Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

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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…

Embodied cognition, abstract concepts, and body manipulation

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Katinka eDijkstra

2014-08-01

Full Text Available Current approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through metaphor activation. Substantial research has been conducted on the activation of common orientational metaphors with bodily manipulations, such as ‘power is up’ and ‘more is up’ representations. We will focus on the political metaphor that has a more complex association between the concept and the concrete domain. However, the outcomes of studies on this political metaphor have not always been consistent, possibly because the experimental manipulation was not implicit enough. The inclusion of new technological devices in this area of research, such as the Wii Balance Board, seems promising in order to assess the groundedness of abstract conceptual spatial metaphors in an implicit manner. This may aid further research to effectively demonstrate the interrelatedness between the body and more abstract representations.

Improving students’ understanding of mathematical concept using maple

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Ningsih, Y. L.; Paradesa, R.

2018-01-01

This study aimed to improve students’ understanding of mathematical concept ability through implementation of using Maple in learning and expository learning. This study used a quasi-experimental research with pretest-posttest control group design. The sample on this study was 61 students in the second semester of Mathematics Education of Universitas PGRI Palembang, South Sumatera in academic year 2016/2017. The sample was divided into two classes, one class as the experiment class who using Maple in learning and the other class as a control class who received expository learning. Data were collective through the test of mathematical initial ability and mathematical concept understanding ability. Data were analyzed by t-test and two ways ANOVA. The results of this study showed (1) the improvement of students’ mathematical concept understanding ability who using Maple in learning is better than those who using expository learning; (2) there is no interaction between learning model and students’ mathematical initial ability toward the improvement of students’ understanding of mathematical concept ability.

Psychological effects and epistemological education through mathematics "abstraction" and "construction"

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Aurel Pera

2015-10-01

Full Text Available This study is part of a broader research which will be found in future work, Psychology and epistemology of mathematical creation, complementary work of experimental research psychology mathematics, whose investigative approach, promoting the combination type cross section paradigms and quantitative methods and qualitative and comparative method and the analytic-synthetic, based on the following idea: to make learning as efficient, contents and methods must be appropriate to the individual particularities of the pupils, a measure of the balance between converging and diverging dosing tasks as a promising opening to the transition from education proficiency in math performance. At this juncture, mathematical existence as ontological approach against the background of a history of "abstraction" mathematical and theoretical observations on the abstraction, realization and other mathematical thought processes, explanatory approach fulfills the context in which s mathematics constituted an important factor in psychological and methodological perspective, in a context of maximizing the educational effectiveness that depends on the quality of the methods used in teaching, focused on knowledge of the general principles of psycho-didactics not only mathematical and mental organization individual student or knowledge of the factors that make possible psycho-educational learning process.

Teachers' Conceptions of Mathematical Modeling

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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…

THE EFFECT OF SELF-CONCEPT ON THE MATHEMATICS LEARNING ACHIEVEMENT

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Rosliana Siregar

2018-05-01

Full Text Available Abstract. This study aims to determine the effect of self-concepts on mathematics learning achievement of students of class X at State Senior High School 14 Medan. The population in this study is all students of class X State Senior High School 14 Medan which amounted to 304 students. Technique of sampling using technique of Proportionate Stratified Random Sampling counted 40 student for research sample. Data collection using questionnaire method and documentation method. Data analysis technique used is regression analysis, correlation analysis and t test with significance level of 5%. Testing data in this study using the help of SPSS 15 for Windows program for each test result. The results showed that there is a significant influence between self-concept and mathematics learning achievement obtained from the t count (3,572> t table (1.68, with a probability significance of 0.01 <0.05. The magnitude of the determination coefficient of 25.1%

Adaptation and extension of the framework of reducing abstraction in the case of differential equations

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Raychaudhuri, Debasree

2014-01-01

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of reducing abstraction maps the abstract nature of mathematics to the nature of knowledge construction by offering three interpretations of how students reduce abstraction while learning mathematical concepts. We apply this framework to explain students' cognition processes as they construct the concept of solution to differential equations and related concepts during a semester long study. Additionally, we refine and extend the framework to elucidate various nuances of the interplay between mathematical structures and human thoughts.

Arche papers on the mathematics of abstraction

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Cook, Roy T

2007-01-01

This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege's enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in pre

Pacifier Overuse and Conceptual Relations of Abstract and Emotional Concepts.

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Barca, Laura; Mazzuca, Claudia; Borghi, Anna M

2017-01-01

This study explores the impact of the extensive use of an oral device since infancy (pacifier) on the acquisition of concrete, abstract, and emotional concepts. While recent evidence showed a negative relation between pacifier use and children's emotional competence (Niedenthal et al., 2012), the possible interaction between use of pacifier and processing of emotional and abstract language has not been investigated. According to recent theories, while all concepts are grounded in sensorimotor experience, abstract concepts activate linguistic and social information more than concrete ones. Specifically, the Words As Social Tools (WAT) proposal predicts that the simulation of their meaning leads to an activation of the mouth (Borghi and Binkofski, 2014; Borghi and Zarcone, 2016). Since the pacifier affects facial mimicry forcing mouth muscles into a static position, we hypothesize its possible interference on acquisition/consolidation of abstract emotional and abstract not-emotional concepts, which are mainly conveyed during social and linguistic interactions, than of concrete concepts. Fifty-nine first grade children, with a history of different frequency of pacifier use, provided oral definitions of the meaning of abstract not-emotional, abstract emotional, and concrete words. Main effect of concept type emerged, with higher accuracy in defining concrete and abstract emotional concepts with respect to abstract not-emotional concepts, independently from pacifier use. Accuracy in definitions was not influenced by the use of pacifier, but correspondence and hierarchical clustering analyses suggest that the use of pacifier differently modulates the conceptual relations elicited by abstract emotional and abstract not-emotional. While the majority of the children produced a similar pattern of conceptual relations, analyses on the few (6) children who overused the pacifier (for more than 3 years) showed that they tend to distinguish less clearly between concrete and

Pacifier Overuse and Conceptual Relations of Abstract and Emotional Concepts

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Laura Barca

2017-12-01

Full Text Available This study explores the impact of the extensive use of an oral device since infancy (pacifier on the acquisition of concrete, abstract, and emotional concepts. While recent evidence showed a negative relation between pacifier use and children's emotional competence (Niedenthal et al., 2012, the possible interaction between use of pacifier and processing of emotional and abstract language has not been investigated. According to recent theories, while all concepts are grounded in sensorimotor experience, abstract concepts activate linguistic and social information more than concrete ones. Specifically, the Words As Social Tools (WAT proposal predicts that the simulation of their meaning leads to an activation of the mouth (Borghi and Binkofski, 2014; Borghi and Zarcone, 2016. Since the pacifier affects facial mimicry forcing mouth muscles into a static position, we hypothesize its possible interference on acquisition/consolidation of abstract emotional and abstract not-emotional concepts, which are mainly conveyed during social and linguistic interactions, than of concrete concepts. Fifty-nine first grade children, with a history of different frequency of pacifier use, provided oral definitions of the meaning of abstract not-emotional, abstract emotional, and concrete words. Main effect of concept type emerged, with higher accuracy in defining concrete and abstract emotional concepts with respect to abstract not-emotional concepts, independently from pacifier use. Accuracy in definitions was not influenced by the use of pacifier, but correspondence and hierarchical clustering analyses suggest that the use of pacifier differently modulates the conceptual relations elicited by abstract emotional and abstract not-emotional. While the majority of the children produced a similar pattern of conceptual relations, analyses on the few (6 children who overused the pacifier (for more than 3 years showed that they tend to distinguish less clearly between

Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

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Misu, La; Ketut Budayasa, I.; Lukito, Agung

2018-03-01

This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

Discovering Mathematics with Magma Reducing the Abstract to the Concrete

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Bosma, Wieb

2006-01-01

With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning theoretical results.

Concept mapping learning strategy to enhance students' mathematical connection ability

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Hafiz, M.; Kadir, Fatra, Maifalinda

2017-05-01

The concept mapping learning strategy in teaching and learning mathematics has been investigated by numerous researchers. However, there are still less researchers who have scrutinized about the roles of map concept which is connected to the mathematical connection ability. Being well understood on map concept, it may help students to have ability to correlate one concept to other concept in order that the student can solve mathematical problems faced. The objective of this research was to describe the student's mathematical connection ability and to analyze the effect of using concept mapping learning strategy to the students' mathematical connection ability. This research was conducted at senior high school in Jakarta. The method used a quasi-experimental with randomized control group design with the total number was 72 students as the sample. Data obtained through using test in the post-test after giving the treatment. The results of the research are: 1) Students' mathematical connection ability has reached the good enough level category; 2) Students' mathematical connection ability who had taught with concept mapping learning strategy is higher than who had taught with conventional learning strategy. Based on the results above, it can be concluded that concept mapping learning strategycould enhance the students' mathematical connection ability, especially in trigonometry.

Abstract concepts, language and sociality: from acquisition to inner speech.

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Borghi, Anna M; Barca, Laura; Binkofski, Ferdinand; Tummolini, Luca

2018-08-05

The problem of representation of abstract concepts, such as 'freedom' and 'justice', has become particularly crucial in recent years, owing to the increased success of embodied and grounded views of cognition. We will present a novel view on abstract concepts and abstract words. Since abstract concepts do not have single objects as referents, children and adults might rely more on input from others to learn them; we, therefore, suggest that linguistic and social experience play an important role for abstract concepts. We will discuss evidence obtained in our and other laboratories showing that processing of abstract concepts evokes linguistic interaction and social experiences, leading to the activation of the mouth motor system. We will discuss the possible mechanisms that underlie this activation. Mouth motor system activation can be due to re-enactment of the experience of conceptual acquisition, which occurred through the mediation of language. Alternatively, it could be due to the re-explanation of the word meaning, possibly through inner speech. Finally, it can be due to a metacognitive process revealing low confidence in the meaning of our concepts. This process induces in us the need to rely on others to ask/negotiate conceptual meaning. We conclude that with abstract concepts language works as a social tool: it extends our thinking abilities and pushes us to rely on others to integrate our knowledge.This article is part of the theme issue 'Varieties of abstract concepts: development, use, and representation in the brain'. © 2018 The Author(s).

Construction of the mathematical concept of pseudo thinking students

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Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

2018-05-01

Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

An Exploratory Study of Taiwanese Mathematics Teachers' Conceptions of School Mathematics, School Statistics, and Their Differences

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Yang, Kai-Lin

2014-01-01

This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and…

Self-concept mediates the relation between achievement and emotions in mathematics.

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Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M

2017-09-01

Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. The aims were (1) to investigate the mediating role of mathematical self-concept in the relation between mathematics achievement and the achievement emotions of enjoyment and anxiety in a comprehensive model, and (2) to test possible differences in this mediating role between low-, average-, and high-achieving students. Participants were ninth-grade students (n = 1,014) from eight secondary schools in the Netherlands. Through an online survey including mathematical problems, students were asked to indicate their levels of mathematics enjoyment, anxiety, and self-concept. Structural equation modelling was used to test the mediating role of self-concept in the relation between mathematics achievement and emotions. Multigroup analyses were performed to compare these relations across the three achievement groups. Results confirmed full mediation of the relation between mathematics achievement and emotions by mathematical self-concept. Furthermore, we found higher self-concepts, more enjoyment and less math anxiety in high-achieving students compared to their average and low-achieving peers. No differences across these achievement groups were found in the relations in the mediational model. Mathematical self-concept plays a pivotal role in students' appraisal of mathematics. Mathematics achievement is only one factor explaining students' self-concept. Likely also classroom instruction and teachers' feedback strategies help to shape students' self-concept. © 2017 The British Psychological Society.

Abstract spatial concept priming dynamically influences real-world actions

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Sarah M Tower-Richardi

2012-09-01

Full Text Available Experienced regularities in our perceptions and actions play important roles in grounding abstract concepts such as social status, time, and emotion. Might we similarly ground abstract spatial concepts in more experienced-based domains? The present experiment explores this possibility by implicitly priming abstract spatial terms (north, south, east, west and then measuring participants’ hand movement trajectories while they respond to a body-referenced spatial target (up, down, left, right in a verbal (Exp. 1 or spatial (Exp. 2 format. Results from two experiments demonstrate temporally-dynamic and prime-biased movement trajectories when the primes are incongruent with the targets (e.g., north – left, west – up. That is, priming abstract coordinate directions influences subsequent actions in response to concrete target directions. These findings provide the first evidence that abstract concepts of world-centered coordinate axes are implicitly understood in the context of concrete body-referenced axes; critically, this abstract-concrete relationship manifests in motor movements, and may have implications for spatial memory organization.

Mathematical Abstraction in the Solving of Ill-Structured Problems by Elementary School Students in Korea

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Hong, Jee Yun; Kim, Min Kyeong

2016-01-01

Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…

Proofs and fundamentals a first course in abstract mathematics

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Bloch, Ethan D

2003-01-01

In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for­ mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces­ sively pedagogical, and too full to distractions. Some of ...

Crafting by concepts fiber arts and mathematics

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Belcastro, Sarah-Marie

2016-01-01

From the editors of the popular Making Mathematics with Needlework, this book presents projects that highlight the relationship between types of needlework and mathematics. Chapters start with accessible overviews presenting the interplay between mathematical concepts and craft expressions. Following sections explain the mathematics in more detail, and provide suggestions for classroom activities. Each chapter ends with specific crafting instructions. Types of needlework included are knitting, crochet, needlepoint, cross-stitch, quilting, temari balls, beading, tatting, and string art. Instructions are written as ordinary patterns, so the formatting and language will be familiar to crafters.

On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

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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.

Teaching Abstract Concepts: Keys to the World of Ideas.

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Flatley, Joannis K.; Gittinger, Dennis J.

1990-01-01

Specific teaching strategies to help hearing-impaired secondary students comprehend abstract concepts include (1) pinpointing facts and fallacies, (2) organizing information visually, (3) categorizing ideas, and (4) reinforcing new vocabulary and concepts. Figures provide examples of strategy applications. (DB)

Using Group Explorer in Teaching Abstract Algebra

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Schubert, Claus; Gfeller, Mary; Donohue, Christopher

2013-01-01

This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in…

Mathematics Undergraduates' Responses to Semantic Abbreviations, 'Geometric' Images and Multi-Level Abstractions in Group Theory.

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Nardi, Elena

2000-01-01

Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…

Moral concepts set decision strategies to abstract values.

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Svenja Caspers

Full Text Available Persons have different value preferences. Neuroimaging studies where value-based decisions in actual conflict situations were investigated suggest an important role of prefrontal and cingulate brain regions. General preferences, however, reflect a superordinate moral concept independent of actual situations as proposed in psychological and socioeconomic research. Here, the specific brain response would be influenced by abstract value systems and moral concepts. The neurobiological mechanisms underlying such responses are largely unknown. Using functional magnetic resonance imaging (fMRI with a forced-choice paradigm on word pairs representing abstract values, we show that the brain handles such decisions depending on the person's superordinate moral concept. Persons with a predominant collectivistic (altruistic value system applied a "balancing and weighing" strategy, recruiting brain regions of rostral inferior and intraparietal, and midcingulate and frontal cortex. Conversely, subjects with mainly individualistic (egocentric value preferences applied a "fight-and-flight" strategy by recruiting the left amygdala. Finally, if subjects experience a value conflict when rejecting an alternative congruent to their own predominant value preference, comparable brain regions are activated as found in actual moral dilemma situations, i.e., midcingulate and dorsolateral prefrontal cortex. Our results demonstrate that superordinate moral concepts influence the strategy and the neural mechanisms in decision processes, independent of actual situations, showing that decisions are based on general neural principles. These findings provide a novel perspective to future sociological and economic research as well as to the analysis of social relations by focusing on abstract value systems as triggers of specific brain responses.

Moral Concepts Set Decision Strategies to Abstract Values

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Caspers, Svenja; Heim, Stefan; Lucas, Marc G.; Stephan, Egon; Fischer, Lorenz; Amunts, Katrin; Zilles, Karl

2011-01-01

Persons have different value preferences. Neuroimaging studies where value-based decisions in actual conflict situations were investigated suggest an important role of prefrontal and cingulate brain regions. General preferences, however, reflect a superordinate moral concept independent of actual situations as proposed in psychological and socioeconomic research. Here, the specific brain response would be influenced by abstract value systems and moral concepts. The neurobiological mechanisms underlying such responses are largely unknown. Using functional magnetic resonance imaging (fMRI) with a forced-choice paradigm on word pairs representing abstract values, we show that the brain handles such decisions depending on the person's superordinate moral concept. Persons with a predominant collectivistic (altruistic) value system applied a “balancing and weighing” strategy, recruiting brain regions of rostral inferior and intraparietal, and midcingulate and frontal cortex. Conversely, subjects with mainly individualistic (egocentric) value preferences applied a “fight-and-flight” strategy by recruiting the left amygdala. Finally, if subjects experience a value conflict when rejecting an alternative congruent to their own predominant value preference, comparable brain regions are activated as found in actual moral dilemma situations, i.e., midcingulate and dorsolateral prefrontal cortex. Our results demonstrate that superordinate moral concepts influence the strategy and the neural mechanisms in decision processes, independent of actual situations, showing that decisions are based on general neural principles. These findings provide a novel perspective to future sociological and economic research as well as to the analysis of social relations by focusing on abstract value systems as triggers of specific brain responses. PMID:21483767

Incorporating Learning Motivation and Self-Concept in Mathematical Communicative Ability

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Rajagukguk, Waminton

2016-01-01

This research is trying to determine of the mathematical concepts, instead by integrating the learning motivation (X[subscript 1]) and self-concept (X[subscript 2]) can contribute to the mathematical communicative ability (Y). The test instruments showed the following results: (1) simple regressive equation Y on X[subscript 1] was Y = 32.891 +…

Mathematical concepts of optical superresolution

International Nuclear Information System (INIS)

Lindberg, Jari

2012-01-01

Optical imaging beyond the diffraction limit, i.e., optical superresolution, has been studied extensively in various contexts. This paper presents an overview of some mathematical concepts relevant to superresolution in linear optical systems. Properties of bandlimited functions are surveyed and are related to both instrumental and computational aspects of superresolution. The phenomenon of superoscillation and its relation to superresolution are discussed. (review article)

Structural Modeling for Influence of Mathematics Self-Concept, Motivation to Learn Mathematics and Self-Regulation Learning on Mathematics Academic Achievement

OpenAIRE

Hamideh Jafari Koshkouei; Ahmad Shahvarani; Mohammad Hassan Behzadi; Mohsen Rostamy-Malkhalifeh

2016-01-01

The present study was carried out to investigate the influence of mathematics self-concept (MSC), motivation to learn mathematics (SMOT) and self-regulation learning (SRL) on students' mathematics academic achievement. This study is of a descriptive survey type. 300 female students at the first grade of high school (the second period) in City Qods, were selected by multiple step cluster sampling method and completed MSC, SMOT and SRL questionnaires. Mathematics academic achievement was measur...

Public Conceptions of Algorithms and Representations in the Common Core State Standards for Mathematics

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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…

Guide to mathematical concepts of quantum theory

International Nuclear Information System (INIS)

Heinosaari, T.; Ziman, M.

2008-01-01

Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory (Authors)

Guide to mathematical concepts of quantum theory

International Nuclear Information System (INIS)

Heinosaari, T.; Ziman, M.

2008-01-01

Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory. (author)

Mathematical modelling in engineering: A proposal to introduce linear algebra concepts

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Andrea Dorila Cárcamo

2016-03-01

Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts:  span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.

The Vector Space as a Unifying Concept in School Mathematics.

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Riggle, Timothy Andrew

The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

Naming a Lego world. The role of language in the acquisition of abstract concepts.

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Granito, Carmen; Scorolli, Claudia; Borghi, Anna Maria

2015-01-01

While embodied approaches of cognition have proved to be successful in explaining concrete concepts and words, they have more difficulties in accounting for abstract concepts and words, and several proposals have been put forward. This work aims to test the Words As Tools proposal, according to which both abstract and concrete concepts are grounded in perception, action and emotional systems, but linguistic information is more important for abstract than for concrete concept representation, due to the different ways they are acquired: while for the acquisition of the latter linguistic information might play a role, for the acquisition of the former it is instead crucial. We investigated the acquisition of concrete and abstract concepts and words, and verified its impact on conceptual representation. In Experiment 1, participants explored and categorized novel concrete and abstract entities, and were taught a novel label for each category. Later they performed a categorical recognition task and an image-word matching task to verify a) whether and how the introduction of language changed the previously formed categories, b) whether language had a major weight for abstract than for concrete words representation, and c) whether this difference had consequences on bodily responses. The results confirm that, even though both concrete and abstract concepts are grounded, language facilitates the acquisition of the latter and plays a major role in their representation, resulting in faster responses with the mouth, typically associated with language production. Experiment 2 was a rating test aiming to verify whether the findings of Experiment 1 were simply due to heterogeneity, i.e. to the fact that the members of abstract categories were more heterogeneous than those of concrete categories. The results confirmed the effectiveness of our operationalization, showing that abstract concepts are more associated with the mouth and concrete ones with the hand, independently from

Naming a Lego world. The role of language in the acquisition of abstract concepts.

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Carmen Granito

Full Text Available While embodied approaches of cognition have proved to be successful in explaining concrete concepts and words, they have more difficulties in accounting for abstract concepts and words, and several proposals have been put forward. This work aims to test the Words As Tools proposal, according to which both abstract and concrete concepts are grounded in perception, action and emotional systems, but linguistic information is more important for abstract than for concrete concept representation, due to the different ways they are acquired: while for the acquisition of the latter linguistic information might play a role, for the acquisition of the former it is instead crucial. We investigated the acquisition of concrete and abstract concepts and words, and verified its impact on conceptual representation. In Experiment 1, participants explored and categorized novel concrete and abstract entities, and were taught a novel label for each category. Later they performed a categorical recognition task and an image-word matching task to verify a whether and how the introduction of language changed the previously formed categories, b whether language had a major weight for abstract than for concrete words representation, and c whether this difference had consequences on bodily responses. The results confirm that, even though both concrete and abstract concepts are grounded, language facilitates the acquisition of the latter and plays a major role in their representation, resulting in faster responses with the mouth, typically associated with language production. Experiment 2 was a rating test aiming to verify whether the findings of Experiment 1 were simply due to heterogeneity, i.e. to the fact that the members of abstract categories were more heterogeneous than those of concrete categories. The results confirmed the effectiveness of our operationalization, showing that abstract concepts are more associated with the mouth and concrete ones with the hand

Embodied cognition, abstract concepts, and the benefits of new technology for implicit body manipulation

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Dijkstra, K.; Eerland, A.; Zijlmans, J.; Post, L.S.

