruction is becoming more common in the United States, particularly in mathematics classes. One of the defining characteristics of this increasingly popular instructional format is the homework teachers assign. In contrast to traditional mathematics classes in which homework consists of problem sets, homework in flipped classes often…
Transformative Learning: Personal Empowerment in Learning Mathematics

ERIC Educational Resources Information Center

Hassi, Marja-Liisa; Laursen, Sandra L.

2015-01-01

This article introduces the concept of personal empowerment as a form of transformative learning. It focuses on commonly ignored but enhancing elements of mathematics learning and argues that crucial personal resources can be essentially promoted by high engagement in mathematical problem solving, inquiry, and collaboration. This personal…
Using Google Apps to Develop the Mathematical Practices

ERIC Educational Resources Information Center

Layton, Rebecca D.; Cady, Jo Ann; Layton, Christopher A.

2017-01-01

Recent recommendations for the teaching of mathematics place an emphasis on the Common Core's Standards for Mathematical Practice (SMP) (CCSSI 2010). The SMPs emphasize constructing viable arguments, critiquing the ideas of others, reasoning abstractly and quantitatively, and using computational procedures. These skills, including the use of…
Eliciting Mathematics Interest: New Directions for Context Personalization and Example Choice

ERIC Educational Resources Information Center

Høgheim, Sigve; Reber, Rolf

2017-01-01

Building on common assumptions in theories of interest and mathematics education, this experimental study examined the effect of context personalization based on individual preferences, group personalization, and example choice with preselected popular examples on middle school students' situational interest and performance in mathematics.…
Understanding the Complexities of Student Motivations in Mathematics Learning

ERIC Educational Resources Information Center

Walter, Janet G.; Hart, Janelle

2009-01-01

Student motivation has long been a concern of mathematics educators. However, commonly held distinctions between intrinsic and extrinsic motivations may be insufficient to inform our understandings of student motivations in learning mathematics or to appropriately shape pedagogical decisions. Here, motivation is defined, in general, as an…
Mathematical Learning Disabilities in Special Populations: Phenotypic Variation and Cross-Disorder Comparisons

PubMed Central

Dennis, Maureen; Berch, Daniel B.; Mazzocco, Michèle M.M.

2011-01-01

What is mathematical learning disability (MLD)? The reviews in this special issue adopt different approaches to defining the construct of MLD. Collectively, they demonstrate the current status of efforts to establish a consensus definition and the challenges faced in this endeavor. In this commentary, we reflect upon the proposed pathways to mathematical learning difficulties and disabilities presented across the reviews. Specifically we consider how each of the reviews contributes to identifying the MLD phenotype by specifying the range of assets and deficits in mathematics, identifying sources of individual variation, and characterizing the natural progression of MLD over the life course. We show how principled comparisons across disorders address issues about the cognitive and behavioral co-morbidities of MLD, and whether commonalities in brain dysmorphology are associated with common mathematics performance profiles. We project the status of MLD research ten years hence with respect to theoretical gains, advances in methodology, and principled intervention studies. PMID:19213019
Exploring how symptoms of attention-deficit/hyperactivity disorder are related to reading and mathematics performance: general genes, general environments.

PubMed

Hart, Sara A; Petrill, Stephen A; Willcutt, Erik; Thompson, Lee A; Schatschneider, Christopher; Deater-Deckard, Kirby; Cutting, Laurie E

2010-11-01

Children with attention-deficit/hyperactivity disorder (ADHD) tend to perform more poorly on tests of reading and mathematical performance than their typical peers. Quantitative genetic analyses allow for a better understanding of the etiology of ADHD and reading and mathematics outcomes, by examining their common and unique genetic and environmental influences. Analyses were conducted on a sample 271 pairs of 10-year-old monozygotic and dizygotic twins drawn from the Western Reserve Reading and Mathematics Project. In general, the results suggested that the associations among ADHD symptoms, reading outcomes, and math outcomes were influenced by both general genetic and general shared-environment factors. The analyses also suggested significant independent genetic effects for ADHD symptoms. The results imply that differing etiological factors underlie the relationships among ADHD and reading and mathematics performance. It appears that both genetic and common family or school environments link ADHD with academic performance.
What do mathematics teachers and teacher trainees know about the history of mathematics?

NASA Astrophysics Data System (ADS)

Gazit, Avikam

2013-06-01

The aim of this study is to present the findings of a study that examined the knowledge of mathematics teachers and teacher trainees, in different tracks, about the concepts, topics and characters from the history of mathematics. The findings indicate a lack of knowledge concerning most of the topics examined. Only about 40% of the participants knew about the origin of our counting system and the only item that reached above 50% was the item relating to the man who edited the book which is the basis for the plane geometry - Euclid (about 83%). Another meaningful finding was that the group with the highest score was that of mathematics teacher trainees in the accelerated track - a unique training scheme for middle school teachers (65.7%). The group with the lowest score was that of the elementary school mathematics student teachers (19.3%). One obvious conclusion is that we need to strengthen the knowledge of the history of mathematics in teacher training and in-service teachers' advanced studies.
Translations on Eastern Europe Scientific Affairs No. 530

DTIC Science & Technology

1976-11-24

candidate of medical sciences, on the basis of his disserta- tion entitled "Glucose Metabolism and Insulin Uptake of Isolated Human Adi- pose Cells" 11...34; Istvan Fodor, candidate of geographical sciences, on the basis of his dis- sertation entitled "Climatological and Bioclimatological Features of the... Human Uterus" Tran Quy Tien, candidate of mathematical sciences, on the basis of his dis- sertation entitled "Investigations in the Field of Rees-Type
Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

PubMed

Muñoz-Tamayo, R; Puillet, L; Daniel, J B; Sauvant, D; Martin, O; Taghipoor, M; Blavy, P

2018-04-01

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.
The System of Coordinates as an Obstacle in Understanding the Concept of Dimension

ERIC Educational Resources Information Center

Skordoulis, Constantine; Vitsas, Theodore; Dafermos, Vassilis; Koleza, Eugenia

2009-01-01

The concept of dimension, one of the most fundamental ideas in mathematics, is firmly rooted in the basis of the school geometry in such a way that mathematics teachers rarely feel the need to mention anything about it. However, the concept of dimension is far from being fully understood by students, even at the college level. In this paper, we…
Guide to Mathematics Released Items: Understanding Scoring

ERIC Educational Resources Information Center

Partnership for Assessment of Readiness for College and Careers, 2017

2017-01-01

The Partnership for Assessment of Readiness for College and Careers (PARCC) mathematics items measure critical thinking, mathematical reasoning, and the ability to apply skills and knowledge to real-world problems. Students are asked to solve problems involving the key knowledge and skills for their grade level as identified by the Common Core…
Building Squares and Discovering Patterns

ERIC Educational Resources Information Center

Whitin, David J.; Whitin, Phyllis

2014-01-01

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) define what children should understand and be able to do in K-grade 12. This document also includes a description of key mathematical processes and proficiencies, the Standards for Mathematical Practice (SMPs), which provide an important overview for the kind of robust thinking…
Mathematical Analogs and the Teaching of Fractions.

ERIC Educational Resources Information Center

Charles, Kathy; Nason, Rod; Cooper, Tom

The literature has noted that some mathematical analogs are more effective than others for the teaching of fractions. This study aimed to evaluate the efficacy of seven mathematical analogs commonly used in the teaching of the partitive quotient fraction construct. A sample of twelve purposively selected Year Three children were presented with…
The WWW, Preservice Teachers and Their Mathematics Courses.

ERIC Educational Resources Information Center

Halpin, Pat; Kossegi, Joanne D.

The use of modern technologies has become common in mathematics education and is considered necessary for good mathematics instruction. To effectively integrate technology into the curriculum, teachers must learn new behaviors and practices and discover that the changes result in positive student outcomes. The inherent difficulties involved with…
Using Generic Examples to Make Viable Arguments

ERIC Educational Resources Information Center

Adams, Anne E.; Ely, Rob; Yopp, David

2017-01-01

The twenty-first century has seen an increased call to train students to craft mathematical arguments. The third of the Common Core's (CCSS) Standards for Mathematical Practice (SMP 3) (CCSSI 2010) calls for all mathematically proficient students to "construct viable arguments" to support the truth of their ideas and to "critique…
CCSSM: Teaching in Grades 3 and 4

ERIC Educational Resources Information Center

Barlow, Angela T.; Harmon, Shannon

2012-01-01

Common Core State Standards for Mathematics (CCSSM) is different from the objectives that many teachers have previously experienced in their state frameworks. Although the mathematical topics of the two may be the same, the mathematical expectations within the Standards require a deeper understanding by teachers and students. In this article, the…
Supporting Mathematical Discussions: The Roles of Comparison and Cognitive Load

ERIC Educational Resources Information Center

Richland, Lindsey E.; Begolli, Kreshnik Nasi; Simms, Nina; Frausel, Rebecca R.; Lyons, Emily A.

2016-01-01

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…
Supporting Mathematical Discussions: The Roles of Comparison and Cognitive Load

ERIC Educational Resources Information Center

Richland, Lindsey E.; Begolli, Kreshnik Nasi; Simms, Nina; Frausel, Rebecca R.; Lyons, Emily A.

2017-01-01

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…
Investigating Integer Restrictions in Linear Programming

ERIC Educational Resources Information Center

Edwards, Thomas G.; Chelst, Kenneth R.; Principato, Angela M.; Wilhelm, Thad L.

2015-01-01

Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…

MATHEMATICS CLUSTERS IN SELECTED AREAS OF VOCATIONAL EDUCATION, REPORT NUMBER 8.

ERIC Educational Resources Information Center

RAHMLOW, HAROLD F.; WINCHELL, LEONARD

IDENTIFICATIONS WERE MADE OF THE MATHEMATICAL KNOWLEDGES COMMONLY USED IN OCCUPATIONS MOST READILY SUITABLE FOR NONCOLLEGE-BOUND YOUTH. TASK ITEMS FROM QUESTIONNAIRES USED IN OFFICE OCCUPATIONS, GENERAL MERCHANDISING, BUILDING TRADES, ELECTRONICS, FOOD SERVICE, CHILD CARE, AND AGRICULTURE STUDIES WERE EXAMINED FOR MATHEMATICAL KNOWLEDGE CONTENT.…
Using Technology to Prompt Good Questions about Distributions in Statistics

ERIC Educational Resources Information Center

Nabbout-Cheiban, Marie; Fisher, Forest; Edwards, Michael Todd

2017-01-01

The Common Core State Standards for Mathematics envisions data analysis as a key component of K-grade 12 mathematics instruction with statistics introduced in the early grades. Nonetheless, deficiencies in statistical learning persist throughout elementary school and beyond. Too often, mathematics teachers lack the statistical knowledge for…
An Intelligent Tutor-Assisted Mathematics Intervention Program for Students with Learning Difficulties

ERIC Educational Resources Information Center

Xin, Yan Ping; Tzur, Ron; Hord, Casey; Liu, Jia; Park, Joo Young; Si, Luo

2017-01-01

The Common Core Mathematics Standards have raised expectations for schools and students in the United States. These standards demand much deeper content knowledge from teachers of mathematics and their students. Given the increasingly diverse student population in today's classrooms and shortage of qualified special education teachers,…
iSTEM: Learning Mathematics through Minecraft

ERIC Educational Resources Information Center

Bos, Beth; Wilder, Lucy; Cook, Marcelina; O'Donnell, Ryan

2014-01-01

The Common Core State Standards can be taught with Minecraft, an interactive creative Lego®-like game. Integrating Science, Technology, Engineering, and Mathematics (iSTEM) authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K-grade 6 classrooms.
Mathematical Working Spaces through Networking Lens

ERIC Educational Resources Information Center

Artigue, Michèle

2016-01-01

This issue of "ZDM" collects research works sharing a common reference to the theoretical framework of Mathematical Working Spaces (MWS), a construction which emerged about one decade ago, and has progressively found its way in the mathematics education community, thanks to the collaborative work of an international group of researchers.…
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2016-01-01

This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
The Representational Value of Hats

ERIC Educational Resources Information Center

Watson, Jane M.; Fitzallen, Noleine E.; Wilson, Karen G.; Creed, Julie F.

2008-01-01

The literature that is available on the topic of representations in mathematics is vast. One commonly discussed item is graphical representations. From the history of mathematics to modern uses of technology, a variety of graphical forms are available for middle school students to use to represent mathematical ideas. The ideas range from algebraic…
The Relation between Patterning, Executive Function, and Mathematics

ERIC Educational Resources Information Center

Schmerold, Katrina Lea

2015-01-01

Patterning, or the ability to understand patterns, is a skill commonly taught to young children as part of school mathematics curricula. While a number of studies have demonstrated that patterning is beneficial for young children acquiring mathematical skills, little research exists that examines the cognitive components of the skill. It seems…
Correlates of Academic Procrastination and Mathematics Achievement of University Undergraduate Students

ERIC Educational Resources Information Center

Akinsola, Mojeed Kolawole; Tella, Adedeji; Tella, Adeyinka

2007-01-01

Procrastination is now a common phenomenon among students, particularly those at the higher level. And this is doing more harm to their academic achievement than good. Therefore, this study examined the correlates between academic procrastination and mathematics achievement among the university mathematics undergraduate students. The study used a…
Science + Maths = A Better Understanding of Science!

ERIC Educational Resources Information Center

Markwick, Andy; Clark, Kris

2016-01-01

Science and mathematics share a common purpose: to explore, understand and explain the pure beauty of our universe and how it works. Using mathematics in science enquiry can enhance children's understanding of science and also provide opportunities for children to apply their mathematical knowledge to "real" contexts. The authors…
Mathematics and Martial Arts as Connected Art Forms

ERIC Educational Resources Information Center

Hekimoglu, Serkan

2010-01-01

Parallels between martial arts and mathematics are explored. Misguided public perception of both disciplines, students' misconceptions, and the similarities between proofs and katas are among the striking commonalities between martial arts and mathematics. The author also reflects on what he has learned in his martial arts training, and how this…
Mathematical Explorations: Freshwater Scarcity: A Proportional Representation

ERIC Educational Resources Information Center

King, Alessandra

2014-01-01

Middle school students' mathematical understanding benefits from connecting mathematics to other content areas in the curriculum. This month's activity explores the issue of the scarcity of freshwater, a natural resource (activity sheets are included). This activity concentrates on the critical areas mentioned in the Common Core State…
Everyday Pedagogical Practices in Mathematical Play Situations in German "Kindergarten"

ERIC Educational Resources Information Center

Brandt, Birgit

2013-01-01

This study describes situations in German daycare facilities (Kindergarten) in which the development of mathematical thinking in children is specifically encouraged through examination of common play objects. Using micro-sociological methods of analysis, the mathematical potential of such interactions between teacher and child is elaborated within…
78 FR 24393 - Agency Information Collection Activities; Comment Request; Promoting Student Success in Algebra I...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-04-25

... learning/ double-dose algebra can serve as possible avenues for improving student success in mathematics... needs in mathematics. This work will make an important contribution by producing actionable information... Common Core State Standards for Mathematics (CCSSM). The study centers around three major research...
The String Task: Not Just for High School

ERIC Educational Resources Information Center

Isler, Isil; Marum, Tim; Stephens, Ana; Blanton, Maria; Knuth, Eric; Gardiner, Angela Murphy

2014-01-01

The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, the…
Building a Discourse Community: Initial Practices

ERIC Educational Resources Information Center

Hodge, Lynn Liao; Walther, Ashley

2017-01-01

Although it is not a new idea, discourse continues to be a topic of discussion among teachers, teacher educators, and researchers in mathematics education. The National Council of Teachers (NCTM) and the Common Core State Standards for Mathematics (CCSSM 2010) describe mathematics classrooms as discourse communities in which whole-class…
Mathematical Communication in State Standards before the Common Core

ERIC Educational Resources Information Center

Kosko, Karl Wesley; Gao, Yang

2017-01-01

Mathematical communication has been an important feature of standards documents since National Council of Teachers of Mathematics' (NCTM) (1989) "Curriculum and Evaluation Standards." Such an emphasis has influenced content standards of states from then to present. This study examined how effective the prevalence of various forms of…
Attending to Precision with Secret Messages

ERIC Educational Resources Information Center

Starling, Courtney; Whitacre, Ian

2016-01-01

Mathematics is a language that is characterized by words and symbols that have precise definitions. Many opportunities exist for miscommunication in mathematics if the words and symbols are interpreted incorrectly or used in imprecise ways. In fact, it is found that imprecision is a common source of mathematical disagreements and misunderstandings…
Practise What You Preach: The Interactive Whiteboard in Preschool Mathematics Education

ERIC Educational Resources Information Center

Bourbour, Maryam; Masoumi, Davoud

2017-01-01

The Interactive Whiteboard (IWB) is now a common technological artefact in Swedish preschools and schools. This study examines preschool teachers' thinking behind the embedding of IWB in the early years' mathematics classroom and how preschool teachers structure their mathematical activities when using IWB. Two complementary empirical studies,…
Common Core State Standards for Mathematics: Love It or Hate It, Understand Those Who Don't

ERIC Educational Resources Information Center

Wagner, Patty Anne

2016-01-01

In this commentary, Wagner points out that the Common Core State Standards for Mathematics (CCSSM) has fueled strong reactions on either end of the spectrum, compelling its supporters and critics to argue their positions. Naturally neither side have interest in entertaining the arguments of the other. Wagner claims, however, that you develop the…

Gearing up to Teach the Common Core State Standards for Mathematics in Rural Northeast Region Schools. REL 2015-031

ERIC Educational Resources Information Center

Walters, Kirk; Torres, Aubrey Scheopner; Smith, Toni; Ford, Jennifer

2014-01-01

This study describes key challenges and necessary supports related to implementation of the Common Core State Standards for Mathematics (CCSSM) identified by rural math educators in the Northeast. The research team interviewed state and district math coordinators and surveyed teachers in Maine, New Hampshire, New York and Vermont, to assess their…
An Astronomical Problem in a Japanese Traditional Mathematical Text: The 49th Problem of the Kenki-sanpo of Takebe Katahiro

NASA Astrophysics Data System (ADS)

Ôhashi, Yukio

During the Edo period (Tokugawa-shogunate period) (1603-1867), there was a mathematical tradition now called "Wasan" which was primarily based on Chinese mathematics, but Japanese mathematicians also created new devices. It was quite popular, and common people could enjoy solving mathematical problems through Wasan regardless of their social status. Some astronomical problems were also treated there.
Utilising a construct of teacher capacity to examine national curriculum reform in mathematics

NASA Astrophysics Data System (ADS)

Zhang, Qinqiong; Stephens, Max

2013-12-01

This study involving 120 Australian and Chinese teachers introduces a construct of teacher capacity to analyse how teachers help students connect arithmetic learning and emerging algebraic thinking. Four criteria formed the basis of our construct of teacher capacity: knowledge of mathematics, interpretation of the intentions of official curriculum documents, understanding of students' thinking, and design of teaching. While these key elements connect to what other researchers refer to as mathematical knowledge for teaching, several differences are made clear. Qualitative and quantitative analyses show that our construct was robust and effective in distinguishing between different levels of teacher capacity.
Calculating the Weather: Deductive Reasoning and Disciplinary "Telos" in Cleveland Abbe's Rhetorical Transformation of Meteorology

ERIC Educational Resources Information Center

Majdik, Zoltan P.; Platt, Carrie Anne; Meister, Mark

2011-01-01

This paper explores the rhetorical basis of a major paradigm change in meteorology, from a focus on inductive observation to deductive, mathematical reasoning. Analysis of Cleveland Abbe's "The Physical Basis of Long-Range Weather Forecasts" demonstrates how in his advocacy for a new paradigm, Abbe navigates the tension between piety to tradition…
Activities for Students: Filling a Square with a Curve

ERIC Educational Resources Information Center

Martin, David R.