2014-01-01

Current approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through metaphor

Embodied cognition, abstract concepts, and the benefits of new technology for implicit body manipulation

NARCIS (Netherlands)

K. Dijkstra (Katinka); A. Eerland (Anita); J. Zijlmans (Josjan); L.S. Post (Lysanne)

2014-01-01

textabstractCurrent approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through

Exploring teachers’ conceptions of representations in mathematics through the lens of positive deliberative interaction

OpenAIRE

Deonarain Brijlall; Sarah Bansilal; Deborah Moore-Russo

2012-01-01

This article reports on an exploration of teachers’ views on the meaning of mathematical representations in a democratic South Africa. We explored teachers’ conceptions of ‘mathematical representations’ as a means to promote dialogue and negotiation. These conceptions helped us to gauge how these teachers viewed representations in mathematics. Semi-structured questionnaires were administered to 76 high school mathematics teachers who were registered for an upgrading mathematics education...

Designing an image retrieval interface for abstract concepts within the domain of journalism

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R. Besseling (Ron)

2011-01-01

htmlabstractResearch has shown that users have difficulties finding images which illustrate abstract concepts. We carried out a user study that confirms the finding that the selection of search terms is perceived difficult and that users find the subjectivity of abstract concepts problematic. In

Developing self-concept instrument for pre-service mathematics teachers

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Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

2018-01-01

This study aimed to develop self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia. Type of this study was development research of non-test instrument in questionnaire form. A Validity test of the instrument was performed with construct validity test by using Pearson product moment and factor analysis, while reliability test used Cronbach’s alpha. The instrument was tested by 65 undergraduate students of mathematics education in one of the universities at Palembang, Indonesia. The instrument consisted of 43 items with 7 aspects of self-concept, that were the individual concern, social identity, individual personality, view of the future, the influence of others who become role models, the influence of the environment inside or outside the classroom, and view of the mathematics. The result of validity test showed there was one invalid item because the value of Pearson’s r was 0.107 less than the critical value (0.244; α = 0.05). The item was included in social identity aspect. After the invalid item was removed, Construct validity test with factor analysis generated only one factor. The Kaiser-Meyer-Olkin (KMO) coefficient was 0.846 and reliability coefficient was 0.91. From that result, we concluded that the self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia was valid and reliable with 42 items.

Are Abstract and Concrete Concepts Organized Differently? Evidence from the Blocked Translation Paradigm

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Zhang, Xiaohong; Han, Zaizhu; Bi, Yanchao

2013-01-01

Using the blocked-translation paradigm with healthy participants, we examined Crutch and Warrington's hypothesis that concrete and abstract concepts are organized by distinct principles: concrete concepts by semantic similarities and abstract ones by associations. In three experiments we constructed two types of experimental blocking (similar…

Development of abstract mathematical reasoning: the case of algebra.

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Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

2014-01-01

Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.

Games in the mathematics curriculum: Some conceptions and ...

African Journals Online (AJOL)

Games in the mathematics curriculum: Some conceptions and experiences of teachers in the Upper West Region of Ghana. ... The study investigated primary school teachers' experiences with games as ... AJOL African Journals Online.

Key Concept Mathematics and Management Science Models

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Macbeth, Thomas G.; Dery, George C.

1973-01-01

The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)

Exploring teachers’ conceptions of representations in mathematics through the lens of positive deliberative interaction

Directory of Open Access Journals (Sweden)

Deonarain Brijlall

2012-12-01

Full Text Available This article reports on an exploration of teachers’ views on the meaning of mathematical representations in a democratic South Africa. We explored teachers’ conceptions of ‘mathematical representations’ as a means to promote dialogue and negotiation. These conceptions helped us to gauge how these teachers viewed representations in mathematics. Semi-structured questionnaires were administered to 76 high school mathematics teachers who were registered for an upgrading mathematics education qualification at a South African university. Common themes in teacher conceptions of representations were investigated as part of an inductive analysis of the written responses, which were considered in terms of practices that support dialogue and negotiation. Findings suggest that these conceptions are in line with progressive notions of classroom interactions such as the inquiry cooperation model. Furthermore, the findings suggest that teachers can support the development of classroom environments that promote democratic values.

Prospective Mathematics Teachers' Understanding of the Base Concept

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Horzum, Tugba; Ertekin, Erhan

2018-01-01

The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers (PMTs) have about the base concept (BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn…

Secondary School Mathematics in Perspective: Conceptions of its Nature and Relevance.

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Frid, Sandra; White, Loren

This study investigated the nature of secondary school students' and teachers' conceptions of what mathematics is, the purposes of school mathematics, and the outcomes of school mathematics. Interviews were conducted with a sample of grades 10, 11, and 12 students (n=40), teachers (n=19), counselors (n=2), and administrators (n=2) from a large…

An Investigation of Mathematical Knowledge Related to Mathematics Teachers' Basic Concepts in Sets Unit

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Nurullah YAZICI

2017-05-01

Full Text Available This research was conducted in order to examine the subject matter of Mathematics teachers in the context of "Mathematical Knowledge For Teaching" (MKT model of "Basic Concepts in Sets" which is the first topic of the 9th class "Sets". The study group, which is one of the qualitative research methods, used the case study design, constitutes 5 mathematics teachers who work in different education levels (primary and secondary education in the academic year of 2015-2016. Open-ended questions and semi-structured interview form developed by the researcher were used for data collection. A descriptive analysis technique was used to analyze the data obtained through interviews. While analyzing the data, teacher and student textbooks, which were prepared by the Ministry of National Education for the purpose of teaching in 2015-2016 academic year, were taken as a reference. According to the research findings, it was determined that the teachers had deficiencies in the subject field of "Basic Concepts in the Sets" and had superficial knowledge rather than in depth knowledge.

Abstract memory representations in the ventromedial prefrontal cortex and hippocampus support concept generalization.

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Bowman, Caitlin R; Zeithamova, Dagmar

2018-02-07

Memory function involves both the ability to remember details of individual experiences and the ability to link information across events to create new knowledge. Prior research has identified the ventromedial prefrontal cortex (VMPFC) and the hippocampus as important for integrating across events in service of generalization in episodic memory. The degree to which these memory integration mechanisms contribute to other forms of generalization, such as concept learning, is unclear. The present study used a concept-learning task in humans (both sexes) coupled with model-based fMRI to test whether VMPFC and hippocampus contribute to concept generalization, and whether they do so by maintaining specific category exemplars or abstract category representations. Two formal categorization models were fit to individual subject data: a prototype model that posits abstract category representations and an exemplar model that posits category representations based on individual category members. Latent variables from each of these models were entered into neuroimaging analyses to determine whether VMPFC and the hippocampus track prototype or exemplar information during concept generalization. Behavioral model fits indicated that almost three quarters of the subjects relied on prototype information when making judgments about new category members. Paralleling prototype dominance in behavior, correlates of the prototype model were identified in VMPFC and the anterior hippocampus with no significant exemplar correlates. These results indicate that the VMPFC and portions of the hippocampus play a broad role in memory generalization and that they do so by representing abstract information integrated from multiple events. SIGNIFICANCE STATEMENT Whether people represent concepts as a set of individual category members or by deriving generalized concept representations abstracted across exemplars has been debated. In episodic memory, generalized memory representations have been shown

Self-concept mediates the relation between achievement and emotions in mathematics

NARCIS (Netherlands)

Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M

BACKGROUND: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions.

Self-concept mediates the relation between achievement and emotions in mathematics

NARCIS (Netherlands)

Beek, J.P.J. van der; Ven, S.H.G. van der; Kroesbergen, E.H.; Leseman, P.P.M.

2017-01-01

Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions.

Mathematical modeling

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Eck, Christof; Knabner, Peter

2017-01-01

Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

Mathematical writing

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Vivaldi, Franco

2014-01-01

This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.   The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.   Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...

Prospective Mathematics Teachers' Ability to Identify Mistakes Related to Angle Concept of Sixth Grade Students

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Arslan, Cigdem; Erbay, Hatice Nur; Guner, Pinar

2017-01-01

In the present study we try to highlight prospective mathematics teachers' ability to identify mistakes of sixth grade students related to angle concept. And also we examined prospective mathematics teachers' knowledge of angle concept. Study was carried out with 30 sixth-grade students and 38 prospective mathematics teachers. Sixth grade students…

Sociocultural context as a facilitator of student learning of function concepts in mathematics

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Evangelina Díaz Obando

2016-03-01

Full Text Available In Costa Rica, many secondary students have serious difficulties to establish relationships between mathematics and real-life contexts. They question the utilitarian role of the school mathematics. This fact motivated the research object of this report which evidences the need to overcome methodologies unrelated to students’ reality, toward new didactical options that help students to value mathematics, reasoning and its  applications, connecting it with their socio-cultural context. The research used a case study as a qualitative methodology and the social constructivism as an educational paradigm in which the knowledge is built by the student; as a product of his social interactions. A collection of learning situations was designed, validated, and implemented. It allowed establishing relationships between mathematical concepts and the socio-cultural context of participants. It analyzed the impact of students’socio-cultural context in their mathematics learning of basic concepts of real variable functions, consistent with the Ministry of Education (MEP Official Program.  Among the results, it was found that using students’sociocultural context improved their motivational processes, mathematics sense making, and promoted cooperative social interactions. It was evidenced that contextualized learning situations favored concepts comprehension that allow students to see mathematics as a discipline closely related with their every-day life.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

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Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

Mathematical knowledge in teaching of fraction concepts using diagrammatical approach

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Veloo, Palanisamy Kathir; Puteh, Marzita

2017-05-01

Teachers need various types of knowledge in order to deliver various fraction concepts at elementary level. In this paper, Balls' framework (2008) or, Mathematical Knowledge for Teaching (MKT) is used as benchmark guideline. This paper investigates and explores component of MKT knowledge among eight experienced teachers of the primary school. Data was collected using paper pencil test, interview and video recording. This paper, narrowed to teacher's knowledge and their practices while teaching of various fractions concepts using diagrammatical approach in present of MKT. The data gathered from teachers were analyzed using thematic analysis techniques. The results indicated that teachers lack various components of MKT knowledge as a proposal by various researchers and assumed that teaching as procedural more than enough due to lack of deep understanding of mathematics and the various types of MKT is not required due to the present of practices in the mathematics classroom.

Prospective elementary teachers' conceptions of multidigit number: exemplifying a replication framework for mathematics education

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Jacobson, Erik; Simpson, Amber

2018-04-01

Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser's (Educational Studies in Mathematics 75:241-251, 2010) study of prospective elementary teachers' conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers' conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology.

Embodied cognition, abstract concepts, and the benefits of new technology for implicit body manipulation

Science.gov (United States)

Dijkstra, Katinka; Eerland, Anita; Zijlmans, Josjan; Post, Lysanne S.

2014-01-01

Current approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through metaphor activation. Substantial research has been conducted on the activation of common orientational metaphors with bodily manipulations, such as “power is up” and “more is up” representations. We will focus on the political metaphor that has a more complex association between the concept and the concrete domain. However, the outcomes of studies on this political metaphor have not always been consistent, possibly because the experimental manipulation was not implicit enough. The inclusion of new technological devices in this area of research, such as the Wii Balance Board, seems promising in order to assess the groundedness of abstract conceptual spatial metaphors in an implicit manner. This may aid further research to effectively demonstrate the interrelatedness between the body and more abstract representations. PMID:25191282

Non-Determinism: An Abstract Concept in Computer Science Studies

Science.gov (United States)

Armoni, Michal; Gal-Ezer, Judith

2007-01-01

Non-determinism is one of the most important, yet abstract, recurring concepts of Computer Science. It plays an important role in Computer Science areas such as formal language theory, computability theory, distributed computing, and operating systems. We conducted a series of studies on the perception of non-determinism. In the current research,…

Self-Concept Mediates the Relation between Achievement and Emotions in Mathematics

Science.gov (United States)

Van der Beek, Jojanneke P. J.; Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Leseman, Paul P. M.

2017-01-01

Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. Aims: The aims were (1) to investigate the…

Students' Conceptions of Function Transformation in a Dynamic Mathematical Environment

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Daher, Wajeeh; Anabousy, Ahlam

2015-01-01

The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…

The concept of stability in numerical mathematics

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Hackbusch, Wolfgang

2014-01-01

In this book, the author compares the meaning of stability in different subfields of numerical mathematics.  Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.  

Abstracting Concepts and Methods.

Science.gov (United States)

Borko, Harold; Bernier, Charles L.

This text provides a complete discussion of abstracts--their history, production, organization, publication--and of indexing. Instructions for abstracting are outlined, and standards and criteria for abstracting are stated. Management, automation, and personnel are discussed in terms of possible economies that can be derived from the introduction…

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

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Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

Abstraction of complex concepts with a refined partial-area taxonomy of SNOMED

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Wang, Yue; Halper, Michael; Wei, Duo; Perl, Yehoshua; Geller, James

2012-01-01

An algorithmically-derived abstraction network, called the partial-area taxonomy, for a SNOMED hierarchy has led to the identification of concepts considered complex. The designation “complex” is arrived at automatically on the basis of structural analyses of overlap among the constituent concept groups of the partial-area taxonomy. Such complex concepts, called overlapping concepts, constitute a tangled portion of a hierarchy and can be obstacles to users trying to gain an understanding of the hierarchy’s content. A new methodology for partitioning the entire collection of overlapping concepts into singly-rooted groups, that are more manageable to work with and comprehend, is presented. Different kinds of overlapping concepts with varying degrees of complexity are identified. This leads to an abstract model of the overlapping concepts called the disjoint partial-area taxonomy, which serves as a vehicle for enhanced, high-level display. The methodology is demonstrated with an application to SNOMED’s Specimen hierarchy. Overall, the resulting disjoint partial-area taxonomy offers a refined view of the hierarchy’s structural organization and conceptual content that can aid users, such as maintenance personnel, working with SNOMED. The utility of the disjoint partial-area taxonomy as the basis for a SNOMED auditing regimen is presented in a companion paper. PMID:21878396

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

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Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

How Preservice Teachers Use Children’s Literature to Teach Mathematical Concepts: Focus on Mathematical Knowledge for Teaching

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Jennifer EDELMAN

2017-06-01

Full Text Available This descriptive study examines the elements of mathematical knowledge for teaching (MKT that elementary teacher candidates exhibit as they plan, teach, and reflect on a mathematics lesson that integrates children’s literature. Data for this study were gathered from observations and written work of preservice elementary teacher candidates enrolled in a methods of teaching mathematics course. The data were analyzed using three criteria: that of knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. The findings suggest a need for further development of teacher candidates’ ability to identify and locate mathematical concepts in children’s literature, as well as the need for supporting teacher candidates’ critical analysis of curricular materials and mathematical representations in children’s literature.

How preservice teachers use children’s literature to teach mathematical concepts: Focus on mathematical knowledge for teaching

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Jennifer Edelman

2017-06-01

Full Text Available This descriptive study examines the elements of mathematical knowledge for teaching (MKT that elementary teacher candidates exhibit as they plan, teach, and reflect on a mathematics lesson that integrates children’s literature. Data for this study were gathered from observations and written work of preservice elementary teacher candidates enrolled in a methods of teaching mathematics course. The data were analyzed using three criteria: that of knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. The findings suggest a need for further development of teacher candidates’ ability to identify and locate mathematical concepts in children’s literature, as well as the need for supporting teacher candidates’ critical analysis of curricular materials and mathematical representations in children’s literature.

Mathematics and art a cultural history

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Gamwell, Lynn

2016-01-01

This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows t...

Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

Science.gov (United States)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

The big-fish-little-pond effect on mathematics self-concept: Evidence from the United Arab Emirates.

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Areepattamannil, Shaljan; Khine, Myint Swe; Al Nuaimi, Samira

2017-08-01

This study examined the big-fish-little-pond effect (BFLPE; Marsh, 1987) on mathematics self-concept of 7404 adolescents (female = 3767 [51%], male = 3637 [49%]; M age  = 15.85 years, SD = 0.28) from 456 schools in the United Arab Emirates, one of the Arab states of the Persian Gulf. The results of multilevel regression analyses indicated good support for the BFLPE's theoretical predictions: the effect of individual student mathematics achievement on individual student mathematics self-concept was positive and statistically significant, whereas the effect of school-average mathematics achievement on individual student mathematics self-concept was negative and statistically significant. Moreover, the interaction between school-average mathematics achievement and individual student mathematics achievement was small and non-significant. Implications of the findings for policy and practice are briefly discussed. Copyright © 2017 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

The origin of the logic of symbolic mathematics Edmund Husserl and Jacob Klein

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Hopkins, Burt C

2011-01-01

Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical abstraction that generates them-have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

Virtual Manipulatives: Tools for Teaching Mathematics to Students with Learning Disabilities

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Shin, Mikyung; Bryant, Diane P.; Bryant, Brian R.; McKenna, John W.; Hou, Fangjuan; Ok, Min Wook

2017-01-01

Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models)…

Temporal Dynamics of Task Switching and Abstract-Concept Learning in Pigeons

Directory of Open Access Journals (Sweden)

Thomas Alexander Daniel

2015-09-01

Full Text Available The current study examined whether pigeons could learn to use abstract concepts as the basis for conditionally switching behavior as a function of time. Using a mid-session reversal task, experienced pigeons were trained to switch from matching-to-sample (MTS to non-matching-to-sample (NMTS conditional discriminations within a session. One group had prior training with MTS, while the other had prior training with NMTS. Over training, stimulus set size was progressively doubled from 3 to 6 to 12 stimuli to promote abstract concept development. Prior experience had an effect on the initial learning at each of the set sizes but by the end of training there were no group differences, as both groups showed similar within-session linear matching functions. After acquiring the 12-item set, abstract-concept learning was tested by placing novel stimuli at the beginning and end of a test session. Prior matching and non-matching experience affected transfer behavior. The matching experienced group transferred to novel stimuli in both the matching and non-matching portion of the sessions using a matching rule. The non-matching experienced group transferred to novel stimuli in both portions of the session using a non-matching rule. The representations used as the basis for mid-session reversal of the conditional discrimination behaviors and subsequent transfer behavior appears to have different temporal sources. The implications for the flexibility and organization of complex behaviors are considered.

Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts

Science.gov (United States)

Marzocchi, Alison S.

2016-01-01

This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…

Il Concetto di Infinito nell'Intuizione Matematica (Concept of Infinity in Mathematical Intuition).

Science.gov (United States)

Ferrari, E.; And Others

1995-01-01

Investigated the acquisition and maturation of the infinity concept in mathematics of students ages 13-15. Found the infinity concept is learned by students only when provided with appropriate guidance. (Author/MKR)

Undergraduate Mathematics Students' Understanding of the Concept of Function

Science.gov (United States)

Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah

2014-01-01

Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…

The enhancement of mathematical analogical reasoning ability of university students through concept attainment model

Science.gov (United States)

Angraini, L. M.; Kusumah, Y. S.; Dahlan, J. A.

2018-05-01

This study aims to see the enhancement of mathematical analogical reasoning ability of the university students through concept attainment model learning based on overall and Prior Mathematical Knowledge (PMK) and interaction of both. Quasi experiments with the design of this experimental-controlled equivalent group involved 54 of second semester students at the one of State Islamic University. The instrument used is pretest-postest. Kolmogorov-Smirnov test, Levene test, t test, two-way ANOVA test were used to analyse the data. The result of this study includes: (1) The enhancement of the mathematical analogical reasoning ability of the students who gets the learning of concept attainment model is better than the enhancement of the mathematical analogical reasoning ability of the students who gets the conventional learning as a whole and based on PMK; (2) There is no interaction between the learning that is used and PMK on enhancing mathematical analogical reasoning ability.

Using the virtual-abstract instructional sequence to teach addition of fractions.

Science.gov (United States)

Bouck, Emily C; Park, Jiyoon; Sprick, Jessica; Shurr, Jordan; Bassette, Laura; Whorley, Abbie

2017-11-01

Limited literature examines mathematics education for students with mild intellectual disability. This study investigated the effects of using the Virtual-Abstract instructional sequenceto teach middle school students, predominantly with mild intellectual disability, to add fractions of unlike denominators. Researchers used a multiple probe across participants design to determine if a functional relation existed between the Virtual-Abstract instructional sequence strategy and students' ability to add fractions with unlike denominators. The study of consisted of three-to-nine baseline sessions, 6-11 intervention sessions, and two maintenance sessions for each student. Data were collected on accuracy across five addition of fractions with unlike denominators problems. The VA instructional strategy was effective in thestudents to add fractions with unlike denominators; a functional relation existed between the VA instructional sequence and adding fractions with unlike denominators for three of the four students. The Virtual-Abstract instructional sequencemay be appropriate to support students with mild intellectual disability in learning mathematics, especially when drawing or representing the mathematical concepts may prove challenging. Copyright © 2017 Elsevier Ltd. All rights reserved.

A mathematics course for political and social research

CERN Document Server

Moore, Will H

2013-01-01

Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a ""math camp"" or a semester-long or yearlong course to acquire the necessary skills. Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social s

An introduction to abstract algebra

CERN Document Server

Robinson, Derek JS

2003-01-01

This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader''s skill and progress. The book should be suitable for students ...

Mathematical Concepts and Proofs from Nicole Oresme: Using the History of Calculus to Teach Mathematics

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Babb, Jeff

2005-01-01

This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…

EFFECTIVENESS OF COOPERATIVE LEARNING IN IMPROVING MATHEMATICAL CONCEPTS AMONG STUDENTS WITH MILD INTELLECTUAL DISABILITY

OpenAIRE

Ibrahim Rajab Abbas Ibrahim

2017-01-01

The purpose of this study was to identify the effectiveness of cooperative learning in improving mathematical concepts among students with mild intellectual disability (SMID). The sample of the study consisted of 8 SMID at Najran in the Kingdom of Saudi Arabia. The sample of the study was divided randomly into two equal groups control and experimental. The students in the experimental group have studied the mathematical concepts by using cooperative learning; however the students in the contr...

LOGO programming contents for supporting mathematical concept development : promotion of the verbalization and imaging of figure concepts

OpenAIRE

杉野, 裕子

2014-01-01

I have been studying to show the importance of adopting a programming in the mathematical education and developed the LOGO teaching materials which is made good use of in the field of Euclidean geometry, in order to improve understanding and learning figure concepts. The present article offers a theoretical framework with consistency about my study and also new programming materials in which I embody my theory. I consider logically the system of mathematical expression with computers and espe...

Learning and Processing Abstract Words and Concepts: Insights From Typical and Atypical Development.

Science.gov (United States)

Vigliocco, Gabriella; Ponari, Marta; Norbury, Courtenay

2018-05-21

The paper describes two plausible hypotheses concerning the learning of abstract words and concepts. According to a first hypothesis, children would learn abstract words by extracting co-occurrences among words in linguistic input, using, for example, mechanisms as described by models of Distributional Semantics. According to a second hypothesis, children would exploit the fact that abstract words tend to have more emotional associations than concrete words to infer that they refer to internal/mental states. Each hypothesis makes specific predictions with regards to when and which abstract words are more likely to be learned; also they make different predictions concerning the impact of developmental disorders. We start by providing a review of work characterizing how abstract words and concepts are learned in development, especially between the ages of 6 and 12. Second, we review some work from our group that tests the two hypotheses above. This work investigates typically developing (TD) children and children with atypical development (developmental language disorders [DLD] and autism spectrum disorder [ASD] with and without language deficits). We conclude that the use of strategies based on emotional information, or on co-occurrences in language, may play a role at different developmental stages. © 2018 Cognitive Science Society Inc.

A Teacher's Conception of Definition and Use of Examples When Doing and Teaching Mathematics

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Johnson, Heather Lynn; Blume, Glendon W.; Shimizu, Jeanne K.; Graysay, Duane; Konnova, Svetlana

2014-01-01

To contribute to an understanding of the nature of teachers' mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher's conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical…

Discrete mathematics using a computer

CERN Document Server

Hall, Cordelia

2000-01-01

Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica­ tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...

PRE-SERVICE MATHEMATICS TEACHERS’ CONCEPTION OF HIGHER-ORDER THINKING LEVEL IN BLOOM'S TAXONOMY

OpenAIRE

Damianus D Samo

2017-01-01

The purpose of this study is to explore pre-service mathematics teachers' conception of higher-order thinking in Bloom's Taxonomy, to explore pre-service mathematics teachers' ability in categorizing six cognitive levels of Bloom's Taxonomy as lower-order thinking and higher-order thinking, and pre-service mathematics teachers' ability in identifying some questionable items as lower-order and higher-order thinking. The higher-order thinking is the type of non-algorithm thinking which include ...

Promoting middle school students’ abstract-thinking ability through cognitive apprenticeship instruction in mathematics learning

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Yusepa, B. G. P.; Kusumah, Y. S.; Kartasasmita, B. G.

2018-01-01

The aim of this study is to get an in-depth understanding of students’ abstract-thinking ability in mathematics learning. This study was an experimental research with pre-test and post-test control group design. The subject of this study was eighth-grade students from two junior high schools in Bandung. In each schools, two parallel groups were selected and assigned into control and experimental groups. The experimental group was exposed to Cognitive Apprenticeship Instruction (CAI) treatment, whereas the control group was exposed to conventional learning. The results showed that abstract-thinking ability of students in experimental group was better than that of those in control group in which it could be observed from the overall and school level. It could be concluded that CAI could be a good alternative learning model to enhance students’ abstract-thinking ability.

Using a Technology-Supported Approach to Preservice Teachers' Multirepresentational Fluency: Unifying Mathematical Concepts and Their Representations

Science.gov (United States)

McGee, Daniel; Moore-Russo, Deborah

2015-01-01

A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to…

Essential concepts and underlying theories from physics, chemistry, and mathematics for "biochemistry and molecular biology" majors.

Science.gov (United States)

Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.

Developing geogebra-assisted reciprocal teaching strategy to improve junior high school students’ abstraction ability, lateral thinking and mathematical persistence

Science.gov (United States)

Priatna, N.; Martadiputra, B. A. P.; Wibisono, Y.

2018-05-01

The development of science and technology requires reform in the utilization of various resources for mathematics teaching and learning process. One of the efforts that can be made is the implementation of GeoGebra-assisted Reciprocal Teaching strategy in mathematics instruction as an effective strategy in improving students’ cognitive, affective, and psychomotor abilities. This research is intended to implement GeoGebra-assisted Reciprocal Teaching strategy in improving abstraction ability, lateral thinking, and mathematical persistence of junior high school students. It employed quasi-experimental method with non-random pre-test and post-test control design. More specifically, it used the 2x3 factorial design, namely the learning factors that included GeoGebra-assisted Reciprocal Teaching and conventional teaching learning, and levels of early mathematical ability (high, middle, and low). The subjects in this research were the eighth grade students of junior high school, taken with purposive sampling. The results of this research show: Abstraction and lateral abilities of students who were taught with GeoGebra-assisted Reciprocal Teaching strategy were significantly higher than those of students who received conventional learning. Mathematical persistence of students taught with GeoGebra-assisted Reciprocal Teaching strategy was also significantly higher than of those taught with conventional learning.

From Abstract Art to Abstracted Artists

Directory of Open Access Journals (Sweden)

Romi Mikulinsky

2016-11-01

Full Text Available What lineage connects early abstract films and machine-generated YouTube videos? Hans Richter’s famous piece Rhythmus 21 is considered to be the first abstract film in the experimental tradition. The Webdriver Torso YouTube channel is composed of hundreds of thousands of machine-generated test patterns designed to check frequency signals on YouTube. This article discusses geometric abstraction vis-à-vis new vision, conceptual art and algorithmic art. It argues that the Webdriver Torso is an artistic marvel indicative of a form we call mathematical abstraction, which is art performed by computers and, quite possibly, for computers.

Handedness shapes children's abstract concepts.

Science.gov (United States)

Casasanto, Daniel; Henetz, Tania

2012-03-01

Can children's handedness influence how they represent abstract concepts like kindness and intelligence? Here we show that from an early age, right-handers associate rightward space more strongly with positive ideas and leftward space with negative ideas, but the opposite is true for left-handers. In one experiment, children indicated where on a diagram a preferred toy and a dispreferred toy should go. Right-handers tended to assign the preferred toy to a box on the right and the dispreferred toy to a box on the left. Left-handers showed the opposite pattern. In a second experiment, children judged which of two cartoon animals looked smarter (or dumber) or nicer (or meaner). Right-handers attributed more positive qualities to animals on the right, but left-handers to animals on the left. These contrasting associations between space and valence cannot be explained by exposure to language or cultural conventions, which consistently link right with good. Rather, right- and left-handers implicitly associated positive valence more strongly with the side of space on which they can act more fluently with their dominant hands. Results support the body-specificity hypothesis (Casasanto, 2009), showing that children with different kinds of bodies think differently in corresponding ways. Copyright © 2011 Cognitive Science Society, Inc.

The Relationship among Self-Concept, Self-Efficacy, and Performance in Mathematics during Secondary School.

Science.gov (United States)

Pietsch, James; Walker, Richard; Chapman, Elaine

2003-01-01

Examines the relationship among self-concept, self-efficacy, and performance in mathematics among 416 high school students. Confirmatory factor analyses supported the existence of two self-concept components--a competency component and an affective component. Self-efficacy items and the competency items of self-concept also loaded on a single…

Understanding Mathematic Concept in Relation and Function Method through Active Learning Type Group to Group Distributed LKS

Science.gov (United States)

Kudri, F.; Rahmi, R.; Haryono, Y.

2018-04-01

This research is motivated by the lack of understanding of mathematical concepts students and teachers have not familiarize students discussed in groups. This researchaims to determine whether an understanding of mathematical concepts junior class VIII SMPN 2 in Ranah Batahan Kabupaten Pasaman Barat by applying active learning strategy group to group types with LKS better than conventional learning. The type of research is experimental the design of randomized trials on the subject. The population in the study were all students VIII SMPN 2 Ranah Batahan Kabupaten Pasaman Barat in year 2012/2013 which consists of our class room experiment to determine the grade and control class with do nerandomly, so that classes VIII1 elected as a experiment class and class VIII4 as a control class. The instruments used in the test empirically understanding mathematical concepts are shaped by the essay with rt=0,82 greater than rt=0,468 means reliable tests used. The data analysis technique used is the test with the help of MINITAB. Based on the results of the data analisis known that both of the sample are normal and homogenity in real rate α = 0,05, so the hypothesis of this research is received. So, it can be concluded students’ understanding mathematical concept applied the active Group to Group learning strategy with LKS is better than the students’ understanding mathematical concept with Conventional Learning.

Semantic size of abstract concepts: it gets emotional when you can't see it.

Science.gov (United States)

Yao, Bo; Vasiljevic, Milica; Weick, Mario; Sereno, Margaret E; O'Donnell, Patrick J; Sereno, Sara C

2013-01-01

Size is an important visuo-spatial characteristic of the physical world. In language processing, previous research has demonstrated a processing advantage for words denoting semantically "big" (e.g., jungle) versus "small" (e.g., needle) concrete objects. We investigated whether semantic size plays a role in the recognition of words expressing abstract concepts (e.g., truth). Semantically "big" and "small" concrete and abstract words were presented in a lexical decision task. Responses to "big" words, regardless of their concreteness, were faster than those to "small" words. Critically, we explored the relationship between semantic size and affective characteristics of words as well as their influence on lexical access. Although a word's semantic size was correlated with its emotional arousal, the temporal locus of arousal effects may depend on the level of concreteness. That is, arousal seemed to have an earlier (lexical) effect on abstract words, but a later (post-lexical) effect on concrete words. Our findings provide novel insights into the semantic representations of size in abstract concepts and highlight that affective attributes of words may not always index lexical access.

Influence of Precollege Experience on Self-Concept among Community College Students in Science, Mathematics, and Engineering

Science.gov (United States)

Starobin, Soko S.; Laanan, Frankie Santos

Female and minority students have historically been underrepresented in the field of science, mathematics, and engineering at colleges and universities. Although a plethora of research has focused on students enrolled in 4-year colleges or universities, limited research addresses the factors that influence gender differences in community college students in science, mathematics, and engineering. Using a target population of 1,599 aspirants in science, mathematics, and engineering majors in public community colleges, this study investigates the determinants of self-concept by examining a hypothetical structural model. The findings suggest that background characteristics, high school academic performance, and attitude toward science have unique contributions to the development of self-concept among female community college students. The results add to the literature by providing new theoretical constructs and the variables that predict students' self-concept.

The Effectiveness of MURDER Cooperative Model towards Students' Mathematics Reasoning Ability and Self Concept of Ten Grade

Directory of Open Access Journals (Sweden)

Sofan Tri Prasetiyo

2017-08-01

Full Text Available The purpose of this research was to know the effectiveness of MURDER cooperative model towards students’ mathematics reasoning ability and self concept of ten grade. Population of this research were students of MIA ten grade Senior High School 1 Kebumen in the academic year 2016/1017. Sampling technique using simple random sampling technique. The data collected by the method of documentation, test methods, observation methods, and questionnaire methods. The analyzed of data are used completeness test and average different test. The results showed that: (1 mathematics reasoning ability of students that following MURDER cooperative model have completed individual and classical study completeness; (2 mathematics reasoning ability of students that following MURDER cooperative model better than mathematics reasoning ability of students that following ekspository learning; (3 self concept of students that following MURDER cooperative model better than self concept of students that following ekspository learning.

Introduction of the Thematic Issue on the Interplay of Physics and Mathematics

DEFF Research Database (Denmark)

Avelar Sotomaior Karam, Ricardo

2015-01-01

for the students. They have a hard time understanding where mathematical concepts come from and why physics has little to do with their experiential world. This problem demands a systematic research effort from experts in different fields, especially the ones who aim at informing educational practices......Since their beginnings Physics (natural philosophy) and mathematics have been deeply interrelated, and this mutual influence has played an essential role in both their developments. However, the image typically found in educational contexts is often quite different. In physics education......, it is usual to find mathematics being seen as a mere tool to describe and calculate, whereas in mathematics education, physics is commonly viewed as a possible context for the application of mathematical concepts that were previously defined abstractly. This dichotomy creates significant learning problems...

Epistemologies, beliefs and conceptions of mathematics teaching and learning : the theory, and what is manifested in mathematics teacher's practices in England, France and Germany

NARCIS (Netherlands)

Pepin, B.; Hudson, B.; Buchberger, F.; Kansanen, P.

1999-01-01

This paper firstly explores the issues raised in the literature concerning epistemologies, beliefs and conceptions of mathematics and its teaching and learning. Secondly, it analyses the ways in which mathematics teachers’ classroom practices in England, France and Germany reflect teachers’ beliefs

An Investigation of K-8 Preservice Teachers' Concept Images and Mathematical Definitions of Polygons

Science.gov (United States)

Ward, Robin A.

2004-01-01

In this paper, the author presents a study which explored K-8 preservice teachers' concept images and mathematical definitions of polygons. This study was carried out in which K-8 teacher candidates enrolled in an elementary mathematics content course were asked to sort, identify, and provide definitions of such shapes including triangles,…

Sound iconicity of abstract concepts: Place of articulation is implicitly associated with abstract concepts of size and social dominance.

Science.gov (United States)

Auracher, Jan

2017-01-01

The concept of sound iconicity implies that phonemes are intrinsically associated with non-acoustic phenomena, such as emotional expression, object size or shape, or other perceptual features. In this respect, sound iconicity is related to other forms of cross-modal associations in which stimuli from different sensory modalities are associated with each other due to the implicitly perceived correspondence of their primal features. One prominent example is the association between vowels, categorized according to their place of articulation, and size, with back vowels being associated with bigness and front vowels with smallness. However, to date the relative influence of perceptual and conceptual cognitive processing on this association is not clear. To bridge this gap, three experiments were conducted in which associations between nonsense words and pictures of animals or emotional body postures were tested. In these experiments participants had to infer the relation between visual stimuli and the notion of size from the content of the pictures, while directly perceivable features did not support-or even contradicted-the predicted association. Results show that implicit associations between articulatory-acoustic characteristics of phonemes and pictures are mainly influenced by semantic features, i.e., the content of a picture, whereas the influence of perceivable features, i.e., size or shape, is overridden. This suggests that abstract semantic concepts can function as an interface between different sensory modalities, facilitating cross-modal associations.

Concept Map as an Assessment Tool in Secondary School Mathematics: An Analysis of Teachers' Perspectives

Science.gov (United States)

Mutodi, Paul; Chigonga, Benard

2016-01-01

This paper reports on teachers' views on concept mapping: its applicability; reliability; advantages and; difficulties. A close-ended questionnaire was administered to 50 purposefully selected secondary school mathematics teachers from Sekhukhune District, Limpopo, South Africa. The findings indicate that mathematics teachers generally perceive…

Prospective mathematics teachers' understanding of the base concept

Science.gov (United States)

Horzum, Tuğba; Ertekin, Erhan

2018-02-01

The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers(PMTs) have about the base concept(BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn by PMTs. As a result, it was determined that PMTs dealt with the BC in a broad range of seven different images. It was also determined that the base perception of PMTs was limited mostly to their usage in daily life and in this context, they have position-dependent and word-dependent images. It was also determined that PMTs named the base to explain the BC or paid attention to the naming of three-dimensional geometric figures through the statement: 'objects are named according to their bases'. At the same time, it was also determined that PMTs had more than one concept imageswhich were contradicting with each other. According to these findings, potential explanations and advices were given.

Artificial Intelligence, Computational Thinking, and Mathematics Education

Science.gov (United States)

Gadanidis, George

2017-01-01

Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…

Semantic Size of Abstract Concepts: It Gets Emotional When You Can’t See It

Science.gov (United States)

Yao, Bo; Vasiljevic, Milica; Weick, Mario; Sereno, Margaret E.; O’Donnell, Patrick J.; Sereno, Sara C.

2013-01-01

Size is an important visuo-spatial characteristic of the physical world. In language processing, previous research has demonstrated a processing advantage for words denoting semantically “big” (e.g., jungle) versus “small” (e.g., needle) concrete objects. We investigated whether semantic size plays a role in the recognition of words expressing abstract concepts (e.g., truth). Semantically “big” and “small” concrete and abstract words were presented in a lexical decision task. Responses to “big” words, regardless of their concreteness, were faster than those to “small” words. Critically, we explored the relationship between semantic size and affective characteristics of words as well as their influence on lexical access. Although a word’s semantic size was correlated with its emotional arousal, the temporal locus of arousal effects may depend on the level of concreteness. That is, arousal seemed to have an earlier (lexical) effect on abstract words, but a later (post-lexical) effect on concrete words. Our findings provide novel insights into the semantic representations of size in abstract concepts and highlight that affective attributes of words may not always index lexical access. PMID:24086421

Influence of Self-Concept, Study Habit and Gender on Attitude and Achievement of Secondary School Students in Mathematics

Science.gov (United States)

Kamoru, Usman; Ramon, Olosunde Gbolagade

2017-01-01

This study examined the relationship between self-concept, attitude of the students towards mathematics, and math achievement. Also, this study investigated the influence of study habits on achievement; study habits on attitude of students to mathematics. The influence of gender and self-concept and study habit group on achievement and attitude…

Viewing Formal Mathematics from Yoruba Conception of the Sky

OpenAIRE

Segla, Aimé

2016-01-01

Yoruba Cosmology resembles a generative system at the foundation of concepts. The traditional thought, which derives from the reality of the identical pair incorporated from cosmology into real life, exemplifies all kind of existing knowledge, culture and practices.  Previous studies by the author show in some detail the scientific interests in Yoruba cosmology. The present paper aims to view formal mathematics through the interpretation of Yoruba sky knowledge. It attempts to demonstrate tha...

Auditing complex concepts of SNOMED using a refined hierarchical abstraction network.

Science.gov (United States)

Wang, Yue; Halper, Michael; Wei, Duo; Gu, Huanying; Perl, Yehoshua; Xu, Junchuan; Elhanan, Gai; Chen, Yan; Spackman, Kent A; Case, James T; Hripcsak, George

2012-02-01

Auditors of a large terminology, such as SNOMED CT, face a daunting challenge. To aid them in their efforts, it is essential to devise techniques that can automatically identify concepts warranting special attention. "Complex" concepts, which by their very nature are more difficult to model, fall neatly into this category. A special kind of grouping, called a partial-area, is utilized in the characterization of complex concepts. In particular, the complex concepts that are the focus of this work are those appearing in intersections of multiple partial-areas and are thus referred to as overlapping concepts. In a companion paper, an automatic methodology for identifying and partitioning the entire collection of overlapping concepts into disjoint, singly-rooted groups, that are more manageable to work with and comprehend, has been presented. The partitioning methodology formed the foundation for the development of an abstraction network for the overlapping concepts called a disjoint partial-area taxonomy. This new disjoint partial-area taxonomy offers a collection of semantically uniform partial-areas and is exploited herein as the basis for a novel auditing methodology. The review of the overlapping concepts is done in a top-down order within semantically uniform groups. These groups are themselves reviewed in a top-down order, which proceeds from the less complex to the more complex overlapping concepts. The results of applying the methodology to SNOMED's Specimen hierarchy are presented. Hypotheses regarding error ratios for overlapping concepts and between different kinds of overlapping concepts are formulated. Two phases of auditing the Specimen hierarchy for two releases of SNOMED are reported on. With the use of the double bootstrap and Fisher's exact test (two-tailed), the auditing of concepts and especially roots of overlapping partial-areas is shown to yield a statistically significant higher proportion of errors. Copyright © 2011 Elsevier Inc. All rights

Auditing Complex Concepts of SNOMED using a Refined Hierarchical Abstraction Network

Science.gov (United States)

Wang, Yue; Halper, Michael; Wei, Duo; Gu, Huanying; Perl, Yehoshua; Xu, Junchuan; Elhanan, Gai; Chen, Yan; Spackman, Kent A.; Case, James T.; Hripcsak, George

2012-01-01

Auditors of a large terminology, such as SNOMED CT, face a daunting challenge. To aid them in their efforts, it is essential to devise techniques that can automatically identify concepts warranting special attention. “Complex” concepts, which by their very nature are more difficult to model, fall neatly into this category. A special kind of grouping, called a partial-area, is utilized in the characterization of complex concepts. In particular, the complex concepts that are the focus of this work are those appearing in intersections of multiple partial-areas and are thus referred to as overlapping concepts. In a companion paper, an automatic methodology for identifying and partitioning the entire collection of overlapping concepts into disjoint, singly-rooted groups, that are more manageable to work with and comprehend, has been presented. The partitioning methodology formed the foundation for the development of an abstraction network for the overlapping concepts called a disjoint partial-area taxonomy. This new disjoint partial-area taxonomy offers a collection of semantically uniform partial-areas and is exploited herein as the basis for a novel auditing methodology. The review of the overlapping concepts is done in a top-down order within semantically uniform groups. These groups are themselves reviewed in a top-down order, which proceeds from the less complex to the more complex overlapping concepts. The results of applying the methodology to SNOMED’s Specimen hierarchy are presented. Hypotheses regarding error ratios for overlapping concepts and between different kinds of overlapping concepts are formulated. Two phases of auditing the Specimen hierarchy for two releases of SNOMED are reported on. With the use of the double bootstrap and Fisher’s exact test (two-tailed), the auditing of concepts and especially roots of overlapping partial-areas is shown to yield a statistically significant higher proportion of errors. PMID:21907827

Multimodal Languaging as a Pedagogical Model—A Case Study of the Concept of Division in School Mathematics

Directory of Open Access Journals (Sweden)

Jorma Joutsenlahti

2017-01-01

Full Text Available The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21 understand the concept of division. The data was collected over six hours of teaching sessions, during which the pupils expressed their mathematical thinking mainly by writing and drawing. Their productions, as well as questionnaire after the process, were analyzed qualitatively. The results show that, in expressing the mathematical problem in verbal form, most of the students saw it as a division into parts. It was evident from the pupils’ texts and drawings that the mathematical expression of subtraction could be interpreted in three different ways. It was found that the pupils enjoyed using writing in the solution of word problems, and it is suggested that the use of different modes in expressing mathematical thinking may both strengthen the learning of mathematical concepts and support the evaluation of learning.