2014-01-01

Finding patterns and making conjectures are important thinking skills for students at all levels of mathematics education. Both the Common Core State Standards for Mathematics and the National Council of Teachers of Mathematics speak to the importance of these thought processes. NCTM suggests that students should be able to recognize reasoning and…
Rethinking Teacher Leader Development: A Study of Early Career Mathematics Teachers

ERIC Educational Resources Information Center

Huggins, Kristin Shawn; Lesseig, Kristin; Rhodes, Heidi

2017-01-01

In the era of standards-based reforms, informal teacher leadership is a critical factor in realizing instructional improvement. In this paper, we report on data from a one-year study of four early career mathematics teachers engaging in professional development around Common Core mathematical practices and leadership. Our findings highlight how…
Plotting Intersections along the Political Axis: The Interior Voice of Dissenting Mathematics Teachers

ERIC Educational Resources Information Center

de Freitas, Elizabeth

2004-01-01

The supposed apolitical nature of mathematics is an institutional frame that functions to sustain specific power structures within schools. This paper disrupts the common assumption that mathematics (as a body of knowledge constructed in situated historical moments) is free from entrenched ideological motives. Using narrative inquiry, the paper…
Assisting Pupils in Mathematics Achievement (The Common Core Standards)

ERIC Educational Resources Information Center

Ediger, Marlow

2011-01-01

Mathematics teachers must expect reasonably high standards of achievement from pupils. Too frequently, pupils attain at a substandard level and more optimal achievement is necessary. Thus, pupils should have self esteem needs met in the school and classroom setting. Thus, learners feel that mathematics is worthwhile and effort must be put forth to…
Identifying Mathematics Content and Integrating It into Science Instruction

ERIC Educational Resources Information Center

Schwols, Amitra; Miller, Kirsten Brush

2012-01-01

Science teachers know that the mathematics concepts taught in the Common Core are critical for students' understanding of science. But what can a teacher do when his/her students lack the necessary mathematics skills to master science content? There may be other reasons besides students not paying attention in their math courses. Maybe the…
Promoting the Understanding of Mathematics in Physics at Secondary Level

ERIC Educational Resources Information Center

Thompson, Alaric

2016-01-01

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…
Goldilocks Discourse--Math Scaffolding That's Just Right

ERIC Educational Resources Information Center

Dale, Rachel; Scherrer, Jimmy

2015-01-01

The Common Core has brought a sharp shift in what it means to be mathematically literate. Becoming mathematically literate is now as much a matter of acquiring mathematical practices as of acquiring any defined set of content standards. This more ambitious definition of literacy presents a challenge not only for students, but also for teachers who…
Mathematical Inqu[ee]ry: Beyond "Add-Queers-and-Stir" Elementary Mathematics Education

ERIC Educational Resources Information Center

Rands, Kathleen

2009-01-01

While elementary educators have developed queer pedagogies and perspectives in many subjects from reading to music, science to English as a second language, queer perspectives on elementary mathematics education are remarkably absent. This article differentiates between two common uses of the term "queer" and delineates two sets of approaches…
Documentation Issues for Mathematics in the Digital Age.

ERIC Educational Resources Information Center

Berard, Pierre

The welfare of mathematics, as a scientific discipline and as a service provider for other sciences and technology, will, in the future, very much depend on how well the profession continues to enrich, to preserve, and to archive the mathematical scholarly literature, its common heritage. It will also depend on the fact that the mathematical…
Playing with Mathematics: How Play Supports Learning and the Common Core State Standards

ERIC Educational Resources Information Center

Zosh, Jennifer Mary; Hassinger-Das, Brenna; Toub, Tamara Spiewak; Hirsh-Pasek, Kathy; Golinkof, Roberta

2016-01-01

International rankings show children in the United States perform well below average in mathematics. There are also large mathematics achievement gaps between children of lower- and higher-socioeconomic status. As today's teachers face these challenges, they are also faced with the pressures of sweeping educational reforms that arrived with the…
Oral Assessment in Mathematics: Implementation and Outcomes

ERIC Educational Resources Information Center

Iannone, P.; Simpson, A.

2012-01-01

In this article, we report the planning and implementation of an oral assessment component in a first-year pure mathematics module of a degree course in mathematics. Our aim was to examine potential barriers to using oral assessments, explore the advantages and disadvantages compared to existing common assessment methods and document the outcomes…
Encouraging Students to Read Mathematics

ERIC Educational Resources Information Center

Shepherd, Mary D.

2005-01-01

It is generally agreed that the ability to read mathematics is an important skill--one that few of our students possess. A number of people have published some suggestions for helping students learn to read their mathematics textbooks. What these have in common is suggestions for getting students more active while reading. Using these resources as…
A Framework for Authenticity in the Mathematics and Statistics Classroom

ERIC Educational Resources Information Center

Garrett, Lauretta; Huang, Li; Charleton, Maria Calhoun

2016-01-01

Authenticity is a term commonly used in reference to pedagogical and curricular qualities of mathematics teaching and learning, but its use lacks a coherent framework. The work of researchers in engineering education provides such a framework. Authentic qualities of mathematics teaching and learning are fit within a model described by Strobel,…
What Is "Repeated Reasoning" in MP 8?

ERIC Educational Resources Information Center

Goldenberg, E. Paul; Carter, Cynthia J.; Mark, June; Nikula, Johannah; Spencer, Deborah B.

2017-01-01

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…
Mathematics and Social Justice: A Symbiotic Pedagogy

ERIC Educational Resources Information Center

Bond, Gareth; Chernoff, Egan J.

2015-01-01

Mathematics can be defined as "the science of pattern and order" (Van de Walle, Folk, Karp, & Bay-Williams, 2009, p. 10). But because there is often a perceived spectrum of approachability to mathematics (based on common misconceptions that envision the subject as a sort of elitist wizardry) it is important to bear in mind different…
Good Questions: Great Ways to Differentiate Mathematics Instruction. Second Edition

ERIC Educational Resources Information Center

Small, Marian

2012-01-01

Expanded to include connections to Common Core State Standards, as well as National Council of Teachers of Mathematics (NCTM) standards, this critically acclaimed book will help every teacher and coach to meet the challenges of differentiating mathematics instruction in the K-8 classroom. In this bestseller, math education expert Marian Small…

Instructional Technologies and Pre-Service Mathematics Teachers' Selection of Technology

ERIC Educational Resources Information Center

Akcay, Ahmet Oguz

2017-01-01

There are many available technologies that can assist future teachers to deliver instruction. The purpose of this paper is to provide a brief review of literature identifying available technology tools in mathematics education and which technologies are selected by PSTs to design mathematics lesson activities. The most commonly used and available…
Order of Operations: The Myth and the Math

ERIC Educational Resources Information Center

Bay-Williams, Jennifer M.; Martinie, Sherri L.

2015-01-01

Many of us embrace the order and beauty in mathematics. The order of operations is an iconic mathematics topic that seems untouchable by time, reform, or mathematical discoveries. Yet, think for a moment about a commonly heard statement in teaching the order of operations: "You work from left to right." At another point in the…
Relating Aspects of Motivation to Facets of Mathematical Competence Varying in Cognitive Demand

ERIC Educational Resources Information Center

Gilbert, Melissa C.

2016-01-01

The author investigated the relationship between aspects of student motivation and performance on mathematical tasks varying in cognitive demand relevant to meeting the expectations of the Common Core State Standards for Mathematics (CCSS-M). A sample of 479 primarily Latino middle school students completed established survey measures of…
A Fruitful Activity for Finding the Greatest Common Factor

ERIC Educational Resources Information Center

Bell, Carol J.; Leisner, Heather J.; Shelley, Kristina

2011-01-01

Posing mathematics problems in different ways will raise students' level of cognitive demand because it will push them to think more deeply about mathematics. By engaging students in a task that requires them to determine their own solution strategies, students will gain a deeper understanding of the mathematical concept explored through the task.…
The Relationship between Elementary Teachers' Background in Mathematics, Teaching Self-Efficacy, and Teaching Outcome Expectancy When Implementing the Common Core State Standards

ERIC Educational Resources Information Center

Stuart, Jennifer Lynn

2017-01-01

The purpose of this correlation study was to identify a possible relationship between elementary teacher background in mathematics as measured by completed college math credit hours, district-provided professional development hours of training in Common Core math standards, and years of teaching experience, and teacher efficacy in math as measured…
Implementing the Common Core State Standards for Mathematics: A Comparison of Current District Content in 41 States. Working Paper #32

ERIC Educational Resources Information Center

Cogan, Leland; Schmidt, William; Houang, Richard

2013-01-01

Beginning in the spring of 2011 the Center for the Study of Curriculum at Michigan State University conducted a survey of school district curriculum directors/supervisors in the 41 states that had officially adopted the new Common Core State Standards for Mathematics (CCSSM). The Center's goal was to provide baseline information to inform and…
Gearing up to Teach the Common Core State Standards for Mathematics in the Rural Northeast Region. Stated Briefly. REL 2015-066

ERIC Educational Resources Information Center

Kirk, Walters; Smith, Toni M.; Ford, Jennifer; Scheopner Torres, Aubrey

2014-01-01

This study describes key challenges and necessary supports related to implementation of the Common Core State Standards for Mathematics (CCSSM) identified by rural math educators in the Northeast. The research team interviewed state and district math coordinators and surveyed teachers in Maine, New Hampshire, New York and Vermont, to assess their…
Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases

PubMed Central

Mossong, Joël; Hens, Niel; Jit, Mark; Beutels, Philippe; Auranen, Kari; Mikolajczyk, Rafael; Massari, Marco; Salmaso, Stefania; Tomba, Gianpaolo Scalia; Wallinga, Jacco; Heijne, Janneke; Sadkowska-Todys, Malgorzata; Rosinska, Magdalena; Edmunds, W. John

2008-01-01

Background Mathematical modelling of infectious diseases transmitted by the respiratory or close-contact route (e.g., pandemic influenza) is increasingly being used to determine the impact of possible interventions. Although mixing patterns are known to be crucial determinants for model outcome, researchers often rely on a priori contact assumptions with little or no empirical basis. We conducted a population-based prospective survey of mixing patterns in eight European countries using a common paper-diary methodology. Methods and Findings 7,290 participants recorded characteristics of 97,904 contacts with different individuals during one day, including age, sex, location, duration, frequency, and occurrence of physical contact. We found that mixing patterns and contact characteristics were remarkably similar across different European countries. Contact patterns were highly assortative with age: schoolchildren and young adults in particular tended to mix with people of the same age. Contacts lasting at least one hour or occurring on a daily basis mostly involved physical contact, while short duration and infrequent contacts tended to be nonphysical. Contacts at home, school, or leisure were more likely to be physical than contacts at the workplace or while travelling. Preliminary modelling indicates that 5- to 19-year-olds are expected to suffer the highest incidence during the initial epidemic phase of an emerging infection transmitted through social contacts measured here when the population is completely susceptible. Conclusions To our knowledge, our study provides the first large-scale quantitative approach to contact patterns relevant for infections transmitted by the respiratory or close-contact route, and the results should lead to improved parameterisation of mathematical models used to design control strategies. PMID:18366252
Expanding the "CBAL"™ Mathematics Assessments to Elementary Grades: The Development of a Competency Model and a Rational Number Learning Progression. Research Report. ETS RR-14-08

ERIC Educational Resources Information Center

Arieli-Attali, Meirav; Cayton-Hodges, Gabrielle

2014-01-01

Prior work on the "CBAL"™ mathematics competency model resulted in an initial competency model for middle school grades with several learning progressions (LPs) that elaborate central ideas in the competency model and provide a basis for connecting summative and formative assessment. In the current project, we created a competency model…
The NIE Conference on Basic Mathematical Skills and Learning (Euclid, Ohio, October 4-6, 1975). Volume II; Reports from the Working Groups.

ERIC Educational Resources Information Center

National Inst. of Education (DHEW), Washington, DC.

In October 1975 a conference was convened in Euclid, Ohio, by the Basic Skills group of the National Institute of Education (NIE). Position papers presented by the 33 participants and status reports from 11 agencies involved in mathematics education were received and analyzed. On the basis of this analysis, four topics were identified as issues…
Correlating subjective and objective descriptors of ultra high molecular weight wear particles from total joint prostheses.

PubMed

McMullin, Brian T; Leung, Ming-Ying; Shanbhag, Arun S; McNulty, Donald; Mabrey, Jay D; Agrawal, C Mauli

2006-02-01

A total of 750 images of individual ultra-high molecular weight polyethylene (UHMWPE) particles isolated from periprosthetic failed hip, knee, and shoulder arthroplasties were extracted from archival scanning electron micrographs. Particle size and morphology was subsequently analyzed using computerized image analysis software utilizing five descriptors found in ASTM F1877-98, a standard for quantitative description of wear debris. An online survey application was developed to display particle images, and allowed ten respondents to classify particle morphologies according to commonly used terminology as fibers, flakes, or granules. Particles were categorized based on a simple majority of responses. All descriptors were evaluated using a one-way ANOVA and Tukey-Kramer test for all-pairs comparison among each class of particles. A logistic regression model using half of the particles included in the survey was then used to develop a mathematical scheme to predict whether a given particle should be classified as a fiber, flake, or granule based on its quantitative measurements. The validity of the model was then assessed using the other half of the survey particles and compared with human responses. Comparison of the quantitative measurements of isolated particles showed that the morphologies of each particle type classified by respondents were statistically different from one another (p<0.05). The average agreement between mathematical prediction and human respondents was 83.5% (standard error 0.16%). These data suggest that computerized descriptors can be feasibly correlated with subjective terminology, thus providing a basis for a common vocabulary for particle description which can be translated into quantitative dimensions.
Correlating subjective and objective descriptors of ultra high molecular weight wear particles from total joint prostheses

PubMed Central

McMullin, Brian T.; Leung, Ming-Ying; Shanbhag, Arun S.; McNulty, Donald; Mabrey, Jay D.; Agrawal, C. Mauli

2014-01-01

A total of 750 images of individual ultra-high molecular weight polyethylene (UHMWPE) particles isolated from periprosthetic failed hip, knee, and shoulder arthroplasties were extracted from archival scanning electron micrographs. Particle size and morphology was subsequently analyzed using computerized image analysis software utilizing five descriptors found in ASTM F1877-98, a standard for quantitative description of wear debris. An online survey application was developed to display particle images, and allowed ten respondents to classify particle morphologies according to commonly used terminology as fibers, flakes, or granules. Particles were categorized based on a simple majority of responses. All descriptors were evaluated using a one-way ANOVA and Tukey–Kramer test for all-pairs comparison among each class of particles. A logistic regression model using half of the particles included in the survey was then used to develop a mathematical scheme to predict whether a given particle should be classified as a fiber, flake, or granule based on its quantitative measurements. The validity of the model was then assessed using the other half of the survey particles and compared with human responses. Comparison of the quantitative measurements of isolated particles showed that the morphologies of each particle type classified by respondents were statistically different from one another (po0:05). The average agreement between mathematical prediction and human respondents was 83.5% (standard error 0.16%). These data suggest that computerized descriptors can be feasibly correlated with subjective terminology, thus providing a basis for a common vocabulary for particle description which can be translated into quantitative dimensions. PMID:16112725
Development of the pump protection system against cavitation on the basis of the stator current signature analysis of drive electric motor

NASA Astrophysics Data System (ADS)

Kipervasser, M. V.; Gerasimuk, A. V.; Simakov, V. P.