Neural reuse leads to associative connections between concrete (physical) and abstract (social) concepts and motives.

Science.gov (United States)

Wang, Yimeng; Bargh, John A

2016-01-01

Consistent with neural reuse theory, empirical tests of the related "scaffolding" principle of abstract concept development show that higher-level concepts "reuse" and are built upon fundamental motives such as survival, safety, and consumption. This produces mutual influence between the two levels, with far-ranging impacts from consumer behavior to political attitudes.

Investigating Upper Secondary School Teachers' Conceptions: Is Mathematical Reasoning Considered Gendered?

Science.gov (United States)

Sumpter, Lovisa

2016-01-01

This study examines Swedish upper secondary school teachers' gendered conceptions about students' mathematical reasoning: whether reasoning was considered gendered and, if so, which type of reasoning was attributed to girls and boys. The sample consisted of 62 teachers from six different schools from four different locations in Sweden. The results…

Formal Methods for Abstract Specifications – A Comparison of Concepts

DEFF Research Database (Denmark)

Instenberg, Martin; Schneider, Axel; Schnetter, Sabine

2006-01-01

In industry formal methods are becoming increasingly important for the verification of hardware and software designs. However current practice for specification of system and protocol functionality on high level of abstraction is textual description. For verification of the system behavior manual...... inspections and tests are usual means. To facilitate the introduction of formal methods in the development process of complex systems and protocols, two different tools evolved from research activities – UPPAAL and SpecEdit – have been investigated and compared regarding their concepts and functionality...

Mathematical models in marketing a collection of abstracts

CERN Document Server

Funke, Ursula H

1976-01-01

Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe­ matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...

Minásbate Equivalents of Mathematical Concepts: Their Socio-Cultural Undertones

Science.gov (United States)

Balbuena, Sherwin E.; Cantoria, Uranus E.; Cantoria, Amancio L., Jr.; Ferriol, Eny B.

2015-01-01

This paper presents the collection and analysis of Minásbate equivalents of some concepts used in the study of arithmetic, counting, and geometry as provided by the elderly residents of the province of Masbate. The glossary of mathematical terms derived from interviews would serve as an authoritative reference for mother tongue teachers in the…

Examining of Perceptions of Gifted Students toward Mathematics Concept

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Mesut ÖZTÜRK

2014-12-01

Full Text Available The purpose of this study bring out owned intellectual image interested in mathematics concept of gifted students. Participant of twenty-eight gifted students that they selected via WISC-R intelligent test. A phenomenology design that one of qualitative research methods was adopted and data collection focus group interview. Data analysis consisted of content analysis. Students who participant made up different sixteen metaphor. The most widely used of them kainite. When examined justifications lie behind of metaphor gifted students have different three perception such as affected with people of math, influence toward math of the nature, the nature of math. The result of examine of math perception according to grade level when grade level increased, gifted students more interested the nature of math whereas depended on needed of people more interested math concept.

A Mixed Methods Analysis of Students' Understanding of Slope and Derivative Concepts and Students' Mathematical Dispositions

Science.gov (United States)

Patel, Rita Manubhai

2013-01-01

This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…

Learning with Technology: Video Modeling with Concrete-Representational-Abstract Sequencing for Students with Autism Spectrum Disorder

Science.gov (United States)

Yakubova, Gulnoza; Hughes, Elizabeth M.; Shinaberry, Megan

2016-01-01

The purpose of this study was to determine the effectiveness of a video modeling intervention with concrete-representational-abstract instructional sequence in teaching mathematics concepts to students with autism spectrum disorder (ASD). A multiple baseline across skills design of single-case experimental methodology was used to determine the…

Implementing CRA with Secondary Students with Learning Disabilities in Mathematics

Science.gov (United States)

Witzel, Bradley S.; Riccomini, Paul J.; Schneider, Elke

2008-01-01

Students with learning disabilities struggle to acquire essential mathematical concepts and skills, especially at the secondary level. One effective approach to improving secondary math performance supported by research is the concrete-to-representational-to-abstract (CRA) sequence of instruction. Although CRA is an evidenced-based instructional…

The concept of competence and its relevance for science, technology, and mathematics education

DEFF Research Database (Denmark)

Ropohl, Mathias; Nielsen, Jan Alexis; Olley, Christopher

2018-01-01

. In contrast to earlier ed-ucational goals that focused more on basic skills and knowledge expectations, competences are more functionally oriented. They involve the ability to solve complex problems in a particular context, e.g. in vocational or everyday situations. In science, technology, and mathematics...... education, the concept of competence is closely linked to the concept of literacy. Apart from these rather cognitive and af-fective perspectives influenced by the need to assess students’ achievement of de-sired learning goals in relation to their interest and motivation, the perspectives of the concept...

Identifying STEM Concepts Associated with Junior Livestock Projects

Science.gov (United States)

Wooten, Kate; Rayfield, John; Moore, Lori L.

2013-01-01

Science, technology, engineering, and mathematics (STEM) education is intended to provide students with a cross-subject, contextual learning experience. To more fully prepare our nation's students to enter the globally competitive workforce, STEM integration allows students to make connections between the abstract concepts learned in core subject…

PRELIMINARY ASSESSMENT OF FAMILIARITY WITH CONCEPTS MATHEMATICAL GEOGRAPHY OF COURSE UNDERGRADUATE

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Luis Alberto Martins Palhares de Melo

2015-12-01

Full Text Available The objective of the work described in this paper was to conduct a preliminary assessment about the familiarity with basic mathematical concepts by undergraduate students of Geography. This work assumed that the domain of basic concepts of mathematics is important for the students for the real understanding of quantification techniques applied to geography, used for better understanding about geographical space. Therefore, it was applied a questionnaire with six questions related to some basic mathematical concepts. 384 questionnaires were applied in undergraduate courses in geography, in six public institutions of higher education and a private college, located in the Federal District, Goias, Tocantins, Mato Grosso do Sul, Paraná and Rio Grande do Sul in May / 2013 June / 2013 August / 2013 and April / 2014. The results showed that the 384 respondents answered correctly on average 2,3 questions of an amount of six questions. This may mean that a priori there is little familiarity of undergraduate Geography students with basic concepts of mathematics. O objetivo do trabalho descrito neste artigo foi realizar uma avaliação preliminar a respeito da familiaridade com conceitos matemáticos em nível de Educação Básica por parte de graduandos de cursos de Geografia. Essa investigação partiu do princípio de que o domínio de conceitos básicos de Matemática é importante para a capacitação em técnicas de quantificação em Geografia, que por sua vez auxiliam o geógrafo, bacharel ou licenciado, a entender melhor o espaço geográfico. Para tanto foi utilizado o instrumento questionário com seis questões versando sobre alguns conceitos matemáticos básicos em nível de Educação Básica. Foram aplicados 384 questionários em cursos de graduação em Geografia, em seis instituições públicas de ensino superior e uma faculdade particular, localizadas no Distrito Federal, Goiás, Tocantins, Mato Grosso do Sul, Paraná e Rio Grande do

The complex road to mathematization in physics instruction

DEFF Research Database (Denmark)

Avelar Sotomaior Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-01-01

to the research in this field, we have analysed a set of lectures given by a distinguished physics professor. In this proposal we present the analysis of two lectures where the abstract concepts of charge density and electric flux are taught. The complexity of the mathematization of these concepts is evident both...... explicitly and made punctual metacognitive remarks. Taking into account the future perspectives of our research, the categorization of the didactical strategies used by this professor shall allows us to develop comparative studies with other lectures on the same topic. Moreover, the derivation promising......How to facilitate students’ understanding of science’s abstract concepts is definitely a major concern of every dedicated physics teacher. However, discussions about promising ways to be successful at this task are not always part of teacher training curricula. With the goal of contributing...

Integration of the development of mathematical concepts and music education in preschool education by means of songs

OpenAIRE

Maričić, Sanja; Ćalić, Maja

2015-01-01

Starting from the fact that in early education the process of learning should be understood in its totality, as a system of activities in which the subject fields are interwoven and woven into every segment of a child's life together with other children and adults in preschool, the authors of the work point out the integration of the development of mathematical concepts and music education. Music education is viewed as a context which can contribute to the acquisition of mathematical concepts...

Logical thinking in the pyramidal schema of concepts the logical and mathematical elements

CERN Document Server

Geldsetzer, Lutz

2014-01-01

This book proposes a new way of formalizing in logic and mathematics - a "pyramidal graph system," devised by the author and based on Porphyrian trees and modern concepts of classification, in both of which pyramids act as the organizing schema.

Young Children's Self-Concepts Include Representations of Abstract Traits and the Global Self.

Science.gov (United States)

Cimpian, Andrei; Hammond, Matthew D; Mazza, Giulia; Corry, Grace

2017-11-01

There is debate about the abstractness of young children's self-concepts-specifically, whether they include representations of (a) general traits and abilities and (b) the global self. Four studies (N = 176 children aged 4-7) suggested these representations are indeed part of early self-concepts. Studies 1 and 2 reexamined prior evidence that young children cannot represent traits and abilities. The results suggested that children's seemingly immature judgments in previous studies were due to peculiarities of the task context not the inadequacy of children's self-concepts. Similarly, Studies 3 and 4 revealed that, contrary to claims of immaturity in reasoning about the global self, young children update their global self-evaluations in flexible, context-sensitive ways. This evidence suggests continuity in the structure of self-concepts across childhood. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

Reflexive (réfléchissante Abstraction and Mathematical Knowledge Production A Abstração Reflexionante e a Produção do Conhecimento Matemático

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Clélia Maria Ignatius Nogueira

2008-10-01

Full Text Available Piaget assumes that reflexive (réfléchissante abstraction is the process by which mathematical knowledge is produced. The aim of this article is to confirm to identify the presence of the reflexive abstraction or its components (réfléchissement and reflection in mathematicians description of the way they produce mathematical new knowledge as well as to discuss possible pedagogical implications of this process in Mathematics classrooms. Keywords: Mathematical education. Reflexive abstraction. Mathematical knowledge.Piaget afirma que a abstração reflexionante é o processo por excelência de produção do conhecimento matemático. Este trabalho teve por objetivo identificar a presença da abstração reflexionante ou de seus componentes (reflexionamento e reflexão na descrição que matemáticos fazem da forma como produzem novos conhecimentos e discutir possíveis implicações pedagógicas deste processo nas aulas de Matemática. Palavras-chave: Educação Matemática. Abstração reflexionante. Conhecimento matemático.

Levels of abstraction in students' understanding of the concept of algorithm : the qualitative perspective

NARCIS (Netherlands)

Perrenet, J.C.; Kaasenbrood, E.J.S.

2006-01-01

In a former, mainly quantitative, study we defined four levels of abstraction in Computer Science students' thinking about the concept of algorithm. We constructed a list of questions about algorithms to measure the answering level as an indication for the thinking level. The answering level

Concepts of mathematical modeling

CERN Document Server

Meyer, Walter J

2004-01-01

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

The language of mathematics: investigating the ways language counts for children's mathematical development.

Science.gov (United States)

Vukovic, Rose K; Lesaux, Nonie K

2013-06-01

This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relation between children's language ability and gains in different domains of mathematical cognition (i.e., arithmetic, data analysis/probability, algebra, and geometry). The results showed that language ability predicts gains in data analysis/probability and geometry, but not in arithmetic or algebra, after controlling for visual-spatial working memory, reading ability, and sex. The effect of language on gains in mathematical cognition did not differ between language minority learners and native English speakers. These findings suggest that language influences how children make meaning of mathematics but is not involved in complex arithmetical procedures whether presented with Arabic symbols as in arithmetic or with abstract symbols as in algebraic reasoning. The findings further indicate that early language experiences are important for later mathematical development regardless of language background, denoting the need for intensive and targeted language opportunities for language minority and native English learners to develop mathematical concepts and representations. Copyright © 2013. Published by Elsevier Inc.

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

Science.gov (United States)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

Metaphor: Bridging embodiment to abstraction.

Science.gov (United States)

Jamrozik, Anja; McQuire, Marguerite; Cardillo, Eileen R; Chatterjee, Anjan

2016-08-01

Embodied cognition accounts posit that concepts are grounded in our sensory and motor systems. An important challenge for these accounts is explaining how abstract concepts, which do not directly call upon sensory or motor information, can be informed by experience. We propose that metaphor is one important vehicle guiding the development and use of abstract concepts. Metaphors allow us to draw on concrete, familiar domains to acquire and reason about abstract concepts. Additionally, repeated metaphoric use drawing on particular aspects of concrete experience can result in the development of new abstract representations. These abstractions, which are derived from embodied experience but lack much of the sensorimotor information associated with it, can then be flexibly applied to understand new situations.

Abstracting Sequences: Reasoning That Is a Key to Academic Achievement.

Science.gov (United States)

Pasnak, Robert; Kidd, Julie K; Gadzichowski, K Marinka; Gallington, Debbie A; Schmerold, Katrina Lea; West, Heather

2015-01-01

The ability to understand sequences of items may be an important cognitive ability. To test this proposition, 8 first-grade children from each of 36 classes were randomly assigned to four conditions. Some were taught sequences that represented increasing or decreasing values, or were symmetrical, or were rotations of an object through 6 or 8 positions. Control children received equal numbers of sessions on mathematics, reading, or social studies. Instruction was conducted three times weekly in 15-min sessions for seven months. In May, the children taught sequences applied their understanding to novel sequences, and scored as well or better on three standardized reading tests as the control children. They outscored all children on tests of mathematics concepts, and scored better than control children on some mathematics scales. These findings indicate that developing an understanding of sequences is a form of abstraction, probably involving fluid reasoning, that provides a foundation for academic achievement in early education.

Abstract quantum computing machines and quantum computational logics

Science.gov (United States)

Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto

2016-06-01

Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.

Quantum language and the migration of scientific concepts

CERN Document Server

Burwell, Jennifer

2018-01-01

How highly abstract quantum concepts were represented in language, and how these concepts were later taken up by philosophers, literary critics, and new-age gurus. The principles of quantum physics -- and the strange phenomena they describe -- are represented most precisely in highly abstract algebraic equations. Why, then, did these mathematically driven concepts compel founders of the field, particularly Erwin Schrödinger, Niels Bohr, and Werner Heisenberg, to spend so much time reflecting on ontological, epistemological, and linguistic concerns? What is it about quantum concepts that appeals to latter-day Eastern mystics, poststructuralist critics, and get-rich-quick schemers? How did their interpretations and misinterpretations of quantum phenomena reveal their own priorities? In this book, Jennifer Burwell examines these questions and considers what quantum phenomena -- in the context of the founders' debates over how to describe them -- reveal about the relationship between everyday experience, percep...

ANALYZING THE MATHEMATICAL DISPOSITION AND ITS CORRELATION WITH MATHEMATICS ACHIEVEMENT OF ABSTRACT SENIOR HIGH SCHOOL STUDENTS

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Louise M. Saija

2012-09-01

Full Text Available Salah satu standar yang diberikan oleh National Council of Teachers of Mathematics (NCTM adalah disposisi matematik. Disposisi  bukan sekedar merujuk pada sikap tetapi suatu kecenderungan untuk berpikir dan bersikap dalam cara yang positif. Penelitian ini bertujuan untuk menganalisa disposisi matematik dan hubungannya dengan hasil belajar matematika siswa-siswa sekolah menengah atas (SMA. Sampel pada penelitian ini adalah 149 siswa SMA di Bandung. Analisa statistik didasarkan pada korelasi peringkat Spearman dan uji-t. Ditemukan bahwa secara rata-rata,  disposisi matematik dari siswa-siswa SMA dikategorikan rendah. Selanjutnya, terdapat korelasi positif dan signifikan antara disposisi matematik dan hasil belajar matematika siswa-siswa SMA, walaupun nilai koefisien korelasinya tidak tinggi. Suatu observasi juga dilakukan untuk menganalisa hubungan ini, dan didapati bahwa walaupun beberapa siswa memiliki disposisi matematik yang baik, kadang kala mereka tidak dapat menyelesaikan ujian dengan baik, karena padatnya kurikulum, dan juga aktifitas sosial mereka, yang membuat hasil belajar matematika mereka lebih rendah. Temuan lainnya adalah bahwa siswa-siswa SMA memerlukan guru-guru matematika dengan lebih banyak strategi mengajar  agar mereka dapat memiliki disposisi matematik yang lebih baik.   Kata Kunci: Disposisi Matematik, Hasil Belajar Matematika       One of the evaluation standards given by the National Council of Teachers of Mathematics (NCTM was mathematical disposition. Disposition refers not simply to attitudes but to a tendency to think and to act in positive ways. This study aimed to analyze the mathematical disposition and its correlation with mathematics achievement of senior high school (SMA students. A total of 149 SMA students in Bandung were procured as samples. Statistical analysis was based on the Spearman rank correlation and on the t-test. The findings showed that at average, the mathematical disposition of the SMA

The Impact of the Flipped Classroom on Mathematics Concept Learning in High School

Science.gov (United States)

Bhagat, Kaushal Kumar; Chang, Cheng-Nan; Chang, Chun-Yen

2016-01-01

The present study aimed to examine the effectiveness of the flipped classroom learning environment on learner's learning achievement and motivation, as well as to investigate the effects of flipped classrooms on learners with different achievement levels in learning mathematics concepts. The learning achievement and motivation were measured by the…

Pre-Service Physics Teachers' Comprehension of Quantum Mechanical Concepts

Science.gov (United States)

Didis, Nilufer; Eryilmaz, Ali; Erkoc, Sakir

2010-01-01

When quantum theory caused a paradigm shift in physics, it introduced difficulties in both learning and teaching of physics. Because of its abstract, counter-intuitive and mathematical structure, students have difficulty in learning this theory, and instructors have difficulty in teaching the concepts of the theory. This case study investigates…

Justification of the concept of mathematical methods and models in making decisions on taxation

OpenAIRE

KORKUNA NATALIA MIKHAYLOVNA

2017-01-01

The paper presents the concept of the application of mathematical methods and models in making decisions on taxation in Ukraine as a phased process. Its performance result is the selection of an effective decision based on regression and optimization models.

The Vital Role of Basic Mathematics in Teaching and Learning the Mole Concept

Science.gov (United States)

Mehrotra, Alka; Koul, Anjni

2016-01-01

This article focuses on the importance of activity-based teaching in understanding the mole concept and the vital role of basic mathematical operations. It describes needs-based training for teachers in a professional development programme in India. Analysis of test results before and after the training indicates that teachers improved their…

Multimodal Languaging as a Pedagogical Model--A Case Study of the Concept of Division in School Mathematics

Science.gov (United States)

Joutsenlahti, Jorma; Kulju, Pirjo

2017-01-01

The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…

Introduction to mathematical physics methods and concepts

CERN Document Server

Wong, Chun Wa

2013-01-01

Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages...

Effects of Computer Graphics Types and Epistemological Beliefs on Students' Learning of Mathematical Concepts.

Science.gov (United States)

Lin, Chi-Hui

2002-01-01

Describes a study that determined the implications of computer graphics types and epistemological beliefs with regard to the design of computer-based mathematical concept learning with elementary school students in Taiwan. Discusses the factor structure of the epistemological belief questionnaire, student performance, and students' attitudes…

Pre-service mathematics student teachers’ conceptions of nominal and effective interest rates

Directory of Open Access Journals (Sweden)

Judah P. Makonye

2017-04-01

Full Text Available The general public consumes financial products such as loans that are administered in the realm of nominal and effective interest rates. It is debatable if most consumers really understand how these rates function. This article explores the conceptions that student teachers have about nominal and effective interest rates. The APOS theory illuminates analysis of students’ levels of conception. Seventy second-year mathematics students’ responses to Grade 12 tasks on effective and nominal interest rates were analysed, after which 12 students were interviewed about their mathematical thinking in solving the tasks. The findings varied. While some students could not do the tasks due to erratic use of formulae (algebra, I ascertained that some students obtained correct answers through scrupulous adherence to the external prompt of formulae. Most of those students remained stuck at the action and process stages and could not view their processes as mathematical objects. A few students had reached the object and schema stages, showing mature understanding of the relationship between nominal and effective interest rates. As most students remained at the operational stages rather than the structural, the findings accentuate that when teaching this topic, teachers ought to take their time to build learners’ schema for these notions. They need to guide their learners through the necessary action-process-object loop and refrain from introducing students to formulae too soon as this stalls their advancement to the object and schema stages which are useful in making them smart consumers of financial products.

The deleuzian abstract machines

DEFF Research Database (Denmark)

Werner Petersen, Erik

2005-01-01

To most people the concept of abstract machines is connected to the name of Alan Turing and the development of the modern computer. The Turing machine is universal, axiomatic and symbolic (E.g. operating on symbols). Inspired by Foucault, Deleuze and Guattari extended the concept of abstract...

Visual arts and the teaching of the mathematical concepts of shape and space in Grade R classrooms

Directory of Open Access Journals (Sweden)

Dianne Wilmot

2015-09-01

Full Text Available This article addresses the need for research in the areas of Grade R curriculum and pedagogy, Grade R teacher professional development, and early years mathematics teaching. More specifically, it responds to the need for teacher professional development in Grade R mathematics teaching of the geometric concepts of space and shape. The article describes a study about teachers’ understanding of how visual arts can be used as pedagogical modality. The study was prompted by the findings of a ‘Maths and Science through Arts and Culture Curriculum’ intervention undertaken with Grade R teachers enrolled for a Bachelor of Education (Foundation Phase degree at a South African university. Post-intervention, teachers’ classroom practices did not change, and they were not using visual arts to teach mathematical concepts. The lessons learned from the research intervention may contribute to the wider debate about Grade R teaching and children’s learning.

On the application of Discrete Time Optimal Control Concepts to ...

African Journals Online (AJOL)

On the application of Discrete Time Optimal Control Concepts to Economic Problems. ... Journal of the Nigerian Association of Mathematical Physics ... Abstract. An extension of the use of the maximum principle to solve Discrete-time Optimal Control Problems (DTOCP), in which the state equations are in the form of general ...