2018-05-01

In the present paper a new registration method of such inadmissible phenomenon as cavitation in the operating mode of centrifugal pump is offered. Influence of cavitation and extent of its development on the value of mechanical power consumed by the pump from the electric motor is studied. On the basis of design formulas the joint mathematical model of centrifugal pumping unit with the synchronous motor is created. In the model the phenomena accompanying the work of a pumping installation in the cavitation mode are considered. Mathematical modeling of the pump operation in the considered emergency operation is carried out. The chart of stator current of the electric motor, depending on the degree of cavitation development of is received. On the basis of the analysis of the obtained data the conclusion on the possibility of registration of cavitation by the current of drive electric motor is made and the functional diagram of the developed protection system is offered, its operation principle is described.
Mathematical Models of the Common-Source and Common-Gate Amplifiers using a Metal-Ferroelectric-Semiconductor Field effect Transistor

NASA Technical Reports Server (NTRS)

Hunt, Mitchell; Sayyah, Rana; Mitchell, Cody; Laws, Crystal; MacLeod, Todd C.; Ho, Fat D.

2013-01-01

Mathematical models of the common-source and common-gate amplifiers using metal-ferroelectric- semiconductor field effect transistors (MOSFETs) are developed in this paper. The models are compared against data collected with MOSFETs of varying channel lengths and widths, and circuit parameters such as biasing conditions are varied as well. Considerations are made for the capacitance formed by the ferroelectric layer present between the gate and substrate of the transistors. Comparisons between the modeled and measured data are presented in depth as well as differences and advantages as compared to the performance of each circuit using a MOSFET.
Mathematical Basis and Test Cases for Colloid-Facilitated Radionuclide Transport Modeling in GDSA-PFLOTRAN

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

Reimus, Paul William

This report provides documentation of the mathematical basis for a colloid-facilitated radionuclide transport modeling capability that can be incorporated into GDSA-PFLOTRAN. It also provides numerous test cases against which the modeling capability can be benchmarked once the model is implemented numerically in GDSA-PFLOTRAN. The test cases were run using a 1-D numerical model developed by the author, and the inputs and outputs from the 1-D model are provided in an electronic spreadsheet supplement to this report so that all cases can be reproduced in GDSA-PFLOTRAN, and the outputs can be directly compared with the 1-D model. The cases include examplesmore » of all potential scenarios in which colloid-facilitated transport could result in the accelerated transport of a radionuclide relative to its transport in the absence of colloids. Although it cannot be claimed that all the model features that are described in the mathematical basis were rigorously exercised in the test cases, the goal was to test the features that matter the most for colloid-facilitated transport; i.e., slow desorption of radionuclides from colloids, slow filtration of colloids, and equilibrium radionuclide partitioning to colloids that is strongly favored over partitioning to immobile surfaces, resulting in a substantial fraction of radionuclide mass being associated with mobile colloids.« less
Exploring How Symptoms of Attention-Deficit/Hyperactivity Disorder Are Related to Reading and Mathematics Performance: General Genes, General Environments

PubMed Central

Hart, Sara A.; Petrill, Stephen A.; Willcutt, Erik; Thompson, Lee A.; Schatschneider, Christopher; Deater-Deckard, Kirby; Cutting, Laurie E.

2013-01-01

Children with attention-deficit/hyperactivity disorder (ADHD) tend to perform more poorly on tests of reading and mathematical performance than their typical peers. Quantitative genetic analyses allow for a better understanding of the etiology of ADHD and reading and mathematics outcomes, by examining their common and unique genetic and environmental influences. Analyses were conducted on a sample 271 pairs of 10-year-old monozygotic and dizygotic twins drawn from the Western Reserve Reading and Mathematics Project. In general, the results suggested that the associations among ADHD symptoms, reading outcomes, and math outcomes were influenced by both general genetic and general shared-environment factors. The analyses also suggested significant independent genetic effects for ADHD symptoms. The results imply that differing etiological factors underlie the relationships among ADHD and reading and mathematics performance. It appears that both genetic and common family or school environments link ADHD with academic performance. PMID:20966487
Silent method for mathematics instruction: An overview of teaching subsets

NASA Astrophysics Data System (ADS)

Sugiman, Apino, Ezi

2017-05-01

Generally, teachers use oral communication for teaching mathematics. Taking an opposite perspective, this paper describes how instructional practices for mathematics can be carried out namely a silent method. Silent method uses body language, written, and oral communication for classroom interaction. This research uses a design research approach consisting of four phases: preliminary, prototyping and developing the instruction, and assessment. There are four stages of silent method. The first stage is conditioning stage in which the teacher introduces the method and makes agreement about the `rule of the game'. It is followed by the second one, elaborating stage, where students guess and explore alternative answers. The third stage is developing mathematical thinking by structuring and symbolizing. Finally, the method is ended by reinforcing stage which aims at strengthening and reflecting student's understanding. In this paper, every stage is described on the basis of practical experiences in a real mathematics classroom setting.
Assessing Student Preparation through Placement Tests

NASA Astrophysics Data System (ADS)

McFate, Craig; Olmsted, John, III

1999-04-01

The chemistry department at California State University, Fullerton, uses a placement test of its own design to assess student readiness to enroll in General Chemistry. This test contains items designed to test cognitive skills more than factual knowledge. We have analyzed the ability of this test to predict student success (defined as passing the first-semester course with a C or better) using data for 845 students from four consecutive semesters. In common with other placement tests, we find a weak but statistically significant correlation between test performance and course grades. More meaningfully, there is a strong correlation (R2 = 0.82) between test score and course success, sufficient to use for counseling purposes. An item analysis was conducted to determine what types of questions provide the best predictability. Six questions from the full set of 25 were identified as strong predictors, on the basis of discrimination indices and coefficients of determination that were more than one standard deviation above the mean values for test items. These questions had little in common except for requiring multistep mathematical operations and formal reasoning.
Genetic models of homosexuality: generating testable predictions

PubMed Central

Gavrilets, Sergey; Rice, William R

2006-01-01

Homosexuality is a common occurrence in humans and other species, yet its genetic and evolutionary basis is poorly understood. Here, we formulate and study a series of simple mathematical models for the purpose of predicting empirical patterns that can be used to determine the form of selection that leads to polymorphism of genes influencing homosexuality. Specifically, we develop theory to make contrasting predictions about the genetic characteristics of genes influencing homosexuality including: (i) chromosomal location, (ii) dominance among segregating alleles and (iii) effect sizes that distinguish between the two major models for their polymorphism: the overdominance and sexual antagonism models. We conclude that the measurement of the genetic characteristics of quantitative trait loci (QTLs) found in genomic screens for genes influencing homosexuality can be highly informative in resolving the form of natural selection maintaining their polymorphism. PMID:17015344
Statistical Mechanics of Coherent Ising Machine — The Case of Ferromagnetic and Finite-Loading Hopfield Models —

NASA Astrophysics Data System (ADS)

Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa

2017-10-01

The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.

Vulnerability survival analysis: a novel approach to vulnerability management

NASA Astrophysics Data System (ADS)

Farris, Katheryn A.; Sullivan, John; Cybenko, George

2017-05-01

Computer security vulnerabilities span across large, enterprise networks and have to be mitigated by security engineers on a routine basis. Presently, security engineers will assess their "risk posture" through quantifying the number of vulnerabilities with a high Common Vulnerability Severity Score (CVSS). Yet, little to no attention is given to the length of time by which vulnerabilities persist and survive on the network. In this paper, we review a novel approach to quantifying the length of time a vulnerability persists on the network, its time-to-death, and predictors of lower vulnerability survival rates. Our contribution is unique in that we apply the cox proportional hazards regression model to real data from an operational IT environment. This paper provides a mathematical overview of the theory behind survival analysis methods, a description of our vulnerability data, and an interpretation of the results.
A Student-Led Feedback Protocol on Writing Assignments in a History of Mathematics Course

ERIC Educational Resources Information Center

White, Diana

2014-01-01

History of math courses are commonly offered in mathematics departments. Such courses naturally lend themselves to writing assignments, and a growing body of research supports writing as a means to learn mathematics. This article details two such assignments, providing an overview of the course in which they are situated, and a student-led…
First Year Pre-Service Teachers' Mathematical Content Knowledge: Methods of Solution for a Ratio Question

ERIC Educational Resources Information Center

Livy, Sharyn; Vale, Colleen

2011-01-01

In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…
Teachers' Implementation of Pre-Constructed Dynamic Geometry Tasks in Technology-Intensive Algebra 1 Classrooms

ERIC Educational Resources Information Center

Cayton, Charity Sue-Adams

2012-01-01

Technology use and a focus on 21st century skills, coupled with recent adoption of Common Core State Standards for Mathematics, marks a new challenge for mathematics teachers. Communication, discourse, and tools for enhancing discourse (NCTM, 1991, 2000) play an integral role in successful implementation of technology and mathematics standards.…
Teaching Mathematics to Secondary Students with Emotional and Behavioral Disorders: Challenges and Practical Suggestions for Teachers

ERIC Educational Resources Information Center

Mulcahy, Candace A.; Krezmien, Michael; Maccini, Paula

2014-01-01

While the Common Core State Standards and state learning standards guide teachers in what mathematical content knowledge should be addressed as well as the processes and proficiencies necessary for developing mathematical competence, several student- and teacher-related factors may hinder student access to the general education curriculum for…
Piloting a Co-Teaching Model for Mathematics Teacher Preparation: Learning to Teach Together

ERIC Educational Resources Information Center

Yopp, Ruth Helen; Ellis, Mark W.; Bonsangue, Martin V.; Duarte, Thomas; Meza, Susanna

2014-01-01

This study offers insights from an initial pilot of a co-teaching model for mathematics teacher preparation developed both to support experienced teachers in shifting their practice toward the vision set forth by NCTM and the Common Core State Standards for Mathematics (National Governors Association, 2010; NCTM, 2000, 2009) and to provide…
Does Knowing More Advanced Mathematics Ensure Effectiveness of Working towards Demonstrating Specialised Mathematical Content Knowledge of Second-Year Pre-Service Teachers?

ERIC Educational Resources Information Center

Livy, Sharyn

2012-01-01

The theoretical understanding that underpins a teacher's foundation knowledge draws on their common content knowledge (CCK) and influences their mathematics' teaching (Rowland, Turner, Thwaites, & Huckstep, 2009). Teachers who have specialised content knowledge (SCK) demonstrate a unique kind of content knowledge which is more than knowing the…
Myths and Motives behind STEM (Science, Technology, Engineering, and Mathematics) Education and the STEM-Worker Shortage Narrartive

ERIC Educational Resources Information Center

Stevenson, Heidi J.

2014-01-01

The Business Roundtable (2013) website presents a common narrative in regard to STEM (Science, Technology, Engineering and Mathematics) education, "American students are falling behind in math and science. Fewer and fewer students are pursuing careers in science, technology, engineering and mathematics, and American students are performing at…
Using Instructional Activities Game to Promote Mathematics: Teachers' Innovative Instruction

ERIC Educational Resources Information Center

Matsuda, Toshiki

2008-01-01

NIER (National Institute of Educational Research, 2004) survey revealed that the most common attitude of Japanese high school students to mathematics is that "it is not useful in daily life but must be learnt for entrance examinations". It was also clarified that only 3.2 percent of mathematics teachers use computers in their classes.…
Assessing Strengths and Weaknesses of Teacher Knowledge in Asia, Eastern Europe, and Western Countries: Differential Item Functioning in TEDS-M

ERIC Educational Resources Information Center

Blömeke, Sigrid; Suhl, Ute; Döhrmann, Martina

2013-01-01

The "Teacher Education and Development Study in Mathematics" assessed the knowledge of primary and lower-secondary teachers at the end of their training. The large-scale assessment represented the common denominator of what constitutes mathematics content knowledge and mathematics pedagogical content knowledge in the 16 participating…
The Development and Scaling of the easyCBM CCSS Middle School Mathematics Measures. Technical Report #1207

ERIC Educational Resources Information Center

Anderson, Daniel; Irvin, P. Shawn; Patarapichayatham, Chalie; Alonzo, Julie; Tindal, Gerald

2012-01-01

In the following technical report, we describe the development and scaling of the easyCBM CCSS middle school mathematics measures, designed for use within a response to intervention framework. All items were developed in collaboration with experienced middle school mathematics teachers and were written to align with the Common Core State…
Mathematical Self-Efficacy and Understanding: Using Geographic Information Systems to Mediate Urban High School Students' Real-World Problem Solving

ERIC Educational Resources Information Center

DeBay, Dennis J.

2013-01-01

To explore student mathematical self-efficacy and understanding of graphical data, this dissertation examines students solving real-world problems in their neighborhood, mediated by professional urban planning technologies. As states and schools are working on the alignment of the Common Core State Standards for Mathematics (CCSSM), traditional…
Getting from x to y without Crashing: Computer Syntax in Mathematics Education

ERIC Educational Resources Information Center

Jeffrey, David J.

2010-01-01

When we use technology to teach mathematics, we hope to focus on the mathematics, restricting the computer software systems to providing support for our pedagogy. It is a matter of common experience, however, that students can become distracted or frustrated by the quirks of the particular software system being used. Here, experience using the…
Closing the Gap between Formalism and Application--PBL and Mathematical Skills in Engineering

ERIC Educational Resources Information Center

Christensen, Ole Ravn

2008-01-01

A common problem in learning mathematics concerns the gap between, on the one hand, doing the formalisms and calculations of abstract mathematics and, on the other hand, applying these in a specific contextualized setting for example the engineering world. The skills acquired through problem-based learning (PBL), in the special model used at…
The Academic Procrastination in Junior High School Students' Mathematics Learning: A Qualitative Study

ERIC Educational Resources Information Center

Asri, Dahlia Novarianing; Setyosari, Punaji; Hitipeuw, Imanuel; Chusniyah, Tutut

2017-01-01

Among the main causes of low learning achievement in mathematics learning is a delayed behavior to do tasks, commonly called academic procrastination. The objectives of this research are to describe and to explain the causal factors and consequences of academic procrastination in learning mathematics for junior high school students. This research…
A Model for Minimizing Numeric Function Generator Complexity and Delay

DTIC Science & Technology

2007-12-01

allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods
Using Maxima in the Mathematics Classroom

ERIC Educational Resources Information Center

Fedriani, Eugenio M.; Moyano, Rafael

2011-01-01

Coming from the Macsyma system and adapted to the Common Lisp standard, Maxima can be regarded as a tool for a frequent use in the mathematics classroom. The main aim of this work is to show some possibilities of Maxima and its graphical interface through our experience as Mathematics teachers in Business degrees, although it can be easily spread…
Examinations in the Final Year of Transition to Mathematical Methods Computer Algebra System (CAS)

ERIC Educational Resources Information Center

Leigh-Lancaster, David; Les, Magdalena; Evans, Michael

2010-01-01

2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key…
Readin', Writin', an' 'Rithmetic: Literacy Strategies in High School Mathematics

ERIC Educational Resources Information Center

Principato, Angela M.

2017-01-01

Stagnant growth on national standardized tests in mathematics and reading and a focus on disciplinary literacy in the Common Core State Standards in ELA, history/social studies, science, and technical subjects has prompted a resurgence in utilizing literacy strategies in the content areas in high school. While literacy standards in mathematics are…
The Effectiveness of Professional Development Using a Checklist of Common Core State Standards for Mathematical Practice for Designing and Delivering Instruction on Algebra I Achievement

ERIC Educational Resources Information Center

Peretin, Janeen

2014-01-01

This study was designed to determine whether or not the use of focused professional development using a checklist based on the Common Core State Standards Mathematical Practices impacted students' math scores as measured by an assessment that requires the use of the practices. Additionally, the researcher sought to determine whether or not the use…

Mathematical Model Taking into Account Nonlocal Effects of Plasmonic Structures on the Basis of the Discrete Source Method

NASA Astrophysics Data System (ADS)

Eremin, Yu. A.; Sveshnikov, A. G.

2018-04-01

The discrete source method is used to develop and implement a mathematical model for solving the problem of scattering electromagnetic waves by a three-dimensional plasmonic scatterer with nonlocal effects taken into account. Numerical results are presented whereby the features of the scattering properties of plasmonic particles with allowance for nonlocal effects are demonstrated depending on the direction and polarization of the incident wave.
Mathematical modelling of bone adaptation of the metacarpal subchondral bone in racehorses.

PubMed

Hitchens, Peta L; Pivonka, Peter; Malekipour, Fatemeh; Whitton, R Chris

2018-06-01

In Thoroughbred racehorses, fractures of the distal limb are commonly catastrophic. Most of these fractures occur due to the accumulation of fatigue damage from repetitive loading, as evidenced by microdamage at the predilection sites for fracture. Adaptation of the bone in response to training loads is important for fatigue resistance. In order to better understand the mechanism of subchondral bone adaptation to its loading environment, we utilised a square root function defining the relationship between bone volume fraction [Formula: see text] and specific surface [Formula: see text] of the subchondral bone of the lateral condyles of the third metacarpal bone (MCIII) of the racehorse, and using this equation, developed a mathematical model of subchondral bone that adapts to loading conditions observed in vivo. The model is expressed as an ordinary differential equation incorporating a formation rate that is dependent on strain energy density. The loading conditions applied to a selected subchondral region, i.e. volume of interest, were estimated based on joint contact forces sustained by racehorses in training. For each of the initial conditions of [Formula: see text] we found no difference between subsequent homoeostatic [Formula: see text] at any given loading condition, but the time to reach equilibrium differed by initial [Formula: see text] and loading condition. We found that the observed values for [Formula: see text] from the mathematical model output were a good approximation to the existing data for racehorses in training or at rest. This model provides the basis for understanding the effect of changes to training strategies that may reduce the risk of racehorse injury.
Expert system development for commonality analysis in space programs

NASA Technical Reports Server (NTRS)

Yeager, Dorian P.

1987-01-01

This report is a combination of foundational mathematics and software design. A mathematical model of the Commonality Analysis problem was developed and some important properties discovered. The complexity of the problem is described herein and techniques, both deterministic and heuristic, for reducing that complexity are presented. Weaknesses are pointed out in the existing software (System Commonality Analysis Tool) and several improvements are recommended. It is recommended that: (1) an expert system for guiding the design of new databases be developed; (2) a distributed knowledge base be created and maintained for the purpose of encoding the commonality relationships between design items in commonality databases; (3) a software module be produced which automatically generates commonality alternative sets from commonality databases using the knowledge associated with those databases; and (4) a more complete commonality analysis module be written which is capable of generating any type of feasible solution.
Mathematical Model of Stress-Strain State of Curved Tube of Non-Circular Cross-Section with Account of Technological Wall Thickness Variation

NASA Astrophysics Data System (ADS)

Pirogov, S. P.; Ustinov, N. N.; Smolin, N. I.

2018-05-01

A mathematical model of the stress-strain state of a curved tube of a non-circular cross-section is presented, taking into account the technological wall thickness variation. On the basis of the semi-membrane shell theory, a system of linear differential equations describing the deformation of a tube under the effect of pressure is obtained. To solve the boundary value problem, the method of shooting is applied. The adequacy of the proposed mathematical model is verified by comparison with the experimental data and the results of the calculation of tubes by the energy method.
Physics and Mathematics as Interwoven Disciplines in Science Education

NASA Astrophysics Data System (ADS)

Galili, Igal

2018-03-01

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.
The equivalence of two phylogenetic biodiversity measures: the Shapley value and Fair Proportion index.

PubMed

Hartmann, Klaas

2013-11-01

Most biodiversity conservation programs are forced to prioritise species in order to allocate their funding. This paper contains a mathematical proof that provides biological support for one common approach based on phylogenetic indices. Phylogenetic trees describe the evolutionary relationships between a group of taxa. Two indices for computing the distinctiveness of each taxon in a phylogenetic tree are considered here-the Shapley value and the Fair Proportion index. These indices provide a measure of the importance of each taxon for overall biodiversity and have been used to prioritise taxa for conservation. The Shapley value is the biodiversity contribution a taxon is expected to make if all taxa are equally likely to become extinct. This interpretation makes it appealing to use the Shapley value in biodiversity conservation applications. The Fair Proportion index lacks a convenient interpretation, however it is significantly easier to calculate and understand. It has been empirically observed that there is a high correlation between the two indices. This paper shows the mathematical basis for this correlation and proves that as the number of taxa increases, the indices become equivalent. Consequently in biodiversity prioritisation the simpler Fair Proportion index can be used whilst retaining the appealing interpretation of the Shapley value.
Sparse approximation problem: how rapid simulated annealing succeeds and fails

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Kabashima, Yoshiyuki

2016-03-01

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an overcomplete basis is termed the sparse approximation. In this paper, we apply simulated annealing, a metaheuristic algorithm for general optimization problems, to sparse approximation in the situation where the given data have a planted sparse representation and noise is present. The result in the noiseless case shows that our simulated annealing works well in a reasonable parameter region: the planted solution is found fairly rapidly. This is true even in the case where a common relaxation of the sparse approximation problem, the G-relaxation, is ineffective. On the other hand, when the dimensionality of the data is close to the number of non-zero components, another metastable state emerges, and our algorithm fails to find the planted solution. This phenomenon is associated with a first-order phase transition. In the case of very strong noise, it is no longer meaningful to search for the planted solution. In this situation, our algorithm determines a solution with close-to-minimum distortion fairly quickly.
Hadamard multimode optical imaging transceiver

DOEpatents

Cooke, Bradly J; Guenther, David C; Tiee, Joe J; Kellum, Mervyn J; Olivas, Nicholas L; Weisse-Bernstein, Nina R; Judd, Stephen L; Braun, Thomas R

2012-10-30

Disclosed is a method and system for simultaneously acquiring and producing results for multiple image modes using a common sensor without optical filtering, scanning, or other moving parts. The system and method utilize the Walsh-Hadamard correlation detection process (e.g., functions/matrix) to provide an all-binary structure that permits seamless bridging between analog and digital domains. An embodiment may capture an incoming optical signal at an optical aperture, convert the optical signal to an electrical signal, pass the electrical signal through a Low-Noise Amplifier (LNA) to create an LNA signal, pass the LNA signal through one or more correlators where each correlator has a corresponding Walsh-Hadamard (WH) binary basis function, calculate a correlation output coefficient for each correlator as a function of the corresponding WH binary basis function in accordance with Walsh-Hadamard mathematical principles, digitize each of the correlation output coefficient by passing each correlation output coefficient through an Analog-to-Digital Converter (ADC), and performing image mode processing on the digitized correlation output coefficients as desired to produce one or more image modes. Some, but not all, potential image modes include: multi-channel access, temporal, range, three-dimensional, and synthetic aperture.
Are relationships between pollen-ovule ratio and pollen and seed size explained by sex allocation?

PubMed

Burd, Martin

2011-10-01

Positive correlations between pollen-ovule ratio and seed size, and negative correlations between pollen-ovule ratio and pollen grain size have been noted frequently in a wide variety of angiosperm taxa. These relationships are commonly explained as a consequence of sex allocation on the basis of a simple model proposed by Charnov. Indeed, the theoretical expectation from the model has been the basis for interest in the empirical pattern. However, the predicted relationship is a necessary consequence of the mathematics of the model, which therefore has little explanatory power, even though its predictions are consistent with empirical results. The evolution of pollen-ovule ratios is likely to depend on selective factors affecting mating system, pollen presentation and dispensing, patterns of pollen receipt, pollen tube competition, female mate choice through embryo abortion, as well as genetic covariances among pollen, ovule, and seed size and other reproductive traits. To the extent the empirical correlations involving pollen-ovule ratios are interesting, they will need explanation in terms of a suite of selective factors. They are not explained simply by sex allocation trade-offs. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.
An Investigation of the Effect of Interventions Based on Common Core Mathematical Practices on the Math Achievement of Struggling Students in Grade 6

ERIC Educational Resources Information Center

Murthy, Geetha J.

2016-01-01

This study examined the effect of the eight Common Core mathematical practices on math achievement and math attitudes for a sample of low-performing students in Grade 6. The treatment sample (n = 63) consisted of four classes of Grade 6 students who had scored below proficient levels in state math assessments. This study was conducted in a…
Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

ERIC Educational Resources Information Center

Ozdemir, Burhanettin

2017-01-01

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…
A Snapshot of the Role of the Textbook in English Secondary Mathematics Classrooms

ERIC Educational Resources Information Center

O'Keeffe, Lisa; White, Bruce

2017-01-01

The role and function of the mathematics textbook has been widely discussed since its inclusion in the Trends in International Mathematics and Science study (TIMSS) in the late nineties. It is a common feature in many classrooms worldwide and has been identified as an important vehicle for the promotion of curricula. However, there has also been…
The Effects of Project-Based Learning Activities on Academic Achievement and Motivation in Mathematics in Eighth-Grade Students

ERIC Educational Resources Information Center

Mudrich, Rachel Marie

2017-01-01

The purpose of this research study was to determine if project-based learning activities (PBLA) incorporated into an eighth-grade mathematics classroom have an effect on students' academic achievement and motivation toward learning. The control group used the traditional instruction method to cover mathematic objective skills that are Common Core…
No Common Denominator: The Preparation of Elementary Teachers in Mathematics by America's Education Schools

ERIC Educational Resources Information Center

Greenberg, Julie; Walsh, Kate

2008-01-01

The nation's higher goals for student learning in mathematics cannot be reached without improved teacher capacity. To accomplish these goals an analysis of current teacher preparation in mathematics is necessary, along with the development of an agenda for improvement. Based on groundwork laid during a meeting in Washington, D.C. in March 2007,…
Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete-Representational-Abstract Sequence and Schema-Based Instruction

ERIC Educational Resources Information Center

Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.

2016-01-01

Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…
Generating a Networked Improvement Community to Improve Secondary Mathematics Teacher Preparation: Network Leadership, Organization, and Operation

ERIC Educational Resources Information Center

Martin, W. Gary; Gobstein, Howard

2015-01-01

The Mathematics Teacher Education Partnership (MTE-Partnership) was formed to address the undersupply of new secondary mathematics teachers who are well prepared to help their students attain the goals of the Common Core State Standards and other college- and career-ready standards. This national consortium of more than 90 universities and 100…
An Examination of the Potential of Secondary Mathematics Curriculum Materials to Support Teacher and Student Learning of Probabiility and Statistics

ERIC Educational Resources Information Center

Williams, Joshua E.

2016-01-01

The Common Core State Standards for Mathematics (CCSSSM) suggest many changes to secondary mathematics education including an increased focus on conceptual understanding and the inclusion of content and processes that are beyond what is currently taught to most high school students. To facilitate these changes, students will need opportunities to…
A Framework for Mathematics Graphical Tasks: The Influence of the Graphic Element on Student Sense Making

ERIC Educational Resources Information Center

Lowrie, Tom; Diezmann, Carmel M.; Logan, Tracy

2012-01-01

Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students' mathematics understandings. Through an iterative design, the investigation described the sense making of 11-12-year-olds as they…
The Effect of Teacher and Student Characteristics on TIMSS 2011 Mathematics Achievement of Fourth- and Eighth-Grade Students in Turkey

ERIC Educational Resources Information Center

Yalcin, Seher; Demirtasli, Rahime Nükhet; Dibek, Munevver Ilgun; Yavuz, Hatice Cigdem

2017-01-01

This study investigated effect of student- and school-level variables on mathematics achievement of fourth- and eighth-grade students using the Trends in International Mathematics and Science Study (TIMSS) 2011 data of Turkey. The common variables addressed in student and school questionnaires were compared. Due to nested structure of the TIMSS…
Conceptual or procedural mathematics for engineering students at University of Samudra

NASA Astrophysics Data System (ADS)

Saiman; Wahyuningsih, Puji; Hamdani

2017-06-01

This study we investigate whether the emphasis in mathematics courses for engineering students would benefit from being more conceptually oriented than more procedurally oriented way of teaching. In this paper, we report in some detail from twenty-five engineering students comes from three departements ; mechanical engineering, civil engineering and industrial engineering. The aim was to explore different kinds of arguments regarding the role of mathematics in engineering courses, as well as some common across contexts. The result of interview showed that most of engineering students feel that conceptual mathematics is more important than procedural mathematics for their job the future.

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.
Radar Polarimetry: Theory, Analysis, and Applications

NASA Astrophysics Data System (ADS)

Hubbert, John Clark

The fields of radar polarimetry and optical polarimetry are compared. The mathematics of optic polarimetry are formulated such that a local right handed coordinate system is always used to describe the polarization states. This is not done in radar polarimetry. Radar optimum polarization theory is redeveloped within the framework of optical polarimetry. The radar optimum polarizations and optic eigenvalues of common scatterers are compared. In addition a novel definition of an eigenpolarization state is given and the accompanying mathematics is developed. The polarization response calculated using optic, radar and novel definitions is presented for a variety of scatterers. Polarimetric transformation provides a means to characterize scatters in more than one polarization basis. Polarimetric transformation for an ensemble of scatters is obtained via two methods: (1) the covariance method and (2) the instantaneous scattering matrix (ISM) method. The covariance method is used to relate the mean radar parameters of a +/-45^circ linear polarization basis to those of a horizontal and vertical polarization basis. In contrast the ISM method transforms the individual time samples. Algorithms are developed for transforming the time series from fully polarimetric radars that switch between orthogonal states. The transformed time series are then used to calculate the mean radar parameters of interest. It is also shown that propagation effects do not need to be removed from the ISM's before transformation. The techniques are demonstrated using data collected by POLDIRAD, the German Aerospace Research Establishment's fully polarimetric C-band radar. The differential phase observed between two copolar states, Psi_{CO}, is composed of two phases: (1) differential propagation phase, phi_{DP}, and (2) differential backscatter phase, delta. The slope of phi_{DP } with range is an estimate of the specific differential phase, K_{DP}. The process of estimating K_{DP} is complicated when delta is present. Algorithms are presented for estimating delta and K_{DP} from range profiles of Psi_ {CO}. Also discussed are procedures for the estimation and interpretation of other radar measurables such as reflectivity, Z_{HH}, differential reflectivity, Z_{DR }, the magnitude of the copolar correlation coefficient, rho_{HV}(0), and Doppler spectrum width, sigma _{v}. The techniques are again illustrated with data collected by POLDIRAD.
Instrument Landing System scattering

DOT National Transportation Integrated Search

1972-12-01

The construction of a mathematical model of the Instrument Landing System (ILS) multipath problem has been undertaken. This report presents the theoretical basis for such a model, and newly achieved developments in ILS model construction.
State and trait effects on individual differences in children's mathematical development.

PubMed

Bailey, Drew H; Watts, Tyler W; Littlefield, Andrew K; Geary, David C

2014-11-01

Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. © The Author(s) 2014.
State and Trait Effects on Individual Differences in Children's Mathematical Development

PubMed Central

Bailey, Drew H.; Watts, Tyler W.; Littlefield, Andrew K.; Geary, David C.

2015-01-01

Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. PMID:25231900
Formal and physical equivalence in two cases in contemporary quantum physics

NASA Astrophysics Data System (ADS)

Fraser, Doreen

2017-08-01

The application of analytic continuation in quantum field theory (QFT) is juxtaposed to T-duality and mirror symmetry in string theory. Analytic continuation-a mathematical transformation that takes the time variable t to negative imaginary time-it-was initially used as a mathematical technique for solving perturbative Feynman diagrams, and was subsequently the basis for the Euclidean approaches within mainstream QFT (e.g., Wilsonian renormalization group methods, lattice gauge theories) and the Euclidean field theory program for rigorously constructing non-perturbative models of interacting QFTs. A crucial difference between theories related by duality transformations and those related by analytic continuation is that the former are judged to be physically equivalent while the latter are regarded as physically inequivalent. There are other similarities between the two cases that make comparing and contrasting them a useful exercise for clarifying the type of argument that is needed to support the conclusion that dual theories are physically equivalent. In particular, T-duality and analytic continuation in QFT share the criterion for predictive equivalence that two theories agree on the complete set of expectation values and the mass spectra and the criterion for formal equivalence that there is a "translation manual" between the physically significant algebras of observables and sets of states in the two theories. The analytic continuation case study illustrates how predictive and formal equivalence are compatible with physical inequivalence, but not in the manner of standard underdetermination cases. Arguments for the physical equivalence of dual theories must cite considerations beyond predictive and formal equivalence. The analytic continuation case study is an instance of the strategy of developing a physical theory by extending the formal or mathematical equivalence with another physical theory as far as possible. That this strategy has resulted in developments in pure mathematics as well as theoretical physics is another feature that this case study has in common with dualities in string theory.
Differentiable representations of finite dimensional Lie groups in rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Wickramasekara, Sujeewa

The inceptive motivation for introducing rigged Hilbert spaces (RHS) in quantum physics in the mid 1960's was to provide the already well established Dirac formalism with a proper mathematical context. It has since become clear, however, that this mathematical framework is lissome enough to accommodate a class of solutions to the dynamical equations of quantum physics that includes some which are not possible in the normative Hilbert space theory. Among the additional solutions, in particular, are those which describe aspects of scattering and decay phenomena that have eluded the orthodox quantum physics. In this light, the RHS formulation seems to provide a mathematical rubric under which various phenomenological observations and calculational techniques, commonly known in the study of resonance scattering and decay as ``effective theories'' (e.g., the Wigner- Weisskopf method), receive a unified theoretical foundation. These observations lead to the inference that a theory founded upon the RHS mathematics may prove to be of better utility and value in understanding quantum physical phenomena. This dissertation primarily aims to contribute to the general formalism of the RHS theory of quantum mechanics by undertaking a study of differentiable representations of finite dimensional Lie groups. In particular, it is shown that a finite dimensional operator Lie algebra G in a rigged Hilbert space can be always integrated, provided one parameter integrability holds true for the elements of any basis for G . This result differs from and extends the well known integration theorem of E. Nelson and the subsequent works of others on unitary representations in that it does not require any assumptions on the existence of analytic vectors. Also presented here is a construction of a particular rigged Hilbert space of Hardy class functions that appears useful in formulating a relativistic version of the RHS theory of resonances and decay. As a contexture for the construction, a synopsis of the new relativistic theory is presented.
Distinct and Overlapping Brain Areas Engaged during Value-Based, Mathematical, and Emotional Decision Processing

PubMed Central

Hsu, Chun-Wei; Goh, Joshua O. S.

2016-01-01

When comparing between the values of different choices, human beings can rely on either more cognitive processes, such as using mathematical computation, or more affective processes, such as using emotion. However, the neural correlates of how these two types of processes operate during value-based decision-making remain unclear. In this study, we investigated the extent to which neural regions engaged during value-based decision-making overlap with those engaged during mathematical and emotional processing in a within-subject manner. In a functional magnetic resonance imaging experiment, participants viewed stimuli that always consisted of numbers and emotional faces that depicted two choices. Across tasks, participants decided between the two choices based on the expected value of the numbers, a mathematical result of the numbers, or the emotional face stimuli. We found that all three tasks commonly involved various cortical areas including frontal, parietal, motor, somatosensory, and visual regions. Critically, the mathematical task shared common areas with the value but not emotion task in bilateral striatum. Although the emotion task overlapped with the value task in parietal, motor, and sensory areas, the mathematical task also evoked responses in other areas within these same cortical structures. Minimal areas were uniquely engaged for the value task apart from the other two tasks. The emotion task elicited a more expansive area of neural activity whereas value and mathematical task responses were in more focal regions. Whole-brain spatial correlation analysis showed that valuative processing engaged functional brain responses more similarly to mathematical processing than emotional processing. While decisions on expected value entail both mathematical and emotional processing regions, mathematical processes have a more prominent contribution particularly in subcortical processes. PMID:27375466
Distinct and Overlapping Brain Areas Engaged during Value-Based, Mathematical, and Emotional Decision Processing.