What is the problem in problem-based learning in higher education mathematics

Science.gov (United States)

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

THE METHODICAL ASPECTS OF THE ALGEBRA AND THE MATHEMATICAL ANALYSIS STUDY USING THE SAGEMATH CLOUD

Directory of Open Access Journals (Sweden)

M. Popel

2014-06-01

Full Text Available The quality of mathematics education depends largely on the quality of education in general. The main idea may be summarized as follows: in order to educate the younger generation of people to be able to meet adequately the demands of the time, it is necessary to create conditions for the high-quality mathematics education. Improving the quality of mathematics education of pupils in secondary school is one of the most pressing problems. Contents of the school course of mathematics and its teaching method has always been the subject of undammed and sometimes stormy scientific debates. There are especially true methods of teaching algebra and the analisis in the high secondary school. Still in the study process the algebraic concepts and principles of analysis are given in such an abstract and generalized form that the student may has considerable difficulties to map these general abstract concepts to the certain concrete images, they are generalizations of. Improving education quality indicators can be achieved by using the appropriate computer technology. The article deals with the use of the cloud-oriented systems of computer mathematics (SCM. The prospects of development of the Web-SCM in terms of cloud-based learning environment are considered. The pedagogical features of the SageMath Cloud use as a tool for mathematics learning are revealed. The methodological aspects of algebra and elementary analysis teaching in a high profile school using the cloud-oriented the SCM SageMath Cloud are revealed.

The Power of Colombian Mathematics Teachers' Conceptions of Social/Institutional Factors of Teaching

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Agudelo-Valderrama, Cecilia

2008-01-01

In this paper I shall discuss data from a study on Colombian mathematics teachers' conceptions of their own teaching practices of beginning algebra, which led to the development of a theoretical model of teachers' thought structures designed as a thinking tool at the initial stage of the study. With a focus on the perspectives of teachers, the…

Introduction to proof in abstract mathematics

CERN Document Server

Wohlgemuth, Andrew

2011-01-01

The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixe

Mathematics Curriculum, the Philosophy of Mathematics and its ...

African Journals Online (AJOL)

It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...

Why Johnny Struggles When Familiar Concepts Are Taken to a New Mathematical Domain: Towards a Polysemous Approach

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Kontorovich, Igor'

2018-01-01

This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

ProofJudge: Automated Proof Judging Tool for Learning Mathematical Logic

DEFF Research Database (Denmark)

Villadsen, Jørgen

2015-01-01

Today we have software in many artefacts, from medical devices to cars and airplanes, and the software must not only be efficient and intelligent but also reliable and secure. Tests can show the presence of bugs but cannot guarantee their absence. A machine-checked proof using mathematical logic...... pen and paper because no adequate tool was available. The learning problem is how to make abstract concepts of logic as concrete as possible. ProofJudge is a computer system and teaching approach for teaching mathematical logic and automated reasoning which augments the e-learning tool NaDeA (Natural...

ProofJudge: Automated Proof Judging Tool for Learning Mathematical Logic

DEFF Research Database (Denmark)

Villadsen, Jørgen

2016-01-01

Today we have software in many artefacts, from medical devices to cars and airplanes, and the software must not only be efficient and intelligent but also reliable and secure. Tests can show the presence of bugs but cannot guarantee their absence. A machine-checked proof using mathematical logic...... using pen and paper because no adequate tool was available. The learning problem is how to make abstract concepts of logic as concrete as possible. ProofJudge is a computer system and teaching approach for teaching mathematical logic and automated reasoning which augments the e-learning tool Na...

Concept Acquisition in Children with Mild Intellectual Disability: Factors Affecting the Abstraction of Prototypical Information.

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Hayes, Brett K.; Conway, Robert N.

2000-01-01

A study investigated effects of variations in the number of instances comprising a category on concept acquisition by 31 children (ages 9-14) with mild intellectual disability and 19 controls. Intellectual disability had little effect on ability to abstract a category prototype but did reduce use of exemplar-specific information for recognition.…

Concept of Gender and Mathematics Education Conceito de Gênero e Educação Matemática

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Maria Celeste Reis Fernandes de Souza

2009-04-01

Full Text Available The text presents the emergence of the concept of gender in education, showing its different nuances, and proposes its incorporation as a category of analysis in the field of Mathematics Education, in which the discussions on gender are rarely detected, especially when we analyze the Brazilian production. Taking as references the female scholars in the field of gender studies, we have reflected on the need of incorporating such concept into the investigation about the processes of teaching and learning Mathematics, the subjects in the pedagogical relations, and the cultural mode of conceiving, using and evaluating mathematical knowledge. Such incorporation would imply, however, the disruption in the ways in which we have thought concepts related to female, male and mathematics. Keywords: Gender. Mathematics Education. Research.O texto expõe a emergência do conceito de gênero no campo da educação, mostrando suas diferentes nuances, e propõe sua incorporação como uma categoria de análise no campo da Educação Matemática, no qual as discussões sobre gênero aparecem muito raramente, especialmente quando se analisa a produção brasileira. Tomando como referência estudiosas do campo dos estudos de gênero, refletimos sobre a necessidade da incorporação de tal conceito às investigações sobre os processos de ensino e aprendizagem da Matemática, sobre os sujeitos das relações pedagógicas e sobre os modos culturais de se conceber, utilizar e avaliar conhecimentos matemáticos. Tal incorporação implicaria, porém, deslocamentos nos modos como temos pensado femininos, masculinos e matemática. Palavras-chave: Gênero. Educação Matemática. Pesquisa.

Explorations in Mathematical Physics The Concepts Behind an Elegant Language

CERN Document Server

Koks, Don

2006-01-01

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis buil...

Internal process: what is abstraction and distortion process?

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Fiantika, F. R.; Budayasa, I. K.; Lukito, A.

2018-03-01

Geometry is one of the branch of mathematics that plays a major role in the development of science and technology. Thus, knowing the geometry concept is needed for students from their early basic level of thinking. A preliminary study showed that the elementary students have difficulty in perceiving parallelogram shape in a 2-dimention of a cube drawing as a square shape. This difficulty makes the students can not solve geometrical problems correctly. This problem is related to the internal thinking process in geometry. We conducted the exploration of students’ internal thinking processes in geometry particularly in distinguishing the square and parallelogram shape. How the students process their internal thinking through distortion and abstraction is the main aim of this study. Analysis of the geometrical test and deep interview are used in this study to obtain the data. The result of this study is there are two types of distortion and abstraction respectively in which the student used in their internal thinking processes.

Understanding in mathematics

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Sierpinska, Anna

1994-01-01

The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.

Direct and Indirect Effects of IQ, Parental Help, Effort, and Mathematics Self-Concept on Mathematics Achievement

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Maher Abu-Hilal

2012-11-01

Full Text Available This study examined the structural relationships among cognitive constructs (intelligence and achievement and affective constructs (perceived parental help, effort and self-concept. It was proposed that the relationships are not invariant across gender. The sample consisted of 219 boys and 133 girls from elementary and preparatory public schools in Al Ain in the United Arab Emirates. Intelligence (IQ was measured by the Test of Non-verbal Intelligence (TONI and parental help was measured by 4-Likert-type items. Effort was measured by 4-Likert-type items. Self-concept (SC was measured by 8-Likert-type items taken from the SDQ I (Abu-Hilal, 2000. Mathematic Achievement was the scores of students in mathematics from school records. The structural model assumed that IQ would have an effect on parental help, effort, SC and achievement. Parental help would have an effect on effort, SC and achievement. Also, effort would have an effect on SC and achievement. Finally, SC would have an effect on achievement. The structural model was tested for invariance across gender. The measurement model proved to be invariant across gender and so was the structural model. The non-constrained model indicated that the structural relationships among the variables do vary according to gender. For example, boys benefited from parental help by exerting more effort while girls did not. Boys with high IQ exerted more effort than boys with low IQ; but girls with high IQ exerted the same amount of effort as girls with low IQ. The model explained 45% and 39% of the variance in math scores for boys and girls, respectively.

On problems in defining abstract and metaphysical concepts--emergence of a new model.

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Nahod, Bruno; Nahod, Perina Vukša

2014-12-01

Basic anthropological terminology is the first project covering terms from the domain of the social sciences under the Croatian Special Field Terminology program (Struna). Problems that have been sporadically noticed or whose existence could have been presumed during the processing of terms mainly from technical fields and sciences have finally emerged in "anthropology". The principles of the General Theory of Terminology (GTT), which are followed in Struna, were put to a truly exacting test, and sometimes stretched beyond their limits when applied to concepts that do not necessarily have references in the physical world; namely, abstract and metaphysical concepts. We are currently developing a new terminographical model based on Idealized Cognitive Models (ICM), which will hopefully ensure a better cross-filed implementation of various types of concepts and their relations. The goal of this paper is to introduce the theoretical bases of our model. Additionally, we will present a pilot study of the series of experiments in which we are trying to investigate the nature of conceptual categorization in special languages and its proposed difference form categorization in general language.

Motivated Forgetting in Early Mathematics: A Proof-of-Concept Study

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Gerardo Ramirez

2017-12-01

Full Text Available Educators assume that students are motivated to retain what they are taught. Yet, students commonly report that they forget most of what they learn, especially in mathematics. In the current study I ask whether students may be motivated to forget mathematics because of academic experiences threaten the self-perceptions they are committed to maintaining. Using a large dataset of 1st and 2nd grade children (N = 812, I hypothesize that math anxiety creates negative experiences in the classroom that threaten children’s positive math self-perceptions, which in turn spurs a motivation to forget mathematics. I argue that this motivation to forget is activated during the winter break, which in turn reduces the extent to which children grow in achievement across the school year. Children were assessed for math self-perceptions, math anxiety and math achievement in the fall before going into winter break. During the spring, children’s math achievement was measured once again. A math achievement growth score was devised from a regression model of fall math achievement predicting spring achievement. Results show that children with higher math self-perceptions showed reduced growth in math achievement across the school year as a function of math anxiety. Children with lower math interest self-perceptions did not show this relationship. Results serve as a proof-of-concept for a scientific account of motivated forgetting within the context of education.

Using Interactive Software to Teach Foundational Mathematical Skills

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Larysa V Lysenko

2016-01-01

Full Text Available The pilot research presented here explores the classroom use of Emerging Literacy in Mathematics (ELM software, a research-based bilingual interactive multimedia instructional tool, and its potential to develop emerging numeracy skills. At the time of the study, a central theme of early mathematics curricula, Number Concept, was fully developed. It was broken down into five mathematical concepts including counting, comparing, adding, subtracting and decomposing. Each of these was further subdivided yielding 22 online activities, each building in a level of complexity and abstraction. In total, 234 grade one students from 12 classes participated in the two-group post-test study that lasted about seven weeks and for which students in the experimental group used ELM for about 30 minutes weekly. The results for the final sample of 186 students showed that ELM students scored higher on the standardized math test (Canadian Achievement Test, 2008 and reported less boredom and lower anxiety as measured on the Academic Emotions Questionnaire than their peers in the control group. This short duration pilot study of one ELM theme holds great promise for ELM’s continued development.

Mathematics and engineering in real life through mathematical competitions

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More, M.

2018-02-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

The Abstraction Ability in Constructing Relation Within Triangles by The Seventh Grade Students of Junior High School

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Annas, Suwardi; Djadir; Mutmainna Hasma, Sitti

2018-01-01

on is an activity to organize a mathematical concept that has been previously owned into a new mathematical structure. Activites in abstraction are recognizing, organizing and constructing. Recognizing is a process of identifying a mathematical structure that had existed before. Organizing is a process of using structural knowledge to be assembled into a solution of a problem and constructing is a process of organizing the characteristics of the object into a new structure that does not exist. In abstraction process, the students use attributes to address the object, including routine attribute, nonroutine attributes, and meaningless attributes. This research applied descriptive qualitative research which aimed to describe the abstraction ability of students from high, moderate, and low groups to construct a relation within triangle. In collecting the data, this research used students’ pre-ability math test, abstraction test, and guided interview. The sampling technique in this research was based on the students’ scores in pre-ability math test, which were divided into three groups. Two students from each group were opted as the subjects of this research. Questions of the test are based on the indicators of steps in abstraction activity. Thus, based on the data gained in this research, researcher determined the tendency of attributes used in each abstraction activity. The result of this research revealed that students from high, moderate and low groups were prone to use routine attributes in recognizing triangles. In organizing the characteristics within triangles, high group tended to organize the triangle correctly, while the moderate and low groups tended to organize the triangle incorrectly. In constructing relation within triangles, students in high, moderate and low groups construct it incompletely.

The motion behind the symbols: a vital role for dynamism in the conceptualization of limits and continuity in expert mathematics.

Science.gov (United States)

Marghetis, Tyler; Núñez, Rafael

2013-04-01

The canonical history of mathematics suggests that the late 19th-century "arithmetization" of calculus marked a shift away from spatial-dynamic intuitions, grounding concepts in static, rigorous definitions. Instead, we argue that mathematicians, both historically and currently, rely on dynamic conceptualizations of mathematical concepts like continuity, limits, and functions. In this article, we present two studies of the role of dynamic conceptual systems in expert proof. The first is an analysis of co-speech gesture produced by mathematics graduate students while proving a theorem, which reveals a reliance on dynamic conceptual resources. The second is a cognitive-historical case study of an incident in 19th-century mathematics that suggests a functional role for such dynamism in the reasoning of the renowned mathematician Augustin Cauchy. Taken together, these two studies indicate that essential concepts in calculus that have been defined entirely in abstract, static terms are nevertheless conceptualized dynamically, in both contemporary and historical practice. Copyright © 2013 Cognitive Science Society, Inc.

Implementation of cooperative learning model type STAD with RME approach to understanding of mathematical concept student state junior high school in Pekanbaru

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Nurhayati, Dian Mita; Hartono

2017-05-01

This study aims to determine whether there is a difference in the ability of understanding the concept of mathematics between students who use cooperative learning model Student Teams Achievement Division type with Realistic Mathematic Education approach and students who use regular learning in seventh grade SMPN 35 Pekanbaru. This study was quasi experiments with Posttest-only Control Design. The populations in this research were all the seventh grade students in one of state junior high school in Pekanbaru. The samples were a class that is used as the experimental class and one other as the control class. The process of sampling is using purposive sampling technique. Retrieval of data in this study using the documentation, observation sheets, and test. The test use t-test formula to determine whether there is a difference in student's understanding of mathematical concepts. Before the t-test, should be used to test the homogeneity and normality. Based in the analysis of these data with t0 = 2.9 there is a difference in student's understanding of mathematical concepts between experimental and control class. Percentage of students experimental class with score more than 65 was 76.9% and 56.4% of students control class. Thus be concluded, the ability of understanding mathematical concepts students who use the cooperative learning model type STAD with RME approach better than students using the regular learning. So that cooperative learning model type STAD with RME approach is well used in learning process.

Non-intellectual predictors of achievement in mathematics

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Milošević Nikoleta M.

2003-01-01

Full Text Available Findings presented herein are a part of a large international study of primary school final grade student achievement in mathematics and science (TIMSS 2003. Studies were also conducted on the degree of correlation between student family socioeconomic status, mathematical self-concept and achievement in mathematics. Pilot studies, whose findings are discussed comprised 112 seventh-grade students. "Family socioeconomic status" was defined by variables such as the number of family members, economically disadvantaged/affluent home, and parental educational status. "Mathematical self-concept" was defined as one of the more narrow domains of academic self-concept. "Achievement in mathematics" was measured by the test assessing two dimensions of knowledge of mathematics: content and cognitive skills. The analyses of partial correlations indicate that the most significant predictors of achievement in mathematics test are as follows mathematical self-concept, mother’s educational status and some indicators of family socioeconomic status (access to the Internet, number of household members, number of books available at home. Concerning the correlation found between family characteristics and mathematical self-concept and achievement in mathematics, the developers of current changes in mathematics teaching should not disregard the findings of this study.

Finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.

The impact of negative emotions on self-concept abstraction depends on accessible information processing styles.

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Isbell, Linda M; Rovenpor, Daniel R; Lair, Elicia C

2016-10-01

Research suggests that anger promotes global, abstract processing whereas sadness and fear promote local, concrete processing (see Schwarz & Clore, 2007 for a review). Contrary to a large and influential body of work suggesting that specific affective experiences are tethered to specific cognitive outcomes, the affect-as-cognitive-feedback account maintains that affective experiences confer positive or negative value on currently dominant processing styles, and thus can lead to either global or local processing (Huntsinger, Isbell, & Clore, 2014). The current work extends this theoretical perspective by investigating the impact of discrete negative emotions on the self-concept. By experimentally manipulating information processing styles and discrete negative emotions that vary in appraisals of certainty, we demonstrate that the impact of discrete negative emotions on the spontaneous self-concept depends on accessible processing styles. When global processing was accessible, individuals in angry (negative, high certainty) states generated more abstract statements about themselves than individuals in either sad (Experiment 1) or fearful (Experiment 2; negative, low certainty) states. When local processing was made accessible, however, the opposite pattern emerged, whereby individuals in angry states generated fewer abstract statements than individuals in sad or fearful states. Together these studies provide new insights into the mechanisms through which discrete emotions influence cognition. In contrast to theories assuming a dedicated link between emotions and processing styles, these results suggest that discrete emotions provide feedback about accessible ways of thinking, and are consistent with recent evidence suggesting that the impact of affect on cognition is highly context-dependent. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

ABSTRACT IMPLEMENTATION OF A KIND TO MANAGE DATA SETS USING PROGRAMMING LANGUAGE C + +

OpenAIRE

Ruiz L., Edgar; Hinojosa L., Hilmar

2014-01-01

This article presents the implementation of a data abstract type to represent the Set Theory Mathematical Concept, The program has been written in C++ Program Language applying the Object Oriented Programming Paradigm through a Dev C++ v.4.1 Compiler, a GNU compiler with GPL licence. El artículo presenta la implementación de un tipo abstracto de datos para representar el concepto matemático de la teoría de conjuntos. El programa ha sido escrito en lenguaje de programación C++ aplicando el ...

Abstracts

Institute of Scientific and Technical Information of China (English)

2011-01-01

The Western Theories of War Ethics and Contemporary Controversies Li Xiaodong U Ruijing （4） [ Abstract] In the field of international relations, war ethics is a concept with distinct westem ideological color. Due to factors of history and reality, the in

A language based on analogy to communicate cultural concepts in SETI

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Musso, Paolo

2011-02-01

The present paper is a synthesis of three presentation given by myself at the Toulouse IAC 2001 ( Analogy as a tool to communicate abstract concepts in SETI), the Bremen IAC 2003 ( From maths to culture: towards an effective message), and the Vancouver IAC 2004 ( Philosophical and religious implications of extraterrestrial intelligent life). Its aim is to find a way to make our cultural concepts understandable to hypothetical extraterrestrials (ETs) in a SETI communication. First of all, I expose the reasons why I think that analogy could be a good tool for this purpose. Then, I try to show that this is possible only in the context of an integrated language, using both abstract symbols and pictures, also sketching two practical examples about some basic concepts of our moral and religious tradition. Further studies are required to determine whether this method could be extended to the higher-level abstract concepts in the other fields of our culture. Finally, I discuss the possible role of mathematics, logic and natural science in the construction of an analogy-based language for interstellar messages with a cultural content and a possible way of managing this matter from a social point of view.

The learning evaluations of the concept function in the mathematical subject I

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Wilmer Valle Castañeda

2018-03-01

Full Text Available The evaluation must be one of the most complex tasks that teachers face today, both for the process itself and for having to issue an assessment about the achievements and deficiencies of the students. It is for them that techniques and instruments were developed, which allow the evaluation of the function concept in the Mathematics I subject´s. Methods of the theoretical level, of the empirical level such as the historical-logical analysis, the surveys, were used in the research carried out. The documentary analyses, as well as procedures such as the analysis - synthesis that made it possible to investigate the theoretical and practical fundament´s learning evaluation´s. The evaluation instruments presented allowed for the evaluation of the students in Mathematics I, less than one of the most important functions of the evaluation: the formative or educational function. These constituted a reference for the continuous improvement of student learning.

The analysis of the mathematics concept comprehension of senior high school student on dynamic fluid material

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Kristian, P. L. Y.; Cari, C.; Sunarno, W.

2018-04-01

This study purposes to describe and analyse the students' concept understanding of dynamic fluid. The subjects of this research are 10 students of senior high school. The data collected finished the essay test that consists of 5 questions have been adapted to the indicators of learning. The data of this research is analysed using descriptive-qualitative approach by referring of the student's argumentations about their answer from the questions that given. The results showed that students still have incorrect understanding the concept of dynamic fluids, especially on the Bernoulli’s principle and its application. Based on the results of this research, the teachers should emphasize the concept understanding of the students therefore the students don not only understand the physics concept in mathematical form.

Adaptation and Extension of the Framework of Reducing Abstraction in the Case of Differential Equations

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Raychaudhuri, Debasree

2014-01-01

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints.

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Benko, Matúš; Gfrerer, Helmut

2018-01-01

In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Formula: see text]-stationarity. We show how the property of [Formula: see text]-stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Formula: see text]-stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Formula: see text]-stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.

Moving toward Positive Mathematics Beliefs and Developing Socio-Mathematical Authority: Urban Preservice Teachers in Mathematics Methods Courses

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Saran, Rupam; Gujarati, Joan

2013-01-01

This article explores how preservice elementary teachers change their negative beliefs toward mathematics into positive ones after taking a mathematics methods course that follows the Concrete-Pictorial-Abstract (CPA) instructional method. Also explored is the relationship between those beliefs and sociomathematical authority. By administering…

Mathematics and Engineering in Real Life through Mathematical Competitions

Science.gov (United States)

More, M.

2018-01-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…

Problem Posing with Realistic Mathematics Education Approach in Geometry Learning

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Mahendra, R.; Slamet, I.; Budiyono

2017-09-01

One of the difficulties of students in the learning of geometry is on the subject of plane that requires students to understand the abstract matter. The aim of this research is to determine the effect of Problem Posing learning model with Realistic Mathematics Education Approach in geometry learning. This quasi experimental research was conducted in one of the junior high schools in Karanganyar, Indonesia. The sample was taken using stratified cluster random sampling technique. The results of this research indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students’ conceptual understanding significantly in geometry learning especially on plane topics. It is because students on the application of Problem Posing with Realistic Mathematics Education Approach are become to be active in constructing their knowledge, proposing, and problem solving in realistic, so it easier for students to understand concepts and solve the problems. Therefore, the model of Problem Posing learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on geometry material. Furthermore, the impact can improve student achievement.

[For the Introduction of a Conceptual Perspective in Mathematics: Dedekind, Noether, van der Waerden].

Science.gov (United States)

Koreuber, Mechthild

2015-09-01

,,She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine - of all that is characterized by the term ‚Begriffliche Mathematik‘.“ The aim of this paper is to illuminate this "new direction", which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831-1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a "free creation of the human spirit". They thus stand for an abstract perspective of mathematics in their entirety, described as 'modern algebra' in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on "general mathematical concepts" [allgemein-mathematische Begriffe], was the success of a cultural movement whose most important protagonists included Emmy Noether (1882-1935) and her pupil Bartel L. van der Waerden (1903-1996). With the use of the term 'conceptual', a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the "working and conceptual methods" [Arbeits- und Auffassungsmethoden] of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term "conceptual world" [Begriffswelt] in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.

The Effect of Using an Educational Website in Achievement of Bachelor Students in the Course of Basic Concepts in Mathematics at Al al-Bayt University

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Qudah, Ahmad Hassan

2016-01-01

The study aimed to detect the effect of using an educational site on the Internet in the collection of bachelor's students in the course of basic concepts in mathematics at Al al-Bayt University, and the study sample consisted of all students in the course basic concepts in mathematics in the first semester of the academic year 2014/2015 and the…

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

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Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

2016-01-01

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

Directory of Open Access Journals (Sweden)

Morten Andersen

Full Text Available The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

Mathematics for physicists

CERN Document Server

Dennery, Philippe

1967-01-01

""A fine example of how to present 'classical' physical mathematics."" - American ScientistWritten for advanced undergraduate and graduate students, this volume provides a thorough background in the mathematics needed to understand today's more advanced topics in physics and engineering. Without sacrificing rigor, the authors develop the theoretical material at length, in a highly readable, and, wherever possible, in an intuitive manner. Each abstract idea is accompanied by a very simple, concrete example, showing the student that the abstraction is merely a generalization from easily understo

Where mathematics come from how the embodied mind brings mathematics into being

CERN Document Server

Lakoff, George

2001-01-01

This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.

THE APPLICATION OF RECIPROCAL TEACHING METHOD FOR IMPROVING THE UNDERSTANDING OF MATHEMATICS CONCEPT OF 7TH GRADE STUDENTS SMP NEGERI 2 DEPOK.

Directory of Open Access Journals (Sweden)

Tatag Bagus Argikas

2016-10-01

Full Text Available This research aims to: (1 describe the implementation of learning mathematics with Reciprocal Teaching methods that is for improving the concept of learning understanding mathematic in class VIIA SMP Negeri 2 Depok. (2 Knowing the increased understanding of student learning in class VIIA SMP Negeri 2 Depok use Reciprocal Teaching methods. This research constitutes an action in class that is according along the teacher. The data of research was collated by sheet observations and each evaluation of cycles. That is done in two cycles. The first was retrieved the average value of student learning achievement of 70.96%. The second was retrieved achievement of 90.32%. Thus this learning model can increase student learning understanding.   Key word: The understanding of Mathematical Concept, Reciprocal Teaching Method.

Basic Definitions and Concepts of Systems Approach, Mathematical Modeling and Information Technologies in Sports Science

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А. Лопатьєв

2017-09-01

Full Text Available The objective is to systematize and adapt the basic definitions and concepts of the systems approach, mathematical modeling and information technologies to sports science. Materials and methods. The research has studied the availability of appropriate terms in shooting sports, which would meet the requirements of modern sports science. It has examined the compliance of the shooting sports training program for children and youth sports schools, the Olympic reserve specialized children and youth schools, schools of higher sports skills, and sports educational institutions with the modern requirements and principles. Research results. The paper suggests the basic definitions adapted to the requirements of technical sports and sports science. The research has thoroughly analyzed the shooting sports training program for children and youth sports schools, the Olympic reserve specialized children and youth schools, schools of higher sports skills, and sports educational institutions. The paper offers options to improve the training program in accordance with the modern tendencies of training athletes.  Conclusions. The research suggests to systematize and adapt the basic definitions and concepts of the systems approach, mathematical modeling and information technologies using the example of technical sports.

Integrated learning of mathematics, science and technology concepts through LEGO/Logo projects

Science.gov (United States)

Wu, Lina

This dissertation examined integrated learning in the domains of mathematics, science and technology based on Piaget's constructivism, Papert's constructionism, and project-based approach to education. Ten fifth grade students were involved in a two-month long after school program where they designed and built their own computer-controlled LEGO/Logo projects that required the use of gears, ratios and motion concepts. The design of this study centered on three notions of integrated learning: (1) integration in terms of what educational materials/settings provide, (2) integration in terms of students' use of those materials, and (3) integration in the psychological sense. In terms of the first notion, the results generally showed that the LEGO/Logo environment supported the integrated learning of math, science and technology concepts. Regarding the second notion, the students all completed impressive projects of their own design. They successfully combined gears, motors, and LEGO parts together to create motion and writing control commands to manipulate the motion. But contrary to my initial expectations, their successful designs did not require numerical reasoning about ratios in designing effective gear systems. When they did reason about gear relationships, they worked with "qualitative" ratios, e.g., "a larger driver gear with a smaller driven gear increases the speed." In terms of the third notion of integrated learning, there was evidence in all four case study students of the psychological processes involved in linking mathematical, scientific, and/or technological concepts together to achieve new conceptual units. The students not only made connections between ideas and experiences, but also recognized decisive patterns and relationships in their project work. The students with stronger overall project performances showed more evidence of synthesis than the students with relatively weaker performances did. The findings support the conclusion that all three

Abstract Algebra to Secondary School Algebra: Building Bridges

Science.gov (United States)

Christy, Donna; Sparks, Rebecca

2015-01-01

The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

Conceptualising inquiry based education in mathematics

DEFF Research Database (Denmark)

Blomhøj, Morten; Artigue, Michéle

2013-01-01

of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical...... frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the Theory of Didactical Situations, the Realistic Mathematics Education programme, the mathematical modelling perspective, the Anthropological Theory of Didactics...

The materiality of mathematics: presenting mathematics at the blackboard.

Science.gov (United States)

Greiffenhagen, Christian

2014-09-01

Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.

Enhancing Students’ Interest through Mathematics Learning

Science.gov (United States)

Azmidar, A.; Darhim, D.; Dahlan, J. A.

2017-09-01

A number of previous researchers indicated that students’ mathematics interest still low because most of them have perceived that mathematics is very difficult, boring, not very practical, and have many abstract theorems that were very hard to understand. Another cause is the teaching and learning process used, which is mechanistic without considering students’ needs. Learning is more known as the process of transferring the knowledge to the students. Let students construct their own knowledge with the physical and mental reflection that is done by activity in the new knowledge. This article is literature study. The purpose of this article is to examine the Concrete-Pictorial-Abstract approach in theoretically to improve students’ mathematics interest. The conclusion of this literature study is the Concrete-Pictorial-Abstract approach can be used as an alternative to improve students’ mathematics interest.

The fundamentals of mathematical analysis

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Fikhtengol'ts, G M

1965-01-01

The Fundamentals of Mathematical Analysis, Volume 1 is a textbook that provides a systematic and rigorous treatment of the fundamentals of mathematical analysis. Emphasis is placed on the concept of limit which plays a principal role in mathematical analysis. Examples of the application of mathematical analysis to geometry, mechanics, physics, and engineering are given. This volume is comprised of 14 chapters and begins with a discussion on real numbers, their properties and applications, and arithmetical operations over real numbers. The reader is then introduced to the concept of function, i

Conference on "Mathematical Technology of Networks"

CERN Document Server

2015-01-01

Bringing together leading researchers in the fields of functional analysis, mathematical physics and graph theory, as well as natural scientists using networks as a tool in their own research fields, such as neuroscience and machine learning, this volume presents recent advances in functional, analytical, probabilistic, and spectral aspects in the study of graphs, quantum graphs, and complex networks. The contributors to this volume explore the interplay between theoretical and applied aspects of discrete and continuous graphs. Their work helps to close the gap between different avenues of research on graphs, including metric graphs and ramified structures. All papers were presented at the conference "Mathematical Technology of Networks," held December 4–7, 2013 at the Zentrum für interdisziplinäre Forschung (ZiF) in Bielefeld, Germany, and are supplemented with detailed figures illustrating both abstract concepts as well as their real-world applications. Dynamical models on graphs or random graphs a...

Mathematical Literacy: A new literacy or a new mathematics?

Directory of Open Access Journals (Sweden)

Renuka Vithal

2006-10-01

Full Text Available Mathematical Literacy is a ‘hot’ topic at present in most countries, whether it is referred to by that name, or in some cases as Numeracy, or Quantitative Literacy, or Matheracy, or as some part of Ethnomathematics, or related to Mathematics in Society. Questions continue to be asked about what is meant by mathematics in any concept of Mathematical Literacy and the use of the very word ‘Literacy’ in its association with Mathematics has been challenged. Its importance, however, lies in changing our perspective on mathematics teaching, away from the elitism so often associated with much mathematics education, and towards a more equitable, accessible and genuinely educational ideal.

Abstracts of Research, July 1973 through June 1974.

Science.gov (United States)

Ohio State Univ., Columbus. Computer and Information Science Research Center.

Abstracts of research papers in the fields of computer and information science are given; 72 papers are abstracted in the areas of information storage and retrieval, information processing, linguistic analysis, artificial intelligence, mathematical techniques, systems programing, and computer networks. In addition, the Ohio State University…

The Role of Games and Simulations to Teach Abstract Concepts of Anarchy, Cooperation, and Conflict in World Politics

Science.gov (United States)

McCarthy, Mary M.

2014-01-01

Games and simulations are increasingly used in courses on international politics. This study explores the hypothesis that games are better than simulations (as well as only reading and lectures) in introducing students to abstract concepts integral to an understanding of world politics. The study compares a two-level Prisoner's Dilemma game…

Abstract Algebra for Teachers: An Evaluative Case Study

Science.gov (United States)

Hoffman, Andrew Joseph

2017-01-01

This manuscript describes the study of an abstract algebra course for preservice secondary mathematics teachers (PSMTs). Often, courses in abstract algebra have not been viewed as productive, beneficial learning experiences for future teachers, both by researchers and PSMTs themselves. This despite calls for increased content knowledge for…

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

Teaching abstraction in introductory courses

NARCIS (Netherlands)

Koppelman, Herman; van Dijk, Betsy

Abstraction is viewed as a key concept in computer science. It is not only an important concept but also one that is difficult to master. This paper focuses on the problems that novices experience when they first encounter this concept. Three assignments from introductory courses are analyzed, to

Mathematical bridges

CERN Document Server

Andreescu, Titu; Tetiva, Marian

2017-01-01

Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

THE CONCEPT OF AGE IN SYSTEMS ANALYSIS

Directory of Open Access Journals (Sweden)

A. Dubi

2012-01-01

Full Text Available

ENGLISH ABSTRACT: This paper discusses the mathematical concept of ageing. It is shown that while in most cases a probabilistic definition of age is sufficient, in some cases a calendaric definition must be added in order to preserve the relationship between time and age.

AFRIKAANSE OPSOMMING: Hierdie artikel bespreek die wiskundige betekenis van veroudering. Daar word getoon dat alhoewel 'n waarskynlikheidsgebaseerde definisie van ouderdom meestal voldoende is, daar in sommige gevalle 'n tydgebaseerde definisie nodig is om die verwantskap tussen tyd en ouderdom te behou.

Meaning in mathematics

CERN Document Server

2011-01-01

Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics.

The Role of Motion Concepts in Understanding Non-Motion Concepts

Directory of Open Access Journals (Sweden)

Omid Khatin-Zadeh

2017-12-01

Full Text Available This article discusses a specific type of metaphor in which an abstract non-motion domain is described in terms of a motion event. Abstract non-motion domains are inherently different from concrete motion domains. However, motion domains are used to describe abstract non-motion domains in many metaphors. Three main reasons are suggested for the suitability of motion events in such metaphorical descriptions. Firstly, motion events usually have high degrees of concreteness. Secondly, motion events are highly imageable. Thirdly, components of any motion event can be imagined almost simultaneously within a three-dimensional space. These three characteristics make motion events suitable domains for describing abstract non-motion domains, and facilitate the process of online comprehension throughout language processing. Extending the main point into the field of mathematics, this article discusses the process of transforming abstract mathematical problems into imageable geometric representations within the three-dimensional space. This strategy is widely used by mathematicians to solve highly abstract and complex problems.

Financial mathematics

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Jothi, A Lenin

2009-01-01

Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m

Mathematics Teachers' Response to the Reform Agenda: Results of the 1993 National Survey of Science and Mathematics Education.

Science.gov (United States)

Weiss, Iris R.

The NCTM Standards call for the introduction of challenging mathematics content for all students beginning in the early grades. If teachers are to guide students in their exploration of mathematics concepts, they must themselves have a firm grasp of powerful mathematics concepts. This paper uses data from the 1993 National Survey of Science and…

Selection of Learning Media Mathematics for Junior School Students

Science.gov (United States)

Widodo, Sri Adi; Wahyudin

2018-01-01

One of the factors that determine the success of mathematics learning is the learning media used. Learning media can help students to create mathematical abstract mathematics that is abstract. In addition to media, meaningful learning is a learning that is adapted to the students' cognitive development. According to Piaget, junior high school…

An original approach to the mathematical concept of graph from braid crafts

Directory of Open Access Journals (Sweden)

Albanese Veronica

2016-01-01

Full Text Available In previous researches we found that a community of Argentinean artisans models its own practices of braiding using graphs. Inspired by these findings, we designed an educational activity to introduce the concept of graphs. The study of graphs helps students to develop combinatorial and systematic thinking as well as skills to model reality and abstract and generalize patterns from particular situations. The tasks proposed aim to construct the concept of graphs, then identify characteristics that allow some graphs to be models of braids and finally use them to invent more graphs for new braids. The activity performed in a secondary school teachers’ educational course, had quite satisfactory results due to the number of braids invented and the small amount of mistakes made by the participants.

DOE Fundamentals Handbook: Mathematics, Volume 1

International Nuclear Information System (INIS)

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

DOE Fundamentals Handbook: Mathematics, Volume 2

International Nuclear Information System (INIS)

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

Book of Abstracts, Logic Colloquium 󈨦, the ASL European Summer Meeting, August 9-15, 1998, Prague, Czech Republic.

Science.gov (United States)

1998-09-23

the First Hypothesis of Plato’s Parmenides and the Undecidable Sentence of Kurt Godel 155 D. Drai Concepts of validity 156 M. L Zelbert, Logical...account of mathematics in the "Tractatus". -154- LC 󈨦 Book of Abstracts A Comparison Between the First Hypothesis of Plato’s Parmenides and the...42)(05)43129386 svandova@jumbo.ped.muni.cz in the second half of the twentieth century there has been a revival of interest in Plato’s Parmenides

Mathematical concepts of quantum mechanics. 2. ed.

International Nuclear Information System (INIS)

Gustafson, Stephen J.; Sigal, Israel Michael

2011-01-01

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory. (orig.)

Mathematics in ancient Greece

CERN Document Server

Dantzig, Tobias

2006-01-01

More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led

Learning abstract algebra with ISETL

CERN Document Server

Dubinsky, Ed

1994-01-01

Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics...

Mathematical modelling

DEFF Research Database (Denmark)

Blomhøj, Morten

2004-01-01

Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

Teaching Mathematics for Social Justice: Examining Preservice Teachers' Conceptions

Science.gov (United States)

Jong, Cindy; Jackson, Christa

2016-01-01

Teaching for social justice is a critical pedagogy used to empower students to be social agents in the world they live. This critical pedagogy has extended to mathematics education. Over the last decade, mathematics education researchers have conceptualized what it means to teach mathematics for social justice, but little is known about preservice…

Mathematics for the nonmathematician

CERN Document Server

Kline, Morris

1967-01-01

Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.

Archbishop Porter Girls' Senior High School Students' Perception of Difficult Concepts in Senior High School Further Mathematics Curriculum in Ghana

OpenAIRE

Senyefia Bosson-Amedenu

2017-01-01

Further Mathematics is frequently perceived as a subject set aside for some exceptional individuals. It often induces feelings of worry; nervousness and panic among students. This study employed the survey research design aimed at investigating difficult concepts in senior secondary school further mathematics curriculum as perceived by students in Archbishop Porter Girls’ Senior High School in Ghana. The study was guided by two research questions and the sample for the study was 100, all of w...

The method of abstraction in the design of databases and the interoperability

Science.gov (United States)

Yakovlev, Nikolay

2018-03-01

When designing the database structure oriented to the contents of indicators presented in the documents and communications subject area. First, the method of abstraction is applied by expansion of the indices of new, artificially constructed abstract concepts. The use of abstract concepts allows to avoid registration of relations many-to-many. For this reason, when built using abstract concepts, demonstrate greater stability in the processes. The example abstract concepts to address structure - a unique house number. Second, the method of abstraction can be used in the transformation of concepts by omitting some attributes that are unnecessary for solving certain classes of problems. Data processing associated with the amended concepts is more simple without losing the possibility of solving the considered classes of problems. For example, the concept "street" loses the binding to the land. The content of the modified concept of "street" are only the relations of the houses to the declared name. For most accounting tasks and ensure communication is enough.

Foundations and fundamental concepts of mathematics

CERN Document Server

Eves, Howard

1997-01-01

Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.

Contemplating Symbolic Literacy of First Year Mathematics Students

Science.gov (United States)

Bardini, Caroline; Pierce, Robyn; Vincent, Jill

2015-01-01

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

Concepts of formal concept analysis

Science.gov (United States)

Žáček, Martin; Homola, Dan; Miarka, Rostislav

2017-07-01

The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.

Ghana Science Abstracts

International Nuclear Information System (INIS)

Entsua-Mensah, C.

2004-01-01

This issue of the Ghana Science Abstracts combines in one publication all the country's bibliographic output in science and technology. The objective is to provide a quick reference source to facilitate the work of information professionals, research scientists, lecturers and policy makers. It is meant to give users an idea of the depth and scope and results of the studies and projects carried out. The scope and coverage comprise research outputs, conference proceedings and periodical articles published in Ghana. It does not capture those that were published outside Ghana. Abstracts reported have been grouped under the following subject areas: Agriculture, Biochemistry, Biodiversity conservation, biological sciences, biotechnology, chemistry, dentistry, engineering, environmental management, forestry, information management, mathematics, medicine, physics, nuclear science, pharmacy, renewable energy and science education

Practice and Conceptions: Communicating Mathematics in the Workplace

Science.gov (United States)

Wood, Leigh N.

2012-01-01

The study examined the experience of communication in the workplace for mathematics graduates with a view to enriching university curriculum. I broaden the work of Burton and Morgan (2000), who investigated the discourse practices of academic mathematicians to examine the discourse used by new mathematics graduates in industry and their…

Student Academic Self-Concept and Perception of Classroom Environment in Single-Sex and Coeducational Middle Grades Mathematics Classes

Science.gov (United States)

Kombe, Dennis; Che, S. Megan; Carter, Traci L.; Bridges, William

2016-01-01

In this article, we present findings from a study that investigated the relationship between all-girls classes, all-boys classes, and coeducational classes on student mathematics self-concept and student perception of classroom environment. Further, we compared responses of girls in all-girls classes to girls in coeducational classes and responses…

Teaching secondary mathematics

CERN Document Server

Rock, David

2013-01-01

Solidly grounded in up-to-date research, theory and technology,?Teaching Secondary Mathematics?is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fourth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and comprehensive companion websi

Contextual Perspectives of School Mathematics: What Determines Mathematical Understanding?

Science.gov (United States)

White, Loren; Frid, Sandra

Results of a study into secondary school students' and teachers' conceptions of what mathematics is and the purposes of school mathematics are outlined. A total of about 220 first year engineering students and 600 high school students in Australia were involved in the surveys while 40 students, 19 teachers, 2 career counselors, and 2…

Mathematics Teacher Identity in the Context of Mathematics Reform: Elementary Teacher Experiences

OpenAIRE

Sun, Jennifer

2017-01-01

ABSTRACT OF THE DISSERTATIONMathematics Teacher Identity in the Context of Mathematics Reform:Elementary Teacher Experiences ByJennifer SunDoctor of Philosophy in EducationUniversity of California, Irvine, 2017Associate Professor Elizabeth A. van Es, ChairReform efforts and changes in mathematics education have brought on a shift towards a new vision of mathematics teaching in the United States. In light of recent accountability standards, the focus on teacher learning within the context of m...

The Joy of Mathematics Discovering Mathematics All Around You

CERN Document Server

Pappas, Theoni

1993-01-01

Part of the joy of mathematics is that it is everywhere-in soap bubbles, electricity, da Vinci's masterpieces, even in an ocean wave. Written by the well-known mathematics teacher consultant, this volume's collection of over 200 clearly illustrated mathematical ideas, concepts, puzzles, and games shows where they turn up in the "real" world. You'll find out what a googol is, visit hotel infinity, read a thorny logic problem that was stumping them back in the 8th century. THE JOY OF MATHEMATICS is designed to be opened at random…it's mini essays are self-contained providing the reader

Making Meaning of Creativity and Mathematics Teaching

DEFF Research Database (Denmark)

Misfeldt, Morten

2014-01-01

. One reason is that it is not clear what relation such creative and innovative skills have to mathematics, and how we should teach them. In this paper, I review different conceptions of creativity in mathematics education and investigate what mathematical innovation and creativity “are......Creativity and innovation are important 21st-century skills, and mathematics education contributes to the development of these skills. However, it is far from clear how we as mathematics educators should respond to the need to contribute to our students’ development of creativity and innovation......” in the mathematical classroom. I show how different conceptions of mathematical innovation and creativity dominate different parts of the mathematics education literature, and explain how these differences can be viewed as framing mathematical creativity toward different domains....

Berkeley's Philosophy of Mathematics

CERN Document Server

Jesseph, Douglas M

1993-01-01

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's r

Modellus: Learning Physics with Mathematical Modelling

Science.gov (United States)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

The Psychological Basis of Learning Mathematics.

Science.gov (United States)

Ruberu, J.