PubMed

Hsu, Chun-Wei; Goh, Joshua O S

2016-01-01

When comparing between the values of different choices, human beings can rely on either more cognitive processes, such as using mathematical computation, or more affective processes, such as using emotion. However, the neural correlates of how these two types of processes operate during value-based decision-making remain unclear. In this study, we investigated the extent to which neural regions engaged during value-based decision-making overlap with those engaged during mathematical and emotional processing in a within-subject manner. In a functional magnetic resonance imaging experiment, participants viewed stimuli that always consisted of numbers and emotional faces that depicted two choices. Across tasks, participants decided between the two choices based on the expected value of the numbers, a mathematical result of the numbers, or the emotional face stimuli. We found that all three tasks commonly involved various cortical areas including frontal, parietal, motor, somatosensory, and visual regions. Critically, the mathematical task shared common areas with the value but not emotion task in bilateral striatum. Although the emotion task overlapped with the value task in parietal, motor, and sensory areas, the mathematical task also evoked responses in other areas within these same cortical structures. Minimal areas were uniquely engaged for the value task apart from the other two tasks. The emotion task elicited a more expansive area of neural activity whereas value and mathematical task responses were in more focal regions. Whole-brain spatial correlation analysis showed that valuative processing engaged functional brain responses more similarly to mathematical processing than emotional processing. While decisions on expected value entail both mathematical and emotional processing regions, mathematical processes have a more prominent contribution particularly in subcortical processes.
The Implementation and Effects of the Mathematics Design Collaborative (MDC): Early Findings from Kentucky Ninth-Grade Algebra 1 Courses. CRESST Report 845

ERIC Educational Resources Information Center

Herman, Joan L.; Matrundola, Deborah La Torre; Epstein, Scott; Leon, Seth; Dai, Yunyun; Reber, Sarah; Choi, Kilchan

2015-01-01

With support from the Bill and Melinda Gates Foundation, researchers and experts in mathematics education developed the Mathematics Design Collaborative (MDC) as a strategy to support the transition to Common Core State Standards in math. MDC provides short formative assessment lessons known as Classroom Challenges for use in middle and high…
Cultivating Parabolas in the Parlor Garden: Reconciling Mathematics Education and Feminine Ideals in Nineteenth-Century America

ERIC Educational Resources Information Center

Fiss, Andrew

2014-01-01

This article introduces the justification problem for mathematics, which it explores through the case study of 1820s-1840s rationales for the teaching of mathematics to women in the United States. It argues that, while educators in the 1820s justified women's studies through mental discipline (a common reason for men's study), those of…
Mathematics Through Science, Part II: Graphing, Equations and Linear Functions. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Bolduc, Elroy J., Jr.; And Others

The purpose of this text is to teach learning and understanding of mathematics at grades seven through nine through the use of science experiments. Previous knowledge of science on the part of students or teachers is not necessary. The text is designed to be usable with any mathematics textbook in common use. The material can be covered in four…
Geometric Theory of Reduction of Nonlinear Control Systems

NASA Astrophysics Data System (ADS)

Elkin, V. I.

2018-02-01

The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).
Removing Fluoride Ions with Continously Fed Activated Alumina.

ERIC Educational Resources Information Center

Wu, Yeun C.; Itemaking, Isara Cholapranee

1979-01-01

Discussed is the mathematical basis for determining fluoride removal during water treatment with activated alumina. The study indicates that decreasing particle size decreases the pore diffusion effect and increases fluoride removal. (AS)
Annette Bunge: developing the principles in percutaneous absorption using chemical engineering principles.

PubMed

Stinchcomb, A L

2013-01-01

Annette Bunge and her research group have had the central theme of mathematically modeling the dermal absorption process. Most of the research focus has been on estimating dermal absorption for the purpose of risk assessment, for exposure scenarios in the environment and in the occupational setting. Her work is the basis for the United States Environmental Protection Agency's estimations for dermal absorption from contaminated water. It is also the basis of the dermal absorption estimates used in determining if chemicals should be assigned a 'skin notation' for potential systemic toxicity following occupational skin exposure. The work is truly translational in that it started with mathematical theory, is validated with preclinical and human experiments, and then is used in guidelines to protect human health. Her valued research has also extended into the topical drug bioavailability and bioequivalence assessment field.
Cognitive and Neural Correlates of Mathematical Giftedness in Adults and Children: A Review

PubMed Central

Myers, Timothy; Carey, Emma; Szűcs, Dénes

2017-01-01

Most mathematical cognition research has focused on understanding normal adult function and child development as well as mildly and moderately impaired mathematical skill, often labeled developmental dyscalculia and/or mathematical learning disability. In contrast, much less research is available on cognitive and neural correlates of gifted/excellent mathematical knowledge in adults and children. In order to facilitate further inquiry into this area, here we review 40 available studies, which examine the cognitive and neural basis of gifted mathematics. Studies associated a large number of cognitive factors with gifted mathematics, with spatial processing and working memory being the most frequently identified contributors. However, the current literature suffers from low statistical power, which most probably contributes to variability across findings. Other major shortcomings include failing to establish domain and stimulus specificity of findings, suggesting causation without sufficient evidence and the frequent use of invalid backward inference in neuro-imaging studies. Future studies must increase statistical power and neuro-imaging studies must rely on supporting behavioral data when interpreting findings. Studies should investigate the factors shown to correlate with math giftedness in a more specific manner and determine exactly how individual factors may contribute to gifted math ability. PMID:29118725
Judging complex movement performances for excellence: a principal components analysis-based technique applied to competitive diving.

PubMed

Young, Cole; Reinkensmeyer, David J

2014-08-01

Athletes rely on subjective assessment of complex movements from coaches and judges to improve their motor skills. In some sports, such as diving, snowboard half pipe, gymnastics, and figure skating, subjective scoring forms the basis for competition. It is currently unclear whether this scoring process can be mathematically modeled; doing so could provide insight into what motor skill is. Principal components analysis has been proposed as a motion analysis method for identifying fundamental units of coordination. We used PCA to analyze movement quality of dives taken from USA Diving's 2009 World Team Selection Camp, first identifying eigenpostures associated with dives, and then using the eigenpostures and their temporal weighting coefficients, as well as elements commonly assumed to affect scoring - gross body path, splash area, and board tip motion - to identify eigendives. Within this eigendive space we predicted actual judges' scores using linear regression. This technique rated dives with accuracy comparable to the human judges. The temporal weighting of the eigenpostures, body center path, splash area, and board tip motion affected the score, but not the eigenpostures themselves. These results illustrate that (1) subjective scoring in a competitive diving event can be mathematically modeled; (2) the elements commonly assumed to affect dive scoring actually do affect scoring (3) skill in elite diving is more associated with the gross body path and the effect of the movement on the board and water than the units of coordination that PCA extracts, which might reflect the high level of technique these divers had achieved. We also illustrate how eigendives can be used to produce dive animations that an observer can distort continuously from poor to excellent, which is a novel approach to performance visualization. Copyright © 2014 Elsevier B.V. All rights reserved.
Simulation of Solar Energy Use in Livelihood of Buildings

NASA Astrophysics Data System (ADS)

Lvocich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2017-11-01

Solar energy can be considered as the most technological and economical type of renewable energy. The purpose of the paper is to increase the efficiency of solar energy utilization on the basis of the mathematical simulation of the solar collector. A mathematical model of the radiant heat transfer vacuum solar collector is clarified. The model was based on the process of radiative heat transfer between glass and copper walls with the defined blackness degrees. A mathematical model of the ether phase transition point is developed. The dependence of the reservoir walls temperature change on the ambient temperature over time is obtained. The results of the paper can be useful for the development of prospective sources using solar energy.
Mathematical model of the glucose-insulin regulatory system: From the bursting electrical activity in pancreatic β-cells to the glucose dynamics in the whole body

NASA Astrophysics Data System (ADS)

Han, Kyungreem; Kang, Hyuk; Choi, M. Y.; Kim, Jinwoong; Lee, Myung-Shik

2012-10-01

A theoretical approach to the glucose-insulin regulatory system is presented. By means of integrated mathematical modeling and extensive numerical simulations, we probe the cell-level dynamics of the membrane potential, intracellular Ca2+ concentration, and insulin secretion in pancreatic β-cells, together with the whole-body level glucose-insulin dynamics in the liver, brain, muscle, and adipose tissues. In particular, the three oscillatory modes of insulin secretion are reproduced successfully. Such comprehensive mathematical modeling may provide a theoretical basis for the simultaneous assessment of the β-cell function and insulin resistance in clinical examination.
Cognitive tutor: applied research in mathematics education.

PubMed

Ritter, Steven; Anderson, John R; Koedinger, Kenneth R; Corbett, Albert

2007-04-01

For 25 years, we have been working to build cognitive models of mathematics, which have become a basis for middle- and high-school curricula. We discuss the theoretical background of this approach and evidence that the resulting curricula are more effective than other approaches to instruction. We also discuss how embedding a well specified theory in our instructional software allows us to dynamically evaluate the effectiveness of our instruction at a more detailed level than was previously possible. The current widespread use of the software is allowing us to test hypotheses across large numbers of students. We believe that this will lead to new approaches both to understanding mathematical cognition and to improving instruction.

Basic statistics (the fundamental concepts).

PubMed

Lim, Eric

2014-12-01

An appreciation and understanding of statistics is import to all practising clinicians, not simply researchers. This is because mathematics is the fundamental basis to which we base clinical decisions, usually with reference to the benefit in relation to risk. Unless a clinician has a basic understanding of statistics, he or she will never be in a position to question healthcare management decisions that have been handed down from generation to generation, will not be able to conduct research effectively nor evaluate the validity of published evidence (usually making an assumption that most published work is either all good or all bad). This article provides a brief introduction to basic statistical methods and illustrates its use in common clinical scenarios. In addition, pitfalls of incorrect usage have been highlighted. However, it is not meant to be a substitute for formal training or consultation with a qualified and experienced medical statistician prior to starting any research project.
The Common Evolution of Geometry and Architecture from a Geodetic Point of View

NASA Astrophysics Data System (ADS)

Bellone, T.; Fiermonte, F.; Mussio, L.

2017-05-01

Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are aesthetically appropriate. Sometimes it is geometry which drives architectural choices, but at other times it is architectural innovation which facilitates the emergence of new ideas in geometry. Among the best known types of geometry (Euclidean, projective, analytical, Topology, descriptive, fractal,…) those most frequently employed in architectural design are: - Euclidean Geometry - Projective Geometry - The non-Euclidean geometries. Entire architectural periods are linked to specific types of geometry. Euclidean geometry, for example, was the basis for architectural styles from Antiquity through to the Romanesque period. Perspective and Projective geometry, for their part, were important from the Gothic period through the Renaissance and into the Baroque and Neo-classical eras, while non-Euclidean geometries characterize modern architecture.
Mathematics, structuralism and biology.

PubMed

Saunders, P T

1988-01-01

A new approach is gaining ground in biology, one that has much in common with the structuralist tradition in other fields. It is very much in the spirit of an earlier view of biology and indeed of science in general. It is also, though this is not generally recognized, in the spirit of twentieth century physics. As in modern physics, however, it is not a question of ignoring all the progress that has been made within the former paradigm. On the contrary, the aim is to use it as a basis for setting out in a somewhat different direction. Complex phenomena do not generally lend themselves to reductionist analyses which seek explanation only in terms of detailed mechanisms, but a proper scientific discussion of structure must make full use of what we have already learned - by whatever means - about the processes that underly the phenomena we are trying to understand.
Estimation of maximum transdermal flux of nonionized xenobiotics from basic physicochemical determinants

PubMed Central

Milewski, Mikolaj; Stinchcomb, Audra L.

2012-01-01

An ability to estimate the maximum flux of a xenobiotic across skin is desirable both from the perspective of drug delivery and toxicology. While there is an abundance of mathematical models describing the estimation of drug permeability coefficients, there are relatively few that focus on the maximum flux. This article reports and evaluates a simple and easy-to-use predictive model for the estimation of maximum transdermal flux of xenobiotics based on three common molecular descriptors: logarithm of octanol-water partition coefficient, molecular weight and melting point. The use of all three can be justified on the theoretical basis of their influence on the solute aqueous solubility and the partitioning into the stratum corneum lipid domain. The model explains 81% of the variability in the permeation dataset comprised of 208 entries and can be used to obtain a quick estimate of maximum transdermal flux when experimental data is not readily available. PMID:22702370
Assimilating data into open ocean tidal models

NASA Astrophysics Data System (ADS)

Kivman, Gennady A.

The problem of deriving tidal fields from observations by reason of incompleteness and imperfectness of every data set practically available has an infinitely large number of allowable solutions fitting the data within measurement errors and hence can be treated as ill-posed. Therefore, interpolating the data always relies on some a priori assumptions concerning the tides, which provide a rule of sampling or, in other words, a regularization of the ill-posed problem. Data assimilation procedures used in large scale tide modeling are viewed in a common mathematical framework as such regularizations. It is shown that they all (basis functions expansion, parameter estimation, nudging, objective analysis, general inversion, and extended general inversion), including those (objective analysis and general inversion) originally formulated in stochastic terms, may be considered as utilizations of one of the three general methods suggested by the theory of ill-posed problems. The problem of grid refinement critical for inverse methods and nudging is discussed.
Mathematical modeling of the gas extraction from the gas hydrate deposit taking into account the replacement technology

NASA Astrophysics Data System (ADS)

Musakaev, N. G.; Khasanov, M. K.; Borodin, S. L.

2018-03-01

In the work on the basis of methods and equations of mechanics of multiphase systems the mathematical model of the process of carbon dioxide burial in the reservoir saturated with methane hydrate is proposed. Estimates are obtained that allow for this problem to neglect diffusion mixing of carbon dioxide and methane. The features of the process of methane displacement from CH4 hydrate by filling them with carbon dioxide are studied.
Comparison of the calculation QRS angle for bundle branch block detection

NASA Astrophysics Data System (ADS)

Goeirmanto, L.; Mengko, R.; Rajab, T. L.

2016-04-01

QRS angle represent condition of blood circulation in the heart. Normally QRS angle is between -30 until 90 degree. Left Axis Defiation (LAD) and Right Axis Defiation (RAD) are abnormality conditions that lead to Bundle Branch Block. QRS angle is calculated using common method from physicians and compared to mathematical method using difference amplitudos and difference areas. We analyzed the standard 12 lead electrocardiogram data from MITBIH physiobank database. All methods using lead I and lead avF produce similar QRS angle and right QRS axis quadrant. QRS angle from mathematical method using difference areas is close to common method from physician. Mathematical method using difference areas can be used as a trigger for detecting heart condition.
The first international workshop on the role and impact of mathematics in medicine: A collective account

PubMed Central

Artzrouni, Marc; Begg, Colin; Chabiniok, Radomir; Clairambault, Jean; Foss, AJE; Hargrove, John; Lee, Eva K; Siggers, Jennifer H; Tindall, Marcus

2011-01-01

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for interdisciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtaining high quality data and seeing things through “by the bedside” are some of the issues discussed by the participants.
Critical Analysis of the Mathematical Formalism of Theoretical Physics. I. Foundations of Differential and Integral Calculus

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2013-04-01

Critical analysis of the standard foundations of differential and integral calculus -- as mathematical formalism of theoretical physics -- is proposed. Methodological basis of the analysis is the unity of formal logic and rational dialectics. It is shown that: (a) the foundations (i.e. d 1ptyd,;=;δ,;->;0,;δ,δ,, δ,;->;0;δ,δ,;=;δ,;->;0;f,( x;+;δ, );-;f,( x )δ,;, d,;=;δ,, d,;=;δ, where y;=;f,( x ) is a continuous function of one argument x; δ, and δ, are increments; d, and d, are differentials) not satisfy formal logic law -- the law of identity; (b) the infinitesimal quantities d,, d, are fictitious quantities. They have neither algebraic meaning, nor geometrical meaning because these quantities do not take numerical values and, therefore, have no a quantitative measure; (c) expressions of the kind x;+;d, are erroneous because x (i.e. finite quantity) and d, (i.e. infinitely diminished quantity) have different sense, different qualitative determinacy; since x;,;,,,,onst under δ,;,;,, a derivative does not contain variable quantity x and depends only on constant c. Consequently, the standard concepts ``infinitesimal quantity (uninterruptedly diminishing quantity)'', ``derivative'', ``derivative as function of variable quantity'' represent incorrect basis of mathematics and theoretical physics.
Constructing the integral concept on the basis of the idea of accumulation: suggestion for a high school curriculum

NASA Astrophysics Data System (ADS)

Kouropatov, Anatoli; Dreyfus, Tommy

2013-07-01

Students have a tendency to see integral calculus as a series of procedures with associated algorithms and many do not develop a conceptual grasp giving them the desirable versatility of thought. Thus, instead of a proceptual view of the symbols in integration, they have, at best, a process-oriented view. On the other hand, it is not surprising that many students find concepts such as the integral difficult when they are unable to experience these processes directly in the classroom. With a view towards improving this situation, constructing the integral concept on the basis of the idea of accumulation has been proposed (Educ Stud Math. 1994;26:229-274; Integral as accumulation: a didactical perspective for school mathematics; Thessaloniki: PME; 2009. p. 417-424). In this paper, we discuss a curriculum that is based on this idea and a design for curriculum materials that are intended to develop an improved cognitive base for a flexible proceptual understanding of the integral and integration in high school. The main focus is on how we (mathematics teachers and mathematics educators) might teach the integral concept in order to help high school students to construct meaningful knowledge alongside acquiring technical abilities.
Student perceptions of writing projects in a university differential-equations course

NASA Astrophysics Data System (ADS)

Latulippe, Christine; Latulippe, Joe

2014-01-01

This qualitative study surveyed 102 differential-equations students in order to investigate how students participating in writing projects in university-level mathematics courses perceive the benefits of writing in the mathematics classroom. Based on previous literature on writing in mathematics, students were asked specifically about the benefits of writing projects as a means to explore practical uses of mathematics, deepen content knowledge, and strengthen communication. Student responses indicated an awareness of these benefits, supporting justifications commonly cited by instructors assigning writing projects. Open-ended survey responses highlighted additional themes which students associated with writing in mathematics, including using software programs and technology, working in groups, and stimulating interest in mathematics. This study provides student feedback to support the use of writing projects in mathematics, as well as student input, which can be utilized to strengthen the impact of writing projects in mathematics.
Origins of the brain networks for advanced mathematics in expert mathematicians

PubMed Central

Amalric, Marie; Dehaene, Stanislas

2016-01-01

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124
Origins of the brain networks for advanced mathematics in expert mathematicians.

PubMed

Amalric, Marie; Dehaene, Stanislas

2016-05-03

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.
The Critical Role of a Well-Articulated, Coherent Design in Professional Development: An Evaluation of a State-Wide Two-Week Program for Mathematics and Science Teachers

ERIC Educational Resources Information Center

Saderholm, Jon; Ronau, Robert N.; Rakes, Christopher R.; Bush, Sarah B.; Mohr-Schroeder, Margaret

2017-01-01

This evaluation study examined a state-wide professional development program composed of two institutes, one for mathematics teachers and one for science teachers, each spanning two weeks. The program was designed to help teachers transform their practice to align with Common Core State Standards for Mathematics and Next Generation Science…
Interrelations of green oak leaf roller population and common oak: results of 30-year monitoring and mathematical modeling

Treesearch

V. V. Rubtsov; I. A. Utkina

2003-01-01

Long-term monitoring followed by mathematical modeling was used to describe the population dynamics of the green oak leaf roller Tortrix viridana L. over a period of 30 years and to study reactions of oak stands to different levels of defoliation. The mathematical model allows us to forecast the population dynamics of the green oak leaf roller and...
ACER Mathematics Profile Series: Number Test. (Test Booklet, Answer and Record Sheet, Score Key, and Teachers Handbook).

ERIC Educational Resources Information Center

Cornish, Greg; Wines, Robin

The Number Test of the ACER Mathematics Profile Series, contains 30 items, for each of three suggested grade levels: 7-8, 8-9, and 9-10. Raw scores on all tests in the ACER Mathematics Profile Series (Number, Operations, Space and Measurement) are converted to a common scale called MAPS, a major feature of the Series. Based on the Rasch Model,…
Let's Get Movin'

ERIC Educational Resources Information Center

Kurz, Terri L.; Serrano, Alejandra

2015-01-01

To support students' development of concepts in mathematics, the use of technology is often encouraged (Common Core State Standards Initiative [CCSSI] 2010). Technology can contextualize learning and provide a meaningful setting for mathematical ideas. Most teachers are supportive regarding the use of technology to encourage learning and…
Sharpen Your Skills: Mathematics and Science Braille.

ERIC Educational Resources Information Center

Eulert, Von E.; Cohn, Doris

1984-01-01

Three articles about mathematics and science braille are provided for braille transcribers and teachers of the visually handicapped. The first article discusses common problems such as setting braille writers incorrectly, duplicating transcribed materials unnecessarily, and incorrectly transcribing from typescript. The second article provides a…
Designing Opportunities to Learn Mathematics Theory-Building Practices

ERIC Educational Resources Information Center

Bass, Hyman

2017-01-01

Mathematicians commonly distinguish two modes of work in the discipline: "Problem solving," and "theory building." Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide supported opportunities for students to…
Collaborative Emission Reduction Model Based on Multi-Objective Optimization for Greenhouse Gases and Air Pollutants.

PubMed

Meng, Qing-chun; Rong, Xiao-xia; Zhang, Yi-min; Wan, Xiao-le; Liu, Yuan-yuan; Wang, Yu-zhi

2016-01-01

CO2 emission influences not only global climate change but also international economic and political situations. Thus, reducing the emission of CO2, a major greenhouse gas, has become a major issue in China and around the world as regards preserving the environmental ecology. Energy consumption from coal, oil, and natural gas is primarily responsible for the production of greenhouse gases and air pollutants such as SO2 and NOX, which are the main air pollutants in China. In this study, a mathematical multi-objective optimization method was adopted to analyze the collaborative emission reduction of three kinds of gases on the basis of their common restraints in different ways of energy consumption to develop an economic, clean, and efficient scheme for energy distribution. The first part introduces the background research, the collaborative emission reduction for three kinds of gases, the multi-objective optimization, the main mathematical modeling, and the optimization method. The second part discusses the four mathematical tools utilized in this study, which include the Granger causality test to analyze the causality between air quality and pollutant emission, a function analysis to determine the quantitative relation between energy consumption and pollutant emission, a multi-objective optimization to set up the collaborative optimization model that considers energy consumption, and an optimality condition analysis for the multi-objective optimization model to design the optimal-pole algorithm and obtain an efficient collaborative reduction scheme. In the empirical analysis, the data of pollutant emission and final consumption of energies of Tianjin in 1996-2012 was employed to verify the effectiveness of the model and analyze the efficient solution and the corresponding dominant set. In the last part, several suggestions for collaborative reduction are recommended and the drawn conclusions are stated.

Collaborative Emission Reduction Model Based on Multi-Objective Optimization for Greenhouse Gases and Air Pollutants

PubMed Central

Zhang, Yi-min; Wan, Xiao-le; Liu, Yuan-yuan; Wang, Yu-zhi

2016-01-01

CO2 emission influences not only global climate change but also international economic and political situations. Thus, reducing the emission of CO2, a major greenhouse gas, has become a major issue in China and around the world as regards preserving the environmental ecology. Energy consumption from coal, oil, and natural gas is primarily responsible for the production of greenhouse gases and air pollutants such as SO2 and NOX, which are the main air pollutants in China. In this study, a mathematical multi-objective optimization method was adopted to analyze the collaborative emission reduction of three kinds of gases on the basis of their common restraints in different ways of energy consumption to develop an economic, clean, and efficient scheme for energy distribution. The first part introduces the background research, the collaborative emission reduction for three kinds of gases, the multi-objective optimization, the main mathematical modeling, and the optimization method. The second part discusses the four mathematical tools utilized in this study, which include the Granger causality test to analyze the causality between air quality and pollutant emission, a function analysis to determine the quantitative relation between energy consumption and pollutant emission, a multi-objective optimization to set up the collaborative optimization model that considers energy consumption, and an optimality condition analysis for the multi-objective optimization model to design the optimal-pole algorithm and obtain an efficient collaborative reduction scheme. In the empirical analysis, the data of pollutant emission and final consumption of energies of Tianjin in 1996–2012 was employed to verify the effectiveness of the model and analyze the efficient solution and the corresponding dominant set. In the last part, several suggestions for collaborative reduction are recommended and the drawn conclusions are stated. PMID:27010658
Specific modes of vibratory technological machines: mathematical models, peculiarities of interaction of system elements

NASA Astrophysics Data System (ADS)

Eliseev, A. V.; Sitov, I. S.; Eliseev, S. V.

2018-03-01

The methodological basis of constructing mathematical models of vibratory technological machines is developed in the article. An approach is proposed that makes it possible to introduce a vibration table in a specific mode that provides conditions for the dynamic damping of oscillations for the zone of placement of a vibration exciter while providing specified vibration parameters in the working zone of the vibration table. The aim of the work is to develop methods of mathematical modeling, oriented to technological processes with long cycles. The technologies of structural mathematical modeling are used with structural schemes, transfer functions and amplitude-frequency characteristics. The concept of the work is to test the possibilities of combining the conditions for reducing loads with working components of a vibration exciter while simultaneously maintaining sufficiently wide limits in variating the parameters of the vibrational field.
In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue.

PubMed

Antonopoulos, Markos; Stamatakos, Georgios

2015-01-01

Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided.
Modeling and simulation for fewer-axis grinding of complex surface

NASA Astrophysics Data System (ADS)

Li, Zhengjian; Peng, Xiaoqiang; Song, Ci

2017-10-01

As the basis of fewer-axis grinding of complex surface, the grinding mathematical model is of great importance. A mathematical model of the grinding wheel was established, and then coordinate and normal vector of the wheel profile could be calculated. Through normal vector matching at the cutter contact point and the coordinate system transformation, the grinding mathematical model was established to work out the coordinate of the cutter location point. Based on the model, interference analysis was simulated to find out the right position and posture of workpiece for grinding. Then positioning errors of the workpiece including the translation positioning error and the rotation positioning error were analyzed respectively, and the main locating datum was obtained. According to the analysis results, the grinding tool path was planned and generated to grind the complex surface, and good form accuracy was obtained. The grinding mathematical model is simple, feasible and can be widely applied.
Reflections on the Notion of Culture in the History of Mathematics: The Example of "Geometrical Equations".

PubMed

Lê, François

2016-09-01

Argument This paper challenges the use of the notion of "culture" to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to "geometrical equations," objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to "geometrical equations," and especially the technical aspects of these activities, is made on the basis of a sociological definition of "culture." More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a "cultural system."
Mathematical subtleties and scientific knowledge: Francis Bacon and mathematics, at the crossing of two traditions.

PubMed

Mori, Giuliano

2017-03-01

This article engages the much-debated role of mathematics in Bacon's philosophy and inductive method at large. The many references to mathematics in Bacon's works are considered in the context of the humanist reform of the curriculum studiorum and, in particular, through a comparison with the kinds of natural and intellectual subtlety as they are defined by many sixteenth-century authors, including Cardano, Scaliger and Montaigne. Additionally, this article gives a nuanced background to the 'subtlety' commonly thought to have been eschewed by Bacon and by Bacon's self-proclaimed followers in the Royal Society of London. The aim of this article is ultimately to demonstrate that Bacon did not reject the use of mathematics in natural philosophy altogether. Instead, he hoped that following the Great Instauration a kind of non-abstract mathematics could be founded: a kind of mathematics which was to serve natural philosophy by enabling men to grasp the intrinsic subtlety of nature. Rather than mathematizing nature, it was mathematics that needed to be 'naturalized'.
What Teachers Understand of Model Lessons

ERIC Educational Resources Information Center

Courtney, Scott A.

2017-01-01

Over the past two decades, researchers in mathematics teacher education have identified characteristics of high quality professional development (PD). This report describes an investigation of a common approach to PD with secondary mathematics teachers, providing teachers with opportunities to experience reform-oriented model lessons as students…
RECEPTOR MODEL DEVELOPMENT AND APPLICATION

EPA Science Inventory

Source apportionment (receptor) models are mathematical procedures for identifying and quantifying the sources of ambient air pollutants and their effects at a site (the receptor), primarily on the basis of species concentration measurements at the receptor, and generally without...
ILS Scattering Problem and Signal Detection Model

DOT National Transportation Integrated Search

1972-02-01

The construction of a mathematical model of The Instrument Landing System (ILS) multipath problem was undertaken. This report presents the theoretical basis for any such model, a critique of previous models and newly achieve developments in ILS model...
PM SOURCE APPORTIONMENT/RECEPTOR MODELING

EPA Science Inventory

Source apportionment (receptor) models are mathematical procedures for identifying and quantifying the sources of ambient air pollutants and their effects at a site (the receptor), primarily on the basis of species concentration measurements at the receptor, and generally without...
Atoms in molecules, an axiomatic approach. I. Maximum transferability

NASA Astrophysics Data System (ADS)

Ayers, Paul W.

2000-12-01

Central to chemistry is the concept of transferability: the idea that atoms and functional groups retain certain characteristic properties in a wide variety of environments. Providing a completely satisfactory mathematical basis for the concept of atoms in molecules, however, has proved difficult. The present article pursues an axiomatic basis for the concept of an atom within a molecule, with particular emphasis devoted to the definition of transferability and the atomic description of Hirshfeld.
Rasch Modeling of the Test of Early Mathematics Ability-Third Edition with a Sample of K1 Children in Singapore

ERIC Educational Resources Information Center

Yao, Shih-Ying; Muñez, David; Bull, Rebecca; Lee, Kerry; Khng, Kiat Hui; Poon, Kenneth

2017-01-01

The Test of Early Mathematics Ability-Third Edition (TEMA-3) is a commonly used measure of early mathematics knowledge for children aged 3 years to 8 years 11 months. In spite of its wide use, research on the psychometric properties of TEMA-3 remains limited. This study applied the Rasch model to investigate the psychometric properties of TEMA-3…
Global Neural Pattern Similarity as a Common Basis for Categorization and Recognition Memory

PubMed Central

Xue, Gui; Love, Bradley C.; Preston, Alison R.; Poldrack, Russell A.

2014-01-01

Familiarity, or memory strength, is a central construct in models of cognition. In previous categorization and long-term memory research, correlations have been found between psychological measures of memory strength and activation in the medial temporal lobes (MTLs), which suggests a common neural locus for memory strength. However, activation alone is insufficient for determining whether the same mechanisms underlie neural function across domains. Guided by mathematical models of categorization and long-term memory, we develop a theory and a method to test whether memory strength arises from the global similarity among neural representations. In human subjects, we find significant correlations between global similarity among activation patterns in the MTLs and both subsequent memory confidence in a recognition memory task and model-based measures of memory strength in a category learning task. Our work bridges formal cognitive theories and neuroscientific models by illustrating that the same global similarity computations underlie processing in multiple cognitive domains. Moreover, by establishing a link between neural similarity and psychological memory strength, our findings suggest that there may be an isomorphism between psychological and neural representational spaces that can be exploited to test cognitive theories at both the neural and behavioral levels. PMID:24872552
An information driven strategy to support multidisciplinary design

NASA Technical Reports Server (NTRS)

Rangan, Ravi M.; Fulton, Robert E.

1990-01-01

The design of complex engineering systems such as aircraft, automobiles, and computers is primarily a cooperative multidisciplinary design process involving interactions between several design agents. The common thread underlying this multidisciplinary design activity is the information exchange between the various groups and disciplines. The integrating component in such environments is the common data and the dependencies that exist between such data. This may be contrasted to classical multidisciplinary analyses problems where there is coupling between distinct design parameters. For example, they may be expressed as mathematically coupled relationships between aerodynamic and structural interactions in aircraft structures, between thermal and structural interactions in nuclear plants, and between control considerations and structural interactions in flexible robots. These relationships provide analytical based frameworks leading to optimization problem formulations. However, in multidisciplinary design problems, information based interactions become more critical. Many times, the relationships between different design parameters are not amenable to analytical characterization. Under such circumstances, information based interactions will provide the best integration paradigm, i.e., there is a need to model the data entities and their dependencies between design parameters originating from different design agents. The modeling of such data interactions and dependencies forms the basis for integrating the various design agents.
[The theory of order from poinsot to Bourgoin: Mathematics, philosophy, ornemental art].

PubMed

Boucard, Jenny; Eckes, Christophe

2015-12-01

The aim of this paper is to understand the dynamics of the theory of order in the nineteenth century and to reveal a specific approach to mathematics, science, philosophy and decorative art in which order plays a prominent role. We will analyze the singular meaning that Poinsot assigns to the notion of order in the mathematical sciences, before describing the circulation of his writings on the order in the nineteenth century. Poinsot is one of the main sources of Cournot, who places the notions of order and form as the basis of his knowledge system. Then we will study the writings of Bourgoin who develops a combinatorics of ornaments based on the categories of order and form.
Seeing mathematics: perceptual experience and brain activity in acquired synesthesia.

PubMed

Brogaard, Berit; Vanni, Simo; Silvanto, Juha

2013-01-01

We studied the patient JP who has exceptional abilities to draw complex geometrical images by hand and a form of acquired synesthesia for mathematical formulas and objects, which he perceives as geometrical figures. JP sees all smooth curvatures as discrete lines, similarly regardless of scale. We carried out two preliminary investigations to establish the perceptual nature of synesthetic experience and to investigate the neural basis of this phenomenon. In a functional magnetic resonance imaging (fMRI) study, image-inducing formulas produced larger fMRI responses than non-image inducing formulas in the left temporal, parietal and frontal lobes. Thus our main finding is that the activation associated with his experience of complex geometrical images emerging from mathematical formulas is restricted to the left hemisphere.
Fraction Representation: The Not-So-Common Denominator among Textbooks

ERIC Educational Resources Information Center

Hodges, Thomas E.; Cady, JoAnn; Collins, Lee

2008-01-01

Three widely used sixth-grade textbooks were studied to see how fraction concepts were represented. The textbooks selected were "Connected Mathematics," "Middle Grades MathThematics," and Glencoe's "Mathematics: Applications and Concepts Course 1." Three specific areas were examined: representation mode, model, and problem context. Results of…
Mathematical Modeling of Chemical Stoichiometry

ERIC Educational Resources Information Center

Croteau, Joshua; Fox, William P.; Varazo, Kristofoland

2007-01-01

In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Modeling Mathematical Ideas: Developing Strategic Competence in Elementary and Middle School

ERIC Educational Resources Information Center

Suh, Jennifer M.; Seshaiyer, Padmanabhan

2016-01-01

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…
On the Meaning of Uniqueness

ERIC Educational Resources Information Center

Shipman, Barbara A.