1982-01-01

Mathematics is a hierarchial build-up of concepts and the process of this systematic building up of concepts is of prime importance in the study of mathematics. Although discovery approaches are currently used, there are limitations. Ausubel's "meaningful learning" approach is suggested as an alternative to discovery learning in…

Teaching Mathematics in Geography Degrees

Science.gov (United States)

Bennett, Robert

1978-01-01

Examines ways of developing college students' motivation for mathematical training; describes the type of mathematical knowledge required in the geography discipline; and explores an applied approach to mathematics teaching based on a systems concept. For journal availability, see SO 506 224. (Author/AV)

Waste management research abstracts No. 18

International Nuclear Information System (INIS)

1987-12-01

The eighteenth issue of this publication contains over 750 abstracts from 33 IAEA member countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed

A mathematical model for the third-body concept

Czech Academy of Sciences Publication Activity Database

Krejčí, Pavel; Petrov, A.

2018-01-01

Roč. 23, č. 3 (2018), s. 420-432 ISSN 1081-2865 R&D Projects: GA ČR(CZ) GA15-12227S Institutional support: RVO:67985840 Keywords : third-body * hysteresis operators * variational inequality Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517732827

Real mathematical analysis

CERN Document Server

Pugh, Charles C

2015-01-01

Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis. New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the un...

Handbook of mathematics

CERN Document Server

Kuipers, L

1969-01-01

International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp

The concept of training in community network for teaching algebraic structures that are aimed to create a methodical competence of a mathematics teacher

Directory of Open Access Journals (Sweden)

Ирина Викторовна Кузнецова

2012-12-01

Full Text Available The paper proposes the concept of learning activities in online communities for teaching algebraic structures of the future teachers of mathematics, including a set of theoretical and methodological positions, laws, principles, factors, and pedagogical conditions of its implementation. Work is executed with support of the Russian fund of basic researches under the initiative project № 11-07-00733 «The Hypertext information retrieval thesaurus» a science Meta language» (structure; mathematical, linguistic and program maintenance; sections linguistics, mathematics, economy».

Fine-grained semantic categorization across the abstract and concrete domains.

Directory of Open Access Journals (Sweden)

Marta Ghio

Full Text Available A consolidated approach to the study of the mental representation of word meanings has consisted in contrasting different domains of knowledge, broadly reflecting the abstract-concrete dichotomy. More fine-grained semantic distinctions have emerged in neuropsychological and cognitive neuroscience work, reflecting semantic category specificity, but almost exclusively within the concrete domain. Theoretical advances, particularly within the area of embodied cognition, have more recently put forward the idea that distributed neural representations tied to the kinds of experience maintained with the concepts' referents might distinguish conceptual meanings with a high degree of specificity, including those within the abstract domain. Here we report the results of two psycholinguistic rating studies incorporating such theoretical advances with two main objectives: first, to provide empirical evidence of fine-grained distinctions within both the abstract and the concrete semantic domains with respect to relevant psycholinguistic dimensions; second, to develop a carefully controlled linguistic stimulus set that may be used for auditory as well as visual neuroimaging studies focusing on the parametrization of the semantic space beyond the abstract-concrete dichotomy. Ninety-six participants rated a set of 210 sentences across pre-selected concrete (mouth, hand, or leg action-related and abstract (mental state-, emotion-, mathematics-related categories, with respect either to different semantic domain-related scales (rating study 1, or to concreteness, familiarity, and context availability (rating study 2. Inferential statistics and correspondence analyses highlighted distinguishing semantic and psycholinguistic traits for each of the pre-selected categories, indicating that a simple abstract-concrete dichotomy is not sufficient to account for the entire semantic variability within either domains.

Measured, modeled, and causal conceptions of fitness

Science.gov (United States)

Abrams, Marshall

2012-01-01

This paper proposes partial answers to the following questions: in what senses can fitness differences plausibly be considered causes of evolution?What relationships are there between fitness concepts used in empirical research, modeling, and abstract theoretical proposals? How does the relevance of different fitness concepts depend on research questions and methodological constraints? The paper develops a novel taxonomy of fitness concepts, beginning with type fitness (a property of a genotype or phenotype), token fitness (a property of a particular individual), and purely mathematical fitness. Type fitness includes statistical type fitness, which can be measured from population data, and parametric type fitness, which is an underlying property estimated by statistical type fitnesses. Token fitness includes measurable token fitness, which can be measured on an individual, and tendential token fitness, which is assumed to be an underlying property of the individual in its environmental circumstances. Some of the paper's conclusions can be outlined as follows: claims that fitness differences do not cause evolution are reasonable when fitness is treated as statistical type fitness, measurable token fitness, or purely mathematical fitness. Some of the ways in which statistical methods are used in population genetics suggest that what natural selection involves are differences in parametric type fitnesses. Further, it's reasonable to think that differences in parametric type fitness can cause evolution. Tendential token fitnesses, however, are not themselves sufficient for natural selection. Though parametric type fitnesses are typically not directly measurable, they can be modeled with purely mathematical fitnesses and estimated by statistical type fitnesses, which in turn are defined in terms of measurable token fitnesses. The paper clarifies the ways in which fitnesses depend on pragmatic choices made by researchers. PMID:23112804

2002 Conference Programme and Book of Abstracts

International Nuclear Information System (INIS)

2002-01-01

The 25th Annual (Silver Jubilee) Conference 2002 Conference Programme and Book of Abstracts gives a brief on the Nigerian Institute of Physics, the Sheda Science and Technology Complex. It carries the Conference programme and carries the abstracts of all the papers presented. The abstracts cover a wide range of subjects including topics in atmospheric physics, education, policy and planning, geophysics, instrumentation, mathematical sciences, theoretical physics, nuclear and health physics, solid state, electronic and health physics. We are grateful to the Nigerian Institute of Physics for this volume

English learners in the mathematics classroom

CERN Document Server

Coggins, Debra S (Susan)

2014-01-01

Research-based strategies to reach English learners - now aligned with the Common Core!Enable your English learners to build higher-level math skills and gain greater fluency in their new language-all while achieving the goals of the Common Core. Now in its second edition, this trusted resource includes:  Mathematics lesson scenarios in every chapter, directly connected to Common Core Standards and the Standards for Mathematical Practice Instructional approaches that promote participation, hands-on learning, and true comprehension of mathematics concepts that benefit ALL students Sample lessons, visuals, and essential vocabulary that connect mathematical concepts with language development.

Mathematics for natural scientists fundamentals and basics

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Kantorovich, Lev

2016-01-01

This book, the first in a two part series, covers a course of mathematics tailored specifically for physics, engineering and chemistry students at the undergraduate level. It is unique in that it begins with logical concepts of mathematics first encountered at A-level and covers them in thorough detail, filling in the gaps in students' knowledge and reasoning. Then the book aids the leap between A-level and university-level mathematics, with complete proofs provided throughout and all complex mathematical concepts and techniques presented in a clear and transparent manner. Numerous examples and problems (with answers) are given for each section and, where appropriate, mathematical concepts are illustrated in a physics context. This text gives an invaluable foundation to students and a comprehensive aid to lecturers. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.

Lectures on Applications-Oriented Mathematics

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Friedman, Bernard

2011-01-01

Meets the need for a program of short courses involving the essentials of a number of mathematical topics taken by physics and engineering students. Basically applications-oriented, the courses do include selected topics of abstract mathematics. While several courses can be used as practical appendices to conventional mathematics, others serve as introductions, providing motivation for self-study in areas of conceptual math.

Ethnomathematics: the cultural aspects of mathematics

Directory of Open Access Journals (Sweden)

Milton Rosa

2011-01-01

Full Text Available Ethnomathematics studies the cultural aspects of mathematics. It presents mathematical concepts of the school curriculum in a way in which these concepts are related to the students¿ cultural and daily experiences, thereby enhancing their abilities to elaborate meaningful connections and deepening their understanding of mathematics. Ethnomathematical approaches to mathematics curriculum are intended to make school mathematics more relevant and meaningful for students and to promote the overall quality of their education. In this context, the implementation of an ethnomathematical perspective in the school mathematics curriculum helps to develop students' intellectual, social, emotional, and political learning by using their own unique cultural referents to impart their knowledge, skills, and attitudes. This kind of curriculum provides ways for students to maintain their identity while succeeding academically.

Mathematics is always invisible, Professor Dowling

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Cable, John

2015-09-01

This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

The Kama Sutra, Romeo and Juliet, and Mathematics: Studying Mathematics for Pleasure

Science.gov (United States)

Padula, Janice

2005-01-01

The motivation of students is of great import to mathematics teachers. Such an abstract powerful language needs to be valued or students will not wish to study it. This article argues that mathematics may be better appreciated through the beauty of the language in which problems are written, respect for the cultures of others and through relevance…

Learning with Technology: Video Modeling with Concrete-Representational-Abstract Sequencing for Students with Autism Spectrum Disorder.

Science.gov (United States)

Yakubova, Gulnoza; Hughes, Elizabeth M; Shinaberry, Megan

2016-07-01

The purpose of this study was to determine the effectiveness of a video modeling intervention with concrete-representational-abstract instructional sequence in teaching mathematics concepts to students with autism spectrum disorder (ASD). A multiple baseline across skills design of single-case experimental methodology was used to determine the effectiveness of the intervention on the acquisition and maintenance of addition, subtraction, and number comparison skills for four elementary school students with ASD. Findings supported the effectiveness of the intervention in improving skill acquisition and maintenance at a 3-week follow-up. Implications for practice and future research are discussed.

Brain Functors: A Mathematical Model of Intentional Perception and Action

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David Ellerman

2016-03-01

Full Text Available Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics - with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. Semiadjunctions (essentially a formulation of universal mapping properties using hets can then be combined in a new way to define the notion of a brain functor that provides an abstract model of the intentionality of perception and action (as opposed to the passive reception of sense-data or the reflex generation of behavior.

Ethnomathematics: the cultural aspects of mathematics

Directory of Open Access Journals (Sweden)

Milton Rosa

2011-09-01

Full Text Available Ethnomathematics studies the cultural aspects of mathematics. It presents mathematical concepts of the school curriculum in a way in which these concepts are related to the students’ cultural and daily experiences, thereby enhancing their abilities to elaborate meaningful connections and deepening their understanding ofmathematics. Ethnomathematical approaches to mathematics curriculum are intended to make school mathematics more relevant and meaningful for students and to promote the overall quality of their education.In this context, the implementation of an ethnomathematical perspective in the school mathematics curriculum helps to develop students’ intellectual, social, emotional, and political learning by using their own unique cultural referents to impart their knowledge, skills, and attitudes. This kind of curriculum providesways for students to maintain their identity while succeeding academically.

Statistical Content in Middle Grades Mathematics Textbooks

Science.gov (United States)

Pickle, Maria Consuelo Capiral

2012-01-01

This study analyzed the treatment and scope of statistical concepts in four, widely-used, contemporary, middle grades mathematics textbook series: "Glencoe Math Connects," "Prentice Hall Mathematics," "Connected Mathematics Project," and "University of Chicago School Mathematics Project." There were three…

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students’ mathematical performance

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Bashirah Ibrahim

2017-10-01

Full Text Available We examine students’ mathematical performance on quantitative “synthesis problems” with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students’ mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students’ simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students’ formulation and combination of equations. Several reasons may explain this difference, including the students’ different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Interactive whiteboard in mathematics education

OpenAIRE

Cendelín, Jan

2013-01-01

Title: Interactive whiteboard in mathematics education Author: Bc. Jan Cendelín Department:Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D., Department of Mathematics Education Abstract: The development of modern technology is very fast. Almost everyone uses the technology at work and at home as well. So it is not unexpected that the technology gets into education at schools. This thesis focuses on the education of modern mathematics, and especially on the use of th...

The influence of second language teaching on undergraduate mathematics performance

Science.gov (United States)

Gerber, Ans; Engelbrecht, Johann; Harding, Ansie; Rogan, John

2005-10-01

Understanding abstract concepts and ideas in mathematics, if instruction takes place in the first language of the student, is difficult. Yet worldwide students often have to master mathematics via a second or third language. The majority of students in South Africa — a country with eleven official languages — has to face this difficulty. In a quantitative study of first year calculus students, we investigated two groups of students. For one group tuition took place in their home language; for the second group, tuition was in English, a second or even a third language. Performance data on their secondary mathematics and first year tertiary calculus were analysed. The study showed that there was no significant difference between the adjusted means of the entire group of first language learners and the entire group of second language learners. Neither was there any statistically significant difference between the performances of the two groups of second language learners (based on the adjusted means). Yet, there did seem to be a significant difference between the achievement of Afrikaans students attending Afrikaans lectures and Afrikaans students attending English lectures.

Science and mathematics teachers’ core teaching conceptions and their implications for engaging in cross-curricular innovations

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Hanne Møller Andersen

2010-04-01

Full Text Available Previous studies have found core teaching conceptions (CTCs to influence teachers’ actions, i.e. how they engage with new teaching practices (e.g. Lotter, Harwood, & Bonner, 2007. This study explores typical CTCs and their subject specific nature in a sample of teachers from physics, biology, and mathematics in Danish upper secondary school. Teachers’ CTCs were investigated through their essay responses to a set of open core questions, administered through a web-platform. Results demonstrate that teachers’ CTCs come in subject specific flavours, encompassing their purpose for teaching the subject, their conceptions of teaching and learning, and their conceptions of interdisciplinary teaching. It is argued that such differences shape teachers’ engagement with new cross-curricular innovations in the Danish context. Assessing and addressing typical and personal CTCs are found to be crucial to a successful implementation of current reform-initiatives, for teacher training, and for self-regulated professional development among teachers.

Mathematical stereochemistry

CERN Document Server

Fujita, Shinsaku

2015-01-01

Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.

Exploring Effects of High School Students' Mathematical Processing Skills and Conceptual Understanding of Chemical Concepts on Algorithmic Problem Solving

Science.gov (United States)

Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya

2013-01-01

The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…

The Effect of Using a Proposed Teaching Strategy Based on the Selective Thinking on Students' Acquisition Concepts in Mathematics

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Qudah, Ahmad Hassan

2016-01-01

This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…

Metaphor Perceptions of Pre-Service Teachers towards Mathematics and Mathematics Education in Preschool Education

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Keles, Oguz; Tas, Isil; Aslan, Durmus

2016-01-01

The aim of this study was to identify the thoughts of pre-service teachers, who play an important role in the early preschool experience of children in mathematics, towards the concepts of mathematics and education of mathematics with the help of metaphors. The study group of the research consists of a total of 227 pre-service teachers at the…

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

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María F. Ayllón

2016-04-01

Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.

Primary Mathematics. A Saxon Teacher's Resource Booklet.

Science.gov (United States)

1997

Saxon's primary mathematics series is a "hands-on," success-oriented program which emphasizes manipulatives and mental math. The series addresses the multisensory approach to teaching. Its use enables all children to develop a solid foundation in the language and basic concepts of mathematics. Concepts are presented in carefully…

The neural representation of abstract words: the role of emotion.

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Vigliocco, Gabriella; Kousta, Stavroula-Thaleia; Della Rosa, Pasquale Anthony; Vinson, David P; Tettamanti, Marco; Devlin, Joseph T; Cappa, Stefano F

2014-07-01

It is generally assumed that abstract concepts are linguistically coded, in line with imaging evidence of greater engagement of the left perisylvian language network for abstract than concrete words (Binder JR, Desai RH, Graves WW, Conant LL. 2009. Where is the semantic system? A critical review and meta-analysis of 120 functional neuroimaging studies. Cerebral Cortex. 19:2767-2796; Wang J, Conder JA, Blitzer DN, Shinkareva SV. 2010. Neural representation of abstract and concrete concepts: A meta-analysis of neuroimaging studies. Hum Brain Map. 31:1459-1468). Recent behavioral work, which used tighter matching of items than previous studies, however, suggests that abstract concepts also entail affective processing to a greater extent than concrete concepts (Kousta S-T, Vigliocco G, Vinson DP, Andrews M, Del Campo E. The representation of abstract words: Why emotion matters. J Exp Psychol Gen. 140:14-34). Here we report a functional magnetic resonance imaging experiment that shows greater engagement of the rostral anterior cingulate cortex, an area associated with emotion processing (e.g., Etkin A, Egner T, Peraza DM, Kandel ER, Hirsch J. 2006. Resolving emotional conflict: A role for the rostral anterior cingulate cortex in modulating activity in the amygdala. Neuron. 52:871), in abstract processing. For abstract words, activation in this area was modulated by the hedonic valence (degree of positive or negative affective association) of our items. A correlation analysis of more than 1,400 English words further showed that abstract words, in general, receive higher ratings for affective associations (both valence and arousal) than concrete words, supporting the view that engagement of emotional processing is generally required for processing abstract words. We argue that these results support embodiment views of semantic representation, according to which, whereas concrete concepts are grounded in our sensory-motor experience, affective experience is crucial in the

Abstracts of Research, July 1975-June 1976.

Science.gov (United States)

Ohio State Univ., Columbus. Computer and Information Science Research Center.

Abstracts of research papers in computer and information science are given for 62 papers in the areas of information storage and retrieval; computer facilities; information analysis; linguistics analysis; artificial intelligence; information processes in physical, biological, and social systems; mathematical technigues; systems programming;…

Mathematical Snippets Exploring mathematical ideas in small bites

CERN Document Server

Pappas, Theoni

2008-01-01

From nutritional labels and box office statistics to terabytes and megapixels, the 21st century world is awash in numbers. How can the average Joe or Jane make sense of all that data? The key, Theoni Pappas argues, is math. In Mathematical Snippets, she draws readers into the fascinating world of math without overwhelming them with mind-numbing equations. Short, engaging sections on everything from golf to game theory introduce mathematical concepts and celebrate math's impact on daily life.

The challenge of computer mathematics.

Science.gov (United States)

Barendregt, Henk; Wiedijk, Freek

2005-10-15

Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

Currents in industrial mathematics from concepts to research to education

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Prätzel-Wolters, Dieter

2015-01-01

Mathematics has many branches: there are the pure, the applied, and the applicable; the theoretical and the practical. There is mathematics for school, for college, and for industry. All these belong to the same family and are bound together by a "mathematical way of thinking." Some mathematicians devote themselves entirely to the well being of this family by preserving it, developing it, and teaching it to the next generation. Others use the familial attributes to help outsiders by taking up their problems and transforming them into mathematical questions in order to solve them. The work of these mathematicians is thus problem driven, based on mathematical models, and oriented on the goal of offering practicable solutions. This second group is sizeable; its members include almost all college graduates working in industry, in the private sector, or in the Fraunhofer Institutes, for example. This group is hardly visible, however, and one seldom hears its voices either. This book remedies this situation by rela...

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

Science.gov (United States)

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.

Comprehension of concrete and abstract words in semantic dementia

Science.gov (United States)

Jefferies, Elizabeth; Patterson, Karalyn; Jones, Roy W.; Lambon Ralph, Matthew A.

2009-01-01

The vast majority of brain-injured patients with semantic impairment have better comprehension of concrete than abstract words. In contrast, several patients with semantic dementia (SD), who show circumscribed atrophy of the anterior temporal lobes bilaterally, have been reported to show reverse imageability effects, i.e., relative preservation of abstract knowledge. Although these reports largely concern individual patients, some researchers have recently proposed that superior comprehension of abstract concepts is a characteristic feature of SD. This would imply that the anterior temporal lobes are particularly crucial for processing sensory aspects of semantic knowledge, which are associated with concrete not abstract concepts. However, functional neuroimaging studies of healthy participants do not unequivocally predict reverse imageability effects in SD because the temporal poles sometimes show greater activation for more abstract concepts. We examined a case-series of eleven SD patients on a synonym judgement test that orthogonally varied the frequency and imageability of the items. All patients had higher success rates for more imageable as well as more frequent words, suggesting that (a) the anterior temporal lobes underpin semantic knowledge for both concrete and abstract concepts, (b) more imageable items – perhaps due to their richer multimodal representations – are typically more robust in the face of global semantic degradation and (c) reverse imageability effects are not a characteristic feature of SD. PMID:19586212

Learning abstract visual concepts via probabilistic program induction in a Language of Thought.

Science.gov (United States)

Overlan, Matthew C; Jacobs, Robert A; Piantadosi, Steven T

2017-11-01

The ability to learn abstract concepts is a powerful component of human cognition. It has been argued that variable binding is the key element enabling this ability, but the computational aspects of variable binding remain poorly understood. Here, we address this shortcoming by formalizing the Hierarchical Language of Thought (HLOT) model of rule learning. Given a set of data items, the model uses Bayesian inference to infer a probability distribution over stochastic programs that implement variable binding. Because the model makes use of symbolic variables as well as Bayesian inference and programs with stochastic primitives, it combines many of the advantages of both symbolic and statistical approaches to cognitive modeling. To evaluate the model, we conducted an experiment in which human subjects viewed training items and then judged which test items belong to the same concept as the training items. We found that the HLOT model provides a close match to human generalization patterns, significantly outperforming two variants of the Generalized Context Model, one variant based on string similarity and the other based on visual similarity using features from a deep convolutional neural network. Additional results suggest that variable binding happens automatically, implying that binding operations do not add complexity to peoples' hypothesized rules. Overall, this work demonstrates that a cognitive model combining symbolic variables with Bayesian inference and stochastic program primitives provides a new perspective for understanding people's patterns of generalization. Copyright © 2017 Elsevier B.V. All rights reserved.

Descartes’s mathematical thought

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Sasaki, Chikara

2003-01-01

Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.

Bingo! Select Games for Mathematical Thinking

Science.gov (United States)

Jackson, Christa; Taylor, Cynthia; Buchheister, Kelley

2013-01-01

Games can both generate excitement among students and motivate them to participate in mathematics. Although games have been used primarily to "review" mathematical concepts at the middle school level, games should, and often do, have other instructional purposes. When teachers use mathematical games as an instructional strategy, they are…

The geometric phase in quantum systems foundations, mathematical concepts, and applications in molecular and condensed matter physics

CERN Document Server

Böhm, Arno; Koizumi, Hiroyasu; Niu, Qian; Zwanziger, Joseph

2003-01-01

Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics) The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them

The Mathematical State of the World

DEFF Research Database (Denmark)

Christensen, Ole Ravn; Skovsmose, Ole; Yasukawa, Keiko

2009-01-01

the concepts of “mathematical description” and “mathematical model” are inadequate to evaluate the use of mathematics in decision-making processes. As a result we develop a conceptual framework that is complex enough to match what goes on in scenarios involving applications of mathematics.......In this article we try to analyse the conditions for describing the world mathematically. We consider the role played by mathematics in discussing and analysing “the state of the world.” We use this discussion to clarify what it means to use a mathematical description. We illustrate why...