2013-01-01

This article analyzes four questions on the meaning of uniqueness that have contrasting answers in common language versus mathematical language. The investigations stem from a scenario in which students interpreted uniqueness according to a definition from standard English, that is, different from the mathematical meaning, in defining an injective…

Technology-Rich Mathematics Instruction

ERIC Educational Resources Information Center

Thach, Kim J.; Norman, Kimberly A.

2008-01-01

This article uses one of the authors' classroom experiences to explore how teachers can create technology-rich learning environments that support upper elementary students' mathematical understanding of algebra and number and operations. They describe a unit that presents a common financial problem (the use of credit cards) to engage sixth graders…
Spatial Reasoning Influences Students' Performance on Mathematics Tasks

ERIC Educational Resources Information Center

Lowrie, Tom; Logan, Tracy; Ramful, Ajay

2016-01-01

Although the psychological literature has demonstrated that spatial reasoning and mathematics performance are correlated, there is scant research on these relationships in the middle years. The current study examined the commonalities and differences in students' performance on instruments that measured three spatial reasoning constructs and two…
Strategically Fostering Dynamic Interactive Environments

ERIC Educational Resources Information Center

Özgün-Koca, S. Asli

2016-01-01

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…
Common-Cause Failure Treatment in Event Assessment: Basis for a Proposed New Model

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

Dana Kelly; Song-Hua Shen; Gary DeMoss

2010-06-01

Event assessment is an application of probabilistic risk assessment in which observed equipment failures and outages are mapped into the risk model to obtain a numerical estimate of the event’s risk significance. In this paper, we focus on retrospective assessments to estimate the risk significance of degraded conditions such as equipment failure accompanied by a deficiency in a process such as maintenance practices. In modeling such events, the basic events in the risk model that are associated with observed failures and other off-normal situations are typically configured to be failed, while those associated with observed successes and unchallenged components aremore » assumed capable of failing, typically with their baseline probabilities. This is referred to as the failure memory approach to event assessment. The conditioning of common-cause failure probabilities for the common cause component group associated with the observed component failure is particularly important, as it is insufficient to simply leave these probabilities at their baseline values, and doing so may result in a significant underestimate of risk significance for the event. Past work in this area has focused on the mathematics of the adjustment. In this paper, we review the Basic Parameter Model for common-cause failure, which underlies most current risk modelling, discuss the limitations of this model with respect to event assessment, and introduce a proposed new framework for common-cause failure, which uses a Bayesian network to model underlying causes of failure, and which has the potential to overcome the limitations of the Basic Parameter Model with respect to event assessment.« less
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2016-03-01

Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.
Quod erat demonstrandum: Understanding and Explaining Equations in Physics Teacher Education

NASA Astrophysics Data System (ADS)

Karam, Ricardo; Krey, Olaf

2015-07-01

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end of their master's degree in two European universities. The course had two main goals: (1) To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and (2) To expand students' repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students' views on the role of mathematics in physics, an increase in the participants' awareness of the difficulties faced by learners to understand physics equations and a broadening in the students' repertoire to answer "Why?" questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived.
An Open Source Simulation Model for Soil and Sediment Bioturbation

PubMed Central

Schiffers, Katja; Teal, Lorna Rachel; Travis, Justin Mark John; Solan, Martin

2011-01-01

Bioturbation is one of the most widespread forms of ecological engineering and has significant implications for the structure and functioning of ecosystems, yet our understanding of the processes involved in biotic mixing remains incomplete. One reason is that, despite their value and utility, most mathematical models currently applied to bioturbation data tend to neglect aspects of the natural complexity of bioturbation in favour of mathematical simplicity. At the same time, the abstract nature of these approaches limits the application of such models to a limited range of users. Here, we contend that a movement towards process-based modelling can improve both the representation of the mechanistic basis of bioturbation and the intuitiveness of modelling approaches. In support of this initiative, we present an open source modelling framework that explicitly simulates particle displacement and a worked example to facilitate application and further development. The framework combines the advantages of rule-based lattice models with the application of parameterisable probability density functions to generate mixing on the lattice. Model parameters can be fitted by experimental data and describe particle displacement at the spatial and temporal scales at which bioturbation data is routinely collected. By using the same model structure across species, but generating species-specific parameters, a generic understanding of species-specific bioturbation behaviour can be achieved. An application to a case study and comparison with a commonly used model attest the predictive power of the approach. PMID:22162997
Burns, metabolism and nutritional requirements.

PubMed

Mendonça Machado, N; Gragnani, A; Masako Ferreira, L

2011-01-01

To review the nutritional evaluation in burned patient, considering the literature descriptions of nutritional evaluation and energy requirements of these patients. Thermal injury is the traumatic event with the highest metabolic response in critically ill patients. Various mathematical formulas have been developed to estimate nutritional requirements in burned patient. Indirect Calorimetry is the only method considered gold standard for measuring caloric expenditure. A survey of the literature and data was collected based on official data bases, LILACS, EMBASE and PubMed. The metabolic changes involved in hypermetabolism are designed to supply energy to support immune function, brain activity, wound healing, and preservation of body tissues. Body weight is considered the easiest indicator and perhaps the best to assess the nutritional status. The most common formulas utilized in these patients are the Curreri, Pennisi, Schofield, Ireton-Jones, Harris-Benedict and the ASPEN recommendations. For children is the Mayes and World Health Organization formula. The majority of mathematical formulas overestimate the nutritional needs. The regular use of Indirect Calorimetry supplies adequate nutritional support to the burn patient. The traditional nutritional evaluation considers anthropometry, biochemical markers and estimation of nutritional requirements. The weight provides a basis for decisions that are established in the clinical context. Classic parameters can be adapted to intensive care environment. The use of Indirect Calorimetry is crucial to ensure the safety of the nutritional support of burn patients and this should be widely encouraged.
An open source simulation model for soil and sediment bioturbation.

PubMed

Schiffers, Katja; Teal, Lorna Rachel; Travis, Justin Mark John; Solan, Martin

2011-01-01

Bioturbation is one of the most widespread forms of ecological engineering and has significant implications for the structure and functioning of ecosystems, yet our understanding of the processes involved in biotic mixing remains incomplete. One reason is that, despite their value and utility, most mathematical models currently applied to bioturbation data tend to neglect aspects of the natural complexity of bioturbation in favour of mathematical simplicity. At the same time, the abstract nature of these approaches limits the application of such models to a limited range of users. Here, we contend that a movement towards process-based modelling can improve both the representation of the mechanistic basis of bioturbation and the intuitiveness of modelling approaches. In support of this initiative, we present an open source modelling framework that explicitly simulates particle displacement and a worked example to facilitate application and further development. The framework combines the advantages of rule-based lattice models with the application of parameterisable probability density functions to generate mixing on the lattice. Model parameters can be fitted by experimental data and describe particle displacement at the spatial and temporal scales at which bioturbation data is routinely collected. By using the same model structure across species, but generating species-specific parameters, a generic understanding of species-specific bioturbation behaviour can be achieved. An application to a case study and comparison with a commonly used model attest the predictive power of the approach.
The study of middle school mathematics and science teachers' practices, perceptions, and attitudes related to mathematics and science integration

NASA Astrophysics Data System (ADS)

Leszczynski, Eliza

The purpose of this qualitative study was to investigate the nature of mathematics and science connections made by sixth and seventh grade mathematics and science teachers in their classrooms. This study also examined the extent to which these connections represented mathematics and science integration and described the teachers' perceptions of and attitudes about mathematics and science integration. The primary data sources included classroom observations and teacher interviews. Findings suggested that teacher practices in making mathematics and science connections in the classroom incorporated many of the characteristics of integrated instruction presented in the literature. Teacher attitudes toward integration were found to be generally positive and supportive of integrated instruction. Mathematics teachers shared a common perception of integration being two separate lessons taught together in one lesson. In contrast, science teachers perceived integration to be a seamless blend of the two disciplines. The researcher related these perceptions and attitudes to the teachers' past experiences with mathematics and science connections and integration, and also to their practices of mathematics and science connections in the study.
High pressure common rail injection system modeling and control.

PubMed

Wang, H P; Zheng, D; Tian, Y

2016-07-01

In this paper modeling and common-rail pressure control of high pressure common rail injection system (HPCRIS) is presented. The proposed mathematical model of high pressure common rail injection system which contains three sub-systems: high pressure pump sub-model, common rail sub-model and injector sub-model is a relative complicated nonlinear system. The mathematical model is validated by the software Matlab and a virtual detailed simulation environment. For the considered HPCRIS, an effective model free controller which is called Extended State Observer - based intelligent Proportional Integral (ESO-based iPI) controller is designed. And this proposed method is composed mainly of the referred ESO observer, and a time delay estimation based iPI controller. Finally, to demonstrate the performances of the proposed controller, the proposed ESO-based iPI controller is compared with a conventional PID controller and ADRC. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
History, Applications, and Philosophy in Mathematics Education: HAPh—A Use of Primary Sources

NASA Astrophysics Data System (ADS)

Jankvist, Uffe Thomas

2013-03-01

The article first investigates the basis for designing teaching activities dealing with aspects of history, applications, and philosophy of mathematics in unison by discussing and analyzing the different `whys' and `hows' of including these three dimensions in mathematics education. Based on the observation that a use of history, applications, and philosophy as a `goal' is best realized through a modules approach, the article goes on to discuss how to actually design such teaching modules. It is argued that a use of primary original sources through a so-called guided reading along with a use of student essay assignments, which are suitable for bringing out relevant meta-issues of mathematics, is a sensible way of realizing a design encompassing the three dimensions. Two concrete teaching modules on aspects of the history, applications, and philosophy of mathematics—HAPh-modules—are outlined and the mathematical cases of these, graph theory and Boolean algebra, are described. Excerpts of student groups' essays from actual implementations of these modules are displayed as illustrative examples of the possible effect such HAPh-modules may have on students' development of an awareness regarding history, applications, and philosophy in relation to mathematics as a (scientific) discipline.
Forging patterns and making waves from biology to geology: a commentary on Turing (1952) 'The chemical basis of morphogenesis'.

PubMed

Ball, Philip

2015-04-19

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, 'The chemical basis of morphogenesis', on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of 'Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
Predicting the risk of sudden cardiac death.

PubMed

Lerma, Claudia; Glass, Leon

2016-05-01

Sudden cardiac death (SCD) is the result of a change of cardiac activity from normal (typically sinus) rhythm to a rhythm that does not pump adequate blood to the brain. The most common rhythms leading to SCD are ventricular tachycardia (VT) or ventricular fibrillation (VF). These result from an accelerated ventricular pacemaker or ventricular reentrant waves. Despite significant efforts to develop accurate predictors for the risk of SCD, current methods for risk stratification still need to be improved. In this article we briefly review current approaches to risk stratification. Then we discuss the mathematical basis for dynamical transitions (called bifurcations) that may lead to VT and VF. One mechanism for transition to VT or VF involves a perturbation by a premature ventricular complex (PVC) during sinus rhythm. We describe the main mechanisms of PVCs (reentry, independent pacemakers and abnormal depolarizations). An emerging approach to risk stratification for SCD involves the development of individualized dynamical models of a patient based on measured anatomy and physiology. Careful analysis and modelling of dynamics of ventricular arrhythmia on an individual basis will be essential in order to improve risk stratification for SCD and to lay a foundation for personalized (precision) medicine in cardiology. © 2015 The Authors. The Journal of Physiology © 2015 The Physiological Society.
Math In-Service Training for Adult Educators.

ERIC Educational Resources Information Center

Llorente, Juan Carlos; Porras, Marta; Martinez, Rosa

In a series of mathematics education workshops in which teachers from adult basic education and vocational education worked together to design teaching situations on particular contents in mathematics in order to make explicit and bring into reflection the teaching strategies used by each group. The workshops constituted a common space of…
Heuristic for Learning Common Emitter Amplification with Bipolar Transistors

ERIC Educational Resources Information Center

Staffas, Kjell

2017-01-01

Mathematics in engineering education causes many thresholds in the courses because of the demand of abstract conceptualisation. Electronics depend heavily on more or less complex mathematics. Therefore the concepts of analogue electronics are hard to learn since a great deal of students struggle with the calculations and procedures needed. A…
Pre-Algebra Lexicon.

ERIC Educational Resources Information Center

Hayden, Dunstan; Cuevas, Gilberto

The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…
The Root of the Problem

ERIC Educational Resources Information Center

Grosser-Clarkson, Dana L.

2015-01-01

The Common Core State Standards for Mathematics expect students to build on their knowledge of the number system, expressions and equations, and functions throughout school mathematics. For example, students learn that they can add something to both sides of an equation and that doing so will not affect the equivalency; however, squaring both…
Stacking Cans: Abstracting from Computation

ERIC Educational Resources Information Center

Roy, George J.; Safi, Farshid; Graul, LuAnn

2015-01-01

As current mathematics standards, such as the Common Core, are being implemented throughout the United States, it has become evident that teachers need support to enact the tenets of those standards. To help in this endeavor, this article was published as a guideline to emphasize to mathematics education stakeholders that "effective teaching…
It All Adds Up: Learning Early Math through Play and Games

ERIC Educational Resources Information Center

Ramani, Geetha B.; Eason, Sarah H.

2015-01-01

Playing and learning mathematics do not have to be mutually exclusive activities, especially in kindergarten. Play and games can give young children opportunities to learn and develop foundational math skills that are aligned with Common Core standards for mathematics through age-appropriate, fun, and engaging activities.

A Vertical Approach to Math Instruction

ERIC Educational Resources Information Center

Gojak, Linda

2012-01-01

In the current era of mathematics standards, whether they are Common Core State Standards or other state standards, effective vertical mathematics teams offer an opportunity for teachers to grow professionally through shared experiences, for leadership to grow among the faculty, and for the school to change its perspective on the teaching and…
Five Keys for Teaching Mental Math

ERIC Educational Resources Information Center

Olsen, James R.

2015-01-01

After studying the Common Core State Standards for Mathematics (CCSSM) and brain-based learning research, James Olsen believes mental math instruction in secondary school mathematics (grades 7-12) and in teacher education programs needs increased attention. The purpose of this article is to share some keys for teaching mental math. Olsen also…
Supporting Mathematics Instruction through Community

ERIC Educational Resources Information Center

Amidon, Joel C.; Trevathan, Morgan L.

2016-01-01

Raising expectations is nothing new. Every iteration of standards elevates the expectations for what students should know and be able to do. The Common Core State Standards for Mathematics (CCSSM) is no exception, with standards for content and practice that move beyond memorization of traditional algorithms to "make sense of problems and…
Using Concept Maps to Show "Connections" in Measurement: An Example from the Australian Curriculum

ERIC Educational Resources Information Center

Marshman, Margaret

2014-01-01

Within the "Australian Curriculum: Mathematics" the Understanding proficiency strand states, "Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and…
Using Financial Calculators in a Business Mathematics Course.

ERIC Educational Resources Information Center

Heller, William H.; Taylor, Monty B.

2000-01-01

Discusses the authors' experiences with integrating financial calculators into a business mathematics course. Presents a brief overview of the operation of financial calculators, reviews some of the more common models, discusses how to use the equation solver utility on other calculators to emulate a financial calculator, and explores the…
Getting a Bead on It

ERIC Educational Resources Information Center

Ferrucci, Beverly J.; McDougall, Jennifer; Carter, Jack

2009-01-01

One challenge that middle school teachers commonly face is finding insightful, hands-on applications when teaching basic mathematical concepts. One concept that is a foundation of middle school mathematics is the notion of "linear functions." Although a variety of models can be used for linear equations, such as temperature conversions,…
Kindergarten Students Solving Mathematical Word Problems

ERIC Educational Resources Information Center

Johnson, Nickey Owen

2013-01-01

The purpose of this study was to explore problem solving with kindergarten students. This line of inquiry is highly significant given that Common Core State Standards emphasize deep, conceptual understanding in mathematics as well as problem solving in kindergarten. However, there is little research on problem solving with kindergarten students.…
The Ways Character Strengths Support K-8 Mathematics and the Common Core State Standards

ERIC Educational Resources Information Center

Bier, Melinda C.; Sherblom, Stephen A.; Berkowitz, Marvin W.; Coulter, Bob

2016-01-01

Character strengths support academic learning and can and should be incorporated into all content areas. This article articulates ways character strengths, including self-efficacy, positive-attitude, perseverance, growth-mindset, intrinsic motivation, intellectual carefulness, and courage specifically support mathematics education (K-8) and can…
Bringing Stories to Life: Integrating Literature and Math Manipulatives

ERIC Educational Resources Information Center

Larson, Lotta C.; Rumsey, Chepina

2018-01-01

This Teaching Tip describes the use of children's literature to help second-grade students meet Common Core State Standards for English Language Arts and for Mathematics. During a shared reading experience, students used manipulatives to represent plot and characters while demonstrating mathematical reasoning. The article offers instructional…
STEAM by Another Name: Transdisciplinary Practice in Art and Design Education

ERIC Educational Resources Information Center

Costantino, Tracie

2018-01-01

The recent movement to include art and design in Science, Technology, Engineering, and Mathematics (STEM) education has made Science, Technology, Engineering, Arts, and Mathematics (STEAM) an increasingly common acronym in the education lexicon. The STEAM movement builds on existing models of interdisciplinary curriculum, but what makes the union…
Sustainability Education: The What and How for Mathematics

ERIC Educational Resources Information Center

Hamilton, Jason; Pfaff, Thomas J.

2014-01-01

In this article we provide a simple way to think about the concept of sustainability and provide a number of examples for incorporating sustainability education into commonly taught mathematics courses. Scientific assessments have concluded that ecosystem services (the benefits that humans derive from the functioning of Earth's natural…
Depth of Teachers' Knowledge: Frameworks for Teachers' Knowledge of Mathematics

ERIC Educational Resources Information Center

Holmes, Vicki-Lynn

2012-01-01

This article describes seven teacher knowledge frameworks and relates these frameworks to the teaching and assessment of elementary teacher's mathematics knowledge. The frameworks classify teachers' knowledge and provide a vocabulary and common language through which knowledge can be discussed and assessed. These frameworks are categorized into…
Planning Questions and Persevering in the Practices

ERIC Educational Resources Information Center

Gurl, Theresa J.; Fox, Ryan; Dabovic, Nikolina; Leavitt, Arielle Eager

2016-01-01

The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…
Common Features of Professional Development Activities for Mathematics and Science Teachers

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Bolyard, Johnna J.; Oh, Hana; Cerar, Nancy Irby

2011-01-01

This study examines professional development activities provided for mathematics and science teachers in the National Science Foundation's Math and Science Partnership Program by analyzing a cross-sectional sample of over 2000 professional development (PD) activities in the program. Data were gathered from secondary source documents and surveys to…
Mathematical versus English Meaning in Implication and Disjunction

ERIC Educational Resources Information Center

Shipman, Barbara A.

2013-01-01

As mathematicians, we assign rigid meanings to words that may have a variety of interpretations in common language. This article considers meanings of "if" and "or" from everyday English that have caused students to misinterpret mathematical statements, and that are consistently overlooked by instructional materials in addressing students'…
Children's Idiosyncratic Symbol-Making.

ERIC Educational Resources Information Center

Barrett, Margaret; And Others

An ethnographic study documented and analyzed the idiosyncratic symbols kindergarten children employ to encode their experiences in the domains of mathematics, music, and visual art, in order to identify any patterns in use and meaning. In the area of mathematics, children were given common objects and asked to sort them. Four categories of…
Poster Power

ERIC Educational Resources Information Center

Bayley, Dawn

2004-01-01

There are many ways for children to engage in learning and experiencing mathematics and posters are one of them. From the author's observation of many classrooms the most common mathematical poster to be seen was the faithful multiplication times-tables. The purpose of this article is to encourage the use of effective posters and other visual…
The Right Time to Start Writing

ERIC Educational Resources Information Center

Casa, Tutita M.

2015-01-01

Communication has long been emphasized in standards-based instruction (NCTM 1991; 2000), yet little distinction has been made between oral and written forms. Nonetheless, both the mathematics and the English language arts Common Core State Standards (CCSS) documents continue to hint at the importance of writing mathematically (CCSSI 2010). The…
Implementing the Common Core: Applying Shifts to Instruction

ERIC Educational Resources Information Center

Gaddy, Angeline K.; Harmon, Shannon E.; Barlow, Angela T.; Milligan, Charles D.; Huang, Rongjin

2014-01-01

With such publications as "Curriculum and Evaluation Standards" (1989) and "Principles and Standards for School Mathematic" (2000), NCTM has played a significant role in defining a vision for school mathematics. In particular, the Curriculum Principle (NCTM 2000, pp. 14-16) described the need for students to learn important…
Cases on Technology Integration in Mathematics Education

ERIC Educational Resources Information Center

Polly, Drew, Ed.

2015-01-01

Common Core education standards establish a clear set of specific ideas and skills that all students should be able to comprehend at each grade level. In an effort to meet these standards, educators are turning to technology for improved learning outcomes. "Cases on Technology Integration in Mathematics Education" provides a compilation…

S.M.P. SEQUENTIAL MATHEMATICS PROGRAM.

ERIC Educational Resources Information Center

CICIARELLI, V; LEONARD, JOSEPH

A SEQUENTIAL MATHEMATICS PROGRAM BEGINNING WITH THE BASIC FUNDAMENTALS ON THE FOURTH GRADE LEVEL IS PRESENTED. INCLUDED ARE AN UNDERSTANDING OF OUR NUMBER SYSTEM, AND THE BASIC OPERATIONS OF WORKING WITH WHOLE NUMBERS--ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION. COMMON FRACTIONS ARE TAUGHT IN THE FIFTH, SIXTH, AND SEVENTH GRADES. A…
Taking It to the Next Level: Students Using Inductive Reasoning

ERIC Educational Resources Information Center

Murawska, Jaclyn M.; Zollman, Alan

2015-01-01

Although discussions about inductive reasoning can be traced back thousands of years (Fitelson 2011), the implementation of the Standards for Mathematical Practice (SMP) within the Common Core State Standards (CCSSI 2010) is generating renewed attention to how students learn mathematics. The third SMP, "Construct viable arguments and critique…
Using Virtual Manipulatives with Pre-Service Mathematics Teachers to Create Representational Models

ERIC Educational Resources Information Center

Cooper, Thomas E.

2012-01-01

In mathematics education, physical manipulatives such as algebra tiles, pattern blocks, and two-colour counters are commonly used to provide concrete models of abstract concepts. With these traditional manipulatives, people can communicate with the tools only in one another's presence. This limitation poses difficulties concerning assessment and…
The Distributive Property in Grade 3?

ERIC Educational Resources Information Center

Benson, Christine C.; Wall, Jennifer J.; Malm, Cheryl

2013-01-01

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…
On laminar and turbulent friction

NASA Technical Reports Server (NTRS)

Von Karman, TH

1946-01-01

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)
Self-similar seismogenic structure of the crust: A review of the problem and a mathematical model

NASA Astrophysics Data System (ADS)

Stakhovsky, I. R.

2007-12-01

The paper presents a brief review of studies of the structural organization of a seismogenic medium showing that the crust of seismically active regions possesses a fractal structure. A new mathematical model of the self-similar seismogenic structure (SSS) of the crust generalizing the reviewed publications is proposed on the basis of the scaling correspondence between the fault, seismic, and seismic energy multifractal fields of the crust. Multifractal fields of other physical origin can also be incorporated in the SSS model.
Selecting optimal structure of burners for tubular cylindrical furnaces by the mathematical experiment planning method

NASA Astrophysics Data System (ADS)

Katin, Viktor; Kosygin, Vladimir; Akhtiamov, Midkhat

2017-10-01

This paper substantiates the method of mathematical planning for experimental research in the process of selecting the most efficient types of burning devices for tubular refinery furnaces of vertical-cylindrical design. This paper provides detailed consideration of an experimental plan of a 4×4 Latin square type when studying the impact of three factors with four levels of variance. On the basis of the experimental research we have developed practical recommendations on the employment of optimal burners for two-step fuel combustion.
Quantitative estimation of time-variable earthquake hazard by using fuzzy set theory

NASA Astrophysics Data System (ADS)

Deyi, Feng; Ichikawa, M.

1989-11-01

In this paper, the various methods of fuzzy set theory, called fuzzy mathematics, have been applied to the quantitative estimation of the time-variable earthquake hazard. The results obtained consist of the following. (1) Quantitative estimation of the earthquake hazard on the basis of seismicity data. By using some methods of fuzzy mathematics, seismicity patterns before large earthquakes can be studied more clearly and more quantitatively, highly active periods in a given region and quiet periods of seismic activity before large earthquakes can be recognized, similarities in temporal variation of seismic activity and seismic gaps can be examined and, on the other hand, the time-variable earthquake hazard can be assessed directly on the basis of a series of statistical indices of seismicity. Two methods of fuzzy clustering analysis, the method of fuzzy similarity, and the direct method of fuzzy pattern recognition, have been studied is particular. One method of fuzzy clustering analysis is based on fuzzy netting, and another is based on the fuzzy equivalent relation. (2) Quantitative estimation of the earthquake hazard on the basis of observational data for different precursors. The direct method of fuzzy pattern recognition has been applied to research on earthquake precursors of different kinds. On the basis of the temporal and spatial characteristics of recognized precursors, earthquake hazards in different terms can be estimated. This paper mainly deals with medium-short-term precursors observed in Japan and China.
Compressed modes for variational problems in mathematical physics and compactly supported multiresolution basis for the Laplace operator

NASA Astrophysics Data System (ADS)

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2014-03-01

We will describe a general formalism for obtaining spatially localized (``sparse'') solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an L1 regularization term to the variational principle, which is shown to yield solutions with compact support (``compressed modes''). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. In addition, we introduce an L1 regularized variational framework for developing a spatially localized basis, compressed plane waves (CPWs), that spans the eigenspace of a differential operator, for instance, the Laplace operator. Our approach generalizes the concept of plane waves to an orthogonal real-space basis with multiresolution capabilities. Supported by NSF Award DMR-1106024 (VO), DOE Contract No. DE-FG02-05ER25710 (RC) and ONR Grant No. N00014-11-1-719 (SO).
[Gaston Bachelard anagogical reverie and surrational at stake].

PubMed

Castellana, Mario

2015-01-01

The latest studies on epistemological thought of Gaston Bachelard, especially in France and Italy, they are highlighting some fundamental issues, such as creative and propulsive assigned to mathematics in the construction of physical reality. The studies of Bachelard on the quantum mechanics of the '30s, and especially on the theoretical physics of Paul Dirac, introduced a particular concept of "anagogical reverie" precisely in order to understand the increasingly abstract and creative thinking of mathematics in the various levels of physical reality. In the wake of what Federigo Enriques called "mathematical poetry", Bachelard comes to propose a real "nouménologie mathématique" which characterizes the contemporary scientific thought and which provides the basis epistemic appropriate to understand the 'rational effectiveness' of mathematics and the real meaning of their application to the real. For these reasons, Bachelard in the '30s used a new term to describe his rationalist engagement, the "surrationalisme", just to understand in depth what Enriques called the "implicit philosophy" in sciences, the "pensée des sciences", where mathematics, thanks to the "anagogical reverie", put in place continue "enjeux" of the rational.
Software and mathematical support of Kazakhstani star tracker

NASA Astrophysics Data System (ADS)

Akhmedov, D.; Yelubayev, S.; Ten, V.; Bopeyev, T.; Alipbayev, K.; Sukhenko, A.

2016-10-01

Currently the specialists of Kazakhstan have been developing the star tracker that is further planned to use on Kazakhstani satellites of various purposes. At the first stage it has been developed the experimental model of star tracker that has following characteristics: field of view 20°, update frequency 2 Hz, exclusion angle 40°, accuracy of attitude determination of optical axis/around optical axis 15/50 arcsec. Software and mathematical support are the most high technology parts of star tracker. The results of software and mathematical support development of experimental model of Kazakhstani star tracker are represented in this article. In particular, there are described the main mathematical models and algorithms that have been used as a basis for program units of preliminary image processing of starry sky, stars identification and star tracker attitude determination. The results of software and mathematical support testing with the help of program simulation complex using various configurations of defects including image sensor noises, point spread function modeling, optical system distortion up to 2% are presented. Analysis of testing results has shown that accuracy of attitude determination of star tracker is within the permissible range
Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.

PubMed

Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

2015-07-22

A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.
Reconstructing Norms

ERIC Educational Resources Information Center

Gorgorio, Nuria; Planas, Nuria

2005-01-01

Starting from the constructs "cultural scripts" and "social representations", and on the basis of the empirical research we have been developing until now, we revisit the construct norms from a sociocultural perspective. Norms, both sociomathematical norms and norms of the mathematical practice, as cultural scripts influenced…
Dog Mathematics: Exploring Base-4

ERIC Educational Resources Information Center

Kurz, Terri L.; Yanik, H. Bahadir; Lee, Mi Yeon

2016-01-01

Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.
RAETRAD MODEL OF RADON GAS GENERATION, TRANSPORT, AND INDOOR ENTRY

EPA Science Inventory

The report describes the theoretical basis, implementation, and validation of the Radon Emanation and Transport into Dwellings (RAETRAD) model, a conceptual and mathematical approach for simulating radon (222Rn) gas generation and transport from soils and building foundations to ...
Rational Density Functional Selection Using Game Theory.

PubMed

McAnanama-Brereton, Suzanne; Waller, Mark P

2018-01-22

Theoretical chemistry has a paradox of choice due to the availability of a myriad of density functionals and basis sets. Traditionally, a particular density functional is chosen on the basis of the level of user expertise (i.e., subjective experiences). Herein we circumvent the user-centric selection procedure by describing a novel approach for objectively selecting a particular functional for a given application. We achieve this by employing game theory to identify optimal functional/basis set combinations. A three-player (accuracy, complexity, and similarity) game is devised, through which Nash equilibrium solutions can be obtained. This approach has the advantage that results can be systematically improved by enlarging the underlying knowledge base, and the deterministic selection procedure mathematically justifies the density functional and basis set selections.
Computer programming in the UK undergraduate mathematics curriculum

NASA Astrophysics Data System (ADS)

Sangwin, Christopher J.; O'Toole, Claire

2017-11-01

This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016, programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first-year courses than a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination).
Complexity VIII. Ontology of closure in complex systems: The C* hypothesis and the O° notation

NASA Astrophysics Data System (ADS)

Chandler, Jerry LR

1999-03-01

Closure is a common characteristic of mathematical, natural and socio-cultural systems. Whether one is describing a graph, a molecule, a cell, a human, or a nation state, closure is implicitly understood. An objective of this paper is to continue a construction of a systematic framework for closure which is sufficient for future quantitative transdisciplinary investigations. A further objective is to extend the Birkhoff-von Neumann criterion for quantum systems to complex natural objects. The C* hypothesis is being constructed to be consistent with algebraic category theory (Ehresmann and Vanbremeersch, 1987, 1997, Chandler, 1990, 1991, Chandler, Ehresmann and Vanbremeersch, 1996). Five aspects of closure will be used to construct a framework for categories of complex systems: 1. Truth functions in mathematics and the natural sciences 2. Systematic descriptions in the mks and O° notations 3. Organizational structures in hierarchical scientific languages 4. Transitive organizational pathways in the causal structures of complex behaviors 5. Composing additive, multiplicative and exponential operations in complex systems Truth functions can be formal or objective or subjective, depending on the complexity of the system and on our capability to represent the fine structure of the system symbolically, observationally or descriptively. "Complete" material representations of the fine structure of a system may allow truth functions to be created over sets of one to one correspondences. Less complete descriptions can support less stringent truth functions based on coherence or subjective judgments. The role of human values in creating and perpetuating truth functions can be placed in context of the degree of fine structure in the system's description. The organization of complex systems are hypothesized to be categorizable into degrees relative to one another, thereby creating an ordering relationship. This ordering relationship is denoted by the symbols: O°1, O°2,O°3... For example, for material systems, an ordering relation such as particles, atoms, molecules, cells, tissues, organs, individuals and social groups might be assigned to classify observations for medical purposes. The C* hypothesis asserts that any complex system can be described in terms of four enumerable concepts: closure, conformation, concatenation and cyclicity. Mappings between objects are constructed within a notation for organization. Causality is organized within C* as pathways of relationships in time. The notation of organizational degrees is used to distinguish a directionality for causality: 1. bottom-up (energy flows) 2. top-down (control processes or dominating variables), 3. outside — inward (ecoment on organism) and 4. inside — outward (organism on ecoment). Closures are asserted to emerge from evolutionary cooperation. It is asserted that truth functions emerged from the necessity of an organism to identify ecoments where life can prosper. For example, basic truth functions of mathematics (operations of addition, multiplication and exponentiation) are made operationally consistent within the biochemical operations of sustaining exponential cellular growth. These fundamental mathematical functions can provide a logical basis (in conjunction with conservation rules) for a construction of complex material categories at higher degrees of organization. It is remarked that these simple functions suggests a biochemical origin for the intuitionistic philosophy of mathematics. The emergence and success of mathematics is conjectured to result from the need to acquire a consistent basis for communication among individuals seeking to cooperate socially. This suggests a cultural closure over a collection of individual closures.
Enhancing Parent Involvement in NC-CCSS for K-2 Mathematics

NASA Astrophysics Data System (ADS)

Johnson, D.

2014-12-01

Key Terms:Parent Involvement, Common Core State Standards, Homework, K - 2 Mathematics In this study, the 2014 REU math team developed and provided a workshop that assisted parents in understanding the North Carolina Common Core State Standards for K-2 Mathematics to assist with student homework assignments. Parent involvement is defined as parent participating in the educational processes and experiences of their children. A chi-square analysis was used to analyze data collected from the pre survey and the post survey administered to participants in the workshop. The study revealed all of the individual components of parent involvement were positively and significantly related to educational goals. The study identified various aspects of parent involvement that yielded statistically significant results in affirming that parent involvement attributed to urban student achievement. These findings were particularly helpful for indicating which kinds of parent involvement influenced academic success. Most notably, parent expectations and styles demonstrated a strong relationship with scholastic outcomes. Parent expectations and styles created an educationally oriented ambience that established an understanding of the certain level of support the child needed to succeed academically. The REU mathematics team focused on three essential questions in this study: (1) What practices will increase parent awareness of K-2 NC-CCSS for mathematics at P. W. Moore Elementary School? (2) What methods can be used to strengthen parent skills in assisting with mathematics homework assignments at P. W. Moore Elementary School? (3) What actions can be taken to motivate parent involvement in the school improvement process focusing on mathematics at P. W. Moore Elementary School?
A Conceptual Basis for Developing Common Curricula in Teacher Education Programs for Occupational Education. Graduate Studies in Education, Number 2, Volume 3.

ERIC Educational Resources Information Center

Courtney, E. Wayne

The purpose of this document was to generate a rationale and a design for planning a conceptual basis for developing common curriculums in vocational teacher education training programs. A review of the literature discusses heuristic approaches to teacher education, the rational basis for common programs, empirical studies in teacher education,…

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