Dienes AEM as an alternative mathematics teaching aid to enhance Indonesian students’ understanding of algebra concept

Science.gov (United States)

Soro, S.; Maarif, S.; Kurniawan, Y.; Raditya, A.

2018-01-01

The aim of this study is to find out the effect of Dienes AEM (Algebra Experience Materials) on the ability of understanding concept of algebra on the senior high school student in Indonesia. This research is an experimental research with subject of all high school students in Indonesia. The samples taken were high school students in three provinces namely DKI Jakarta Province, West Java Province and Banten Province. From each province was taken senior high school namely SMA N 9 Bekasi West Java, SMA N 94 Jakarta and SMA N 5 Tangerang, Banten. The number of samples in this study was 114 high school students of tenth grade as experimental class and 115 high school students of tenth grade as control class. Learning algebra concept is needed in learning mathematics, besides it is needed especially to educate students to be able to think logically, systematically, critically, analytically, creatively, and cooperation. Therefore in this research will be developed an effective algebra learning by using Dienes AEM. The result of this research is that there is a significant influence on the students’ concept comprehension ability taught by using Dienes AEM learning as an alternative to instill the concept of algebra compared to the students taught by conventional learning. Besides, the students’ learning motivation increases because students can construct the concept of algebra with props.

Mathematical statistics essays on history and methodology

CERN Document Server

Pfanzagl, Johann

2017-01-01

This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated...

Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

Science.gov (United States)

Carrier, Jim

2014-01-01

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

New Challenges in the Teaching of Mathematics.

Science.gov (United States)

Bourguignon, Jean Pierre

The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

International seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications

CERN Document Server

Rancic, Milica

2016-01-01

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The book consists of contributed chapters covering research developed as a result of a focused interna...

Mathematical foundation of computer science

CERN Document Server

Singh, YN

2005-01-01

The interesting feature of this book is its organization and structure. That consists of systematizing of the definitions, methods, and results that something resembling a theory. Simplicity, clarity, and precision of mathematical language makes theoretical topics more appealing to the readers who are of mathematical or non-mathematical background. For quick references and immediate attentions¾concepts and definitions, methods and theorems, and key notes are presented through highlighted points from beginning to end. Whenever, necessary and probable a visual approach of presentation is used. The amalgamation of text and figures make mathematical rigors easier to understand. Each chapter begins with the detailed contents, which are discussed inside the chapter and conclude with a summary of the material covered in the chapter. Summary provides a brief overview of all the topics covered in the chapter. To demonstrate the principles better, the applicability of the concepts discussed in each topic are illustrat...

Applied Mathematics Seminar 1982

International Nuclear Information System (INIS)

1983-01-01

This report contains the abstracts of the lectures delivered at 1982 Applied Mathematics Seminar of the DPD/LCC/CNPq and Colloquy on Applied Mathematics of LCC/CNPq. The Seminar comprised 36 conferences. Among these, 30 were presented by researchers associated to brazilian institutions, 9 of them to the LCC/CNPq, and the other 6 were given by visiting lecturers according to the following distribution: 4 from the USA, 1 from England and 1 from Venezuela. The 1981 Applied Mathematics Seminar was organized by Leon R. Sinay and Nelson do Valle Silva. The Colloquy on Applied Mathematics was held from october 1982 on, being organized by Ricardo S. Kubrusly and Leon R. Sinay. (Author) [pt

Bottle Caps as Prekindergarten Mathematical Tools

Science.gov (United States)

Raisor, Jill M.; Hudson, Rick A.

2018-01-01

Early childhood provides a time of crucial growth in all developmental domains. Prekindergarten is an optimal time for young children to use objects of play as a medium to explore new cognitive concepts, including mathematical structure. Mathematical structure plays an important role in providing students a means to reason about mathematics,…

Problem posing as a didactic resource in formal mathematics courses to train future secondary school mathematics teachers

Directory of Open Access Journals (Sweden)

Lorena Salazar Solórzano

2015-06-01

Full Text Available Beginning university training programs must focus on different competencies for mathematics teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematical activity. This paper reports the results of an exploratory study conducted with future secondary school mathematics teachers on the introduction of problem-posing tasks in formal mathematics courses, specifically in abstract algebra and real analysis courses. Evidence was found that training which includes problem-posing tasks has a positive impact on the students’ understanding of definitions, theorems and exercises within formal mathematics, as well as on their competency in reflecting on the mathematical activity. 

Abstract Datatypes in PVS

Science.gov (United States)

Owre, Sam; Shankar, Natarajan

1997-01-01

PVS (Prototype Verification System) is a general-purpose environment for developing specifications and proofs. This document deals primarily with the abstract datatype mechanism in PVS which generates theories containing axioms and definitions for a class of recursive datatypes. The concepts underlying the abstract datatype mechanism are illustrated using ordered binary trees as an example. Binary trees are described by a PVS abstract datatype that is parametric in its value type. The type of ordered binary trees is then presented as a subtype of binary trees where the ordering relation is also taken as a parameter. We define the operations of inserting an element into, and searching for an element in an ordered binary tree; the bulk of the report is devoted to PVS proofs of some useful properties of these operations. These proofs illustrate various approaches to proving properties of abstract datatype operations. They also describe the built-in capabilities of the PVS proof checker for simplifying abstract datatype expressions.

International note: Are Emirati parents' attitudes toward mathematics linked to their adolescent children's attitudes toward mathematics and mathematics achievement?

Science.gov (United States)

Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F

2015-10-01

Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

A new hierarchy of infinitary logics in abstract algebraic logic

Czech Academy of Sciences Publication Activity Database

Lávička, Tomáš; Noguera, Carles

2017-01-01

Roč. 105, č. 3 (2017), s. 521-551 ISSN 0039-3215 R&D Projects: GA ČR GA13-14654S EU Projects: European Commission(XE) 689176 - SYSMICS Institutional support: RVO:67985556 ; RVO:67985807 Keywords : Abstract algebraic logic * consequence relations * infinitary logics * completeness properties Subject RIV: BA - General Mathematics; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics; Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) (UIVT-O) Impact factor: 0.589, year: 2016 http://library.utia.cas.cz/separaty/2017/MTR/noguera-0469118.pdf

Mathematical and physical theory of turbulence

CERN Document Server

Cannon, John

2006-01-01

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities a...

Special relativity from observer's mathematics point of view

Science.gov (United States)

Khots, Boris; Khots, Dmitriy

2015-09-01

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

Modal abstractions of concurrent behavior

DEFF Research Database (Denmark)

Nielson, Flemming; Nanz, Sebastian; Nielson, Hanne Riis

2011-01-01

We present an effective algorithm for the automatic construction of finite modal transition systems as abstractions of potentially infinite concurrent processes. Modal transition systems are recognized as valuable abstractions for model checking because they allow for the validation as well...... as refutation of safety and liveness properties. However, the algorithmic construction of finite abstractions from potentially infinite concurrent processes is a missing link that prevents their more widespread usage for model checking of concurrent systems. Our algorithm is a worklist algorithm using concepts...... from abstract interpretation and operating upon mappings from sets to intervals in order to express simultaneous over- and underapprox-imations of the multisets of process actions available in a particular state. We obtain a finite abstraction that is 3-valued in both states and transitions...

A modern theory of random variation with applications in stochastic calculus, financial mathematics, and Feynman integration

CERN Document Server

Muldowney, Patrick

2012-01-01

A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. I...

Epistemological obstacles on the concepts of limit and continuity in courses of differential calculus in engineering programs

Directory of Open Access Journals (Sweden)

Cesar Augusto Hernandez-Suarez

2017-07-01

Full Text Available Many investigations have been carried out with the objective of identifying the difficulties that students have in the learning process of the different mathematical concepts. Some studies have highlighted that the process of teaching mathematical knowledge by teachers in secondary and secondary education in Colombia, has been limited to a minimalist expression of algebraic processes that in no way contribute to the understanding and appropriation of these concepts of origin abstract. Students who enter the various engineering programs in the university must immediately face a Differential Calculus course, which will demand from the student a whole series of competences around the numerical, variational and spatial thoughts. It is in this scenario where we seek to identify the epistemological obstacles presented by the students of the Faculty of Engineering programs at the beginning of the academic training process at the UFPS. An instrument was designed that incorporates a series of activities that use diverse registers of semiotic representation tending to determine the level of appropriation that the students have around the concepts of limit and continuity. From the findings it is highlighted that students assume the concepts of limit and continuity as equals.

Learning Mathematics or Losing Money--Betting as a Topic for Mathematical Education

Science.gov (United States)

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 Princeton companion to mathematics

CERN Document Server

Barrow-Green, June; Leader, Imre

2008-01-01

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more

Examination of Pre-Service Mathematics Teachers' Knowledge of Teaching Function Concept

Science.gov (United States)

Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit

2017-01-01

Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT)…

Exploring Mathematical Definition Construction Processes

Science.gov (United States)

Ouvrier-Buffet, Cecile

2006-01-01

The definition of "definition" cannot be taken for granted. The problem has been treated from various angles in different journals. Among other questions raised on the subject we find: the notions of "concept definition" and "concept image", conceptions of mathematical definitions, redefinitions, and from a more axiomatic point of view, how to…

Psychology and Didactics of Mathematics in France--An Overview.

Science.gov (United States)

Vergnaud, Gerard

1983-01-01

Examples are given of the variety of mathematical concepts and problems being studied by psychologically oriented researchers in France. Work on decimals, circles, natural numbers, decimal and real numbers, and didactic transposition are included. Comments on designing research on mathematics concept formation conclude the article. (MNS)

Bernhard Riemann 1826-1866 Turning Points in the Conception of Mathematics

CERN Document Server

Laugwitz, Detlef

2008-01-01

The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hi...

Mathematics, anxiety, and the brain.

Science.gov (United States)

Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

2017-05-24

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

Mathematical programming in multiperson cooperative games

Energy Technology Data Exchange (ETDEWEB)

Lucas, W.

1994-12-31

Many fundamental solution notions in mathematical economics relate to mathematical programming. This includes various types of equilibrium points for the noncooperative (strategic) competitions, as well as the core for the cooperative (coalitional) models. This talk concerns alternate cooperative solution concepts such as various nucleoli points and other proposed fairness outcomes. These concepts become of particular interest for those cases when the core is an empty set. Recent results on these alternate solutions for classes of assignment games will be presented.

Preservice Mathematics Teachers' Metaphorical Perceptions towards Proof and Proving

Science.gov (United States)

Ersen, Zeynep Bahar

2016-01-01

Since mathematical proof and proving are in the center of mathematics; preservice mathematics teachers' perceptions against these concepts have a great importance. Therefore, the study aimed to determine preservice mathematics teachers' perceptions towards proof and proving through metaphors. The participants consisted of 192 preservice…

GOClonto: an ontological clustering approach for conceptualizing PubMed abstracts.

Science.gov (United States)

Zheng, Hai-Tao; Borchert, Charles; Kim, Hong-Gee

2010-02-01

Concurrent with progress in biomedical sciences, an overwhelming of textual knowledge is accumulating in the biomedical literature. PubMed is the most comprehensive database collecting and managing biomedical literature. To help researchers easily understand collections of PubMed abstracts, numerous clustering methods have been proposed to group similar abstracts based on their shared features. However, most of these methods do not explore the semantic relationships among groupings of documents, which could help better illuminate the groupings of PubMed abstracts. To address this issue, we proposed an ontological clustering method called GOClonto for conceptualizing PubMed abstracts. GOClonto uses latent semantic analysis (LSA) and gene ontology (GO) to identify key gene-related concepts and their relationships as well as allocate PubMed abstracts based on these key gene-related concepts. Based on two PubMed abstract collections, the experimental results show that GOClonto is able to identify key gene-related concepts and outperforms the STC (suffix tree clustering) algorithm, the Lingo algorithm, the Fuzzy Ants algorithm, and the clustering based TRS (tolerance rough set) algorithm. Moreover, the two ontologies generated by GOClonto show significant informative conceptual structures.

Applying Mathematical Concepts with Hands-On, Food-Based Science Curriculum

Science.gov (United States)

Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.

2015-01-01

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the…

What Is Mathematical Modelling? Exploring Prospective Teachers' Use of Experiments to Connect Mathematics to the Study of Motion

Science.gov (United States)

Carrejo, David J.; Marshall, Jill

2007-01-01

This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…

Undergraduate Students' Perceptions of the Mathematics Courses Included in the Primary School Teacher Education Program

Science.gov (United States)

Serin, Mehmet Koray; Incikabi, Semahat

2017-01-01

Mathematics educators have reported on many issues regarding students' mathematical education, particularly students who received mathematics education at different departments such as engineering, science or primary school, including their difficulties with mathematical concepts, their understanding of and preferences for mathematical concepts.…

On the dialectical foundations of mathematics

NARCIS (Netherlands)

Damsma, D.

2008-01-01

This paper tracks the systematic dialectical determination of mathematical concepts in Hegel's Encyclopädie der philosophischen Wissenschaften (1830, 1817) and investigates the insights that can be gained from such a perspective on the mathematical. To begin with, the determination of Numbers and

Abstract concepts: sensory-motor grounding, metaphors, and beyond

NARCIS (Netherlands)

Pecher, D.; Boot, I.; van Dantzig, S.

2011-01-01

In the last decade many researchers have obtained evidence for the idea that cognition shares processing mechanisms with perception and action. Most of the evidence supporting the grounded cognition framework focused on representations of concrete concepts, which leaves open the question how

Abstract algebra for physicists

International Nuclear Information System (INIS)

Zeman, J.

1975-06-01

Certain recent models of composite hadrons involve concepts and theorems from abstract algebra which are unfamiliar to most theoretical physicists. The algebraic apparatus needed for an understanding of these models is summarized here. Particular emphasis is given to algebraic structures which are not assumed to be associative. (2 figures) (auth)

The working out of architectural concept for a new type public building — multi-information and education center by using information technologies and mathematical models

Directory of Open Access Journals (Sweden)

Михаил Владимирович Боровиков

2012-12-01

Full Text Available Architectural concept of multifunctional information and educational center and its implementation is given in the author's project. Advanced information technology and mathematical models used in the development of the author project.

On Double-Entry Bookkeeping: The Mathematical Treatment

Science.gov (United States)

Ellerman, David

2014-01-01

Double-entry bookkeeping (DEB) implicitly uses a specific mathematical construction, the group of differences using pairs of unsigned numbers ("T-accounts"). That construction was only formulated abstractly in mathematics in the nineteenth century, even though DEB had been used in the business world for over five centuries. Yet the…

Mayr, mathematics and the study of evolution

Directory of Open Access Journals (Sweden)

Crow James F

2009-02-01

Full Text Available Abstract In 1959 Ernst Mayr challenged the relevance of mathematical models to evolutionary studies and was answered by JBS Haldane in a witty and convincing essay. Fifty years on, I conclude that the importance of mathematics has in fact increased and will continue to do so.

Triangular Norms, Triangular Conorms, and Some Related Concepts

Directory of Open Access Journals (Sweden)

Angel Garrido

2011-01-01

Full Text Available Abstract. Mathematically considered, a Triangular Norm is a kind of binary operation frequently used in the context of Probabilistic Metric Spaces, but also in other very interesting fields, as may be Fuzzy Logic, or in general, in Multi-Valued Logic (MVL. The T-conorm, or S-norm, is a dual concept. Both ideas allow us to generalize the intersection and the union in a Lattice, or disjunction and conjunction in Logic. Also may be very interesting to introduce a special class of real monotone operations. We refer to the so-called Copulas, very useful in many fields. So, we offer now a comprehensive analysis of all these aggregation operators.

The Mathematics-language symbiosis: The learners' benefits ...

African Journals Online (AJOL)

On their own part, those whose course of study is mathematics are curious ... of Applied Linguistics propounded by Leonard Bloomfield in 1941 guides the study. ... a mathematics classroom so as to continue learning advanced concepts.

The left inferior frontal gyrus: A neural crossroads between abstract and concrete knowledge.

Science.gov (United States)

Della Rosa, Pasquale Anthony; Catricalà, Eleonora; Canini, Matteo; Vigliocco, Gabriella; Cappa, Stefano F

2018-07-15

Evidence from both neuropsychology and neuroimaging suggests that different types of information are necessary for representing and processing concrete and abstract word meanings. Both abstract and concrete concepts, however, conjointly rely on perceptual, verbal and contextual knowledge, with abstract concepts characterized by low values of imageability (IMG) (low sensory-motor grounding) and low context availability (CA) (more difficult to contextualize). Imaging studies supporting differences between abstract and concrete concepts show a greater recruitment of the left inferior frontal gyrus (LIFG) for abstract concepts, which has been attributed either to the representation of abstract-specific semantic knowledge or to the request for more executive control than in the case of concrete concepts. We conducted an fMRI study on 27 participants, using a lexical decision task involving both abstract and concrete words, whose IMG and CA values were explicitly modelled in separate parametric analyses. The LIFG was significantly more activated for abstract than for concrete words, and a conjunction analysis showed a common activation for words with low IMG or low CA only in the LIFG, in the same area reported for abstract words. A regional template map of brain activations was then traced for words with low IMG or low CA, and BOLD regional time-series were extracted and correlated with the specific LIFG neural activity elicited for abstract words. The regions associated to low IMG, which were functionally correlated with LIFG, were mainly in the left hemisphere, while those associated with low CA were in the right hemisphere. Finally, in order to reveal which LIFG-related network increased its connectivity with decreases of IMG or CA, we conducted generalized psychophysiological interaction analyses. The connectivity strength values extracted from each region connected with the LIFG were correlated with specific LIFG neural activity for abstract words, and a regression

Local Stability Analysis of an Infection-Age Mathematical Model for ...

African Journals Online (AJOL)

Timothy

1Department of Mathematics/Statistics/Computer Science, Federal University of Agriculture, Makurdi, ... ABSTRACT: An infection age structured mathematical model for tuberculosis disease ...... its applications to optimal vaccination strategies.

On the dialectical foundations of mathematics

NARCIS (Netherlands)

Damsma, D.

2011-01-01

This paper tracks the systematic dialectical determination of mathematical concepts in Hegel’s Encyclopädie der philosophischen Wissenschaften (1830,1817) and investigates the insights that can be gained from such a perspective on the mathematical. To begin with, the determination of Numbers and

Developing mathematical modelling competence

DEFF Research Database (Denmark)

Blomhøj, Morten; Jensen, Tomas Højgaard

2003-01-01

In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....

Abstracting event-based control models for high autonomy systems

Science.gov (United States)

Luh, Cheng-Jye; Zeigler, Bernard P.

1993-01-01

A high autonomy system needs many models on which to base control, management, design, and other interventions. These models differ in level of abstraction and in formalism. Concepts and tools are needed to organize the models into a coherent whole. The paper deals with the abstraction processes for systematic derivation of related models for use in event-based control. The multifaceted modeling methodology is briefly reviewed. The morphism concepts needed for application to model abstraction are described. A theory for supporting the construction of DEVS models needed for event-based control is then presented. An implemented morphism on the basis of this theory is also described.

Mathematical subtleties and scientific knowledge: Francis Bacon and mathematics, at the crossing of two traditions.

Science.gov (United States)

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'.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Shobha Madan. Articles written in Proceedings – Mathematical Sciences. Volume 113 Issue 2 May 2003 pp 171-178. Wavelet Subspaces Invariant Under Groups of Translation Operators · Biswaranjan Behera Shobha Madan · More Details Abstract Fulltext PDF.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. MOHAMED KHALIL ZGHAL. Articles written in Proceedings – Mathematical Sciences. Volume 128 Issue 1 March 2018 pp 13 Research Article. Sharp Adams-type inequality invoking Hardy inequalities · MOHAMED KHALIL ZGHAL · More Details Abstract Fulltext PDF.

Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory

CERN Document Server

Yushkevich, A

1992-01-01

This multi-authored effort, Mathematics of the nineteenth century (to be fol­ lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend...

Mathematics for physics with calculus

CERN Document Server

Das, Biman

2005-01-01

Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.

Discourses of power in mathematics education research: Concepts and possibilities for action

DEFF Research Database (Denmark)

Valero, Paola

2008-01-01

Mathematics education is powerful. This is an assertion that appears often in mathematics education research papers. However, the meaning of the assertion is far from being clear. An analysis of different ways of talking about power in relation to mathematics education, in research literature, is...

Extension Properties and Subdirect Representation in Abstract Algebraic Logic

Czech Academy of Sciences Publication Activity Database

Lávička, Tomáš; Noguera, Carles

(2018) ISSN 0039-3215 R&D Projects: GA ČR GA17-04630S Institutional support: RVO:67985556 Keywords : Abstract algebraic logic * Infinitary logics * Natural extensions * Natural expansions * Semilinear logics * Subdirect representation Subject RIV: BA - General Mathematics Impact factor: 0.589, year: 2016

Squeezed States and Uncertainty Relations. Abstracts

International Nuclear Information System (INIS)

Masahito, Hayashi; Reynaud, S.; Jaekel, M.Th.; Fiuraaek, J.; Garcia-Patron, R.; Cerf, N.J.; Hage, B.; Chelkowski, S.; Franzen, A.; Lastzka, N.; Vahlbruch, N.; Danzmann, K.; Schnabel, R.; Hassan, S.S.; Joshi, A.; Jakob, M.; Bergou, J.A.; Kozlovskii, A.V.; Prakash, H.; Kumar, R.

2005-01-01

The purpose of the conference was to bring together people working in the field of quantum optics, with special emphasis on non-classical light sources and related areas, quantum computing, statistical mechanics and mathematical physics. As a novelty, this edition will include the topics of quantum imaging, quantum phase noise and number theory in quantum mechanics. This document gives the program of the conference and gathers the abstracts

Competence with fractions predicts gains in mathematics achievement.

Science.gov (United States)

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

2012-11-01

Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, pmathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

THE MATHEMATICS-LANGUAGE SYMBIOSIS: THE LEARNERS ...

African Journals Online (AJOL)

JONATHAN

2016-07-01

Jul 1, 2016 ... will touch some basic concepts in grammar or language. The consequence is that such ..... programming. The concept of the function ..... mathematical problems solving are closely related to language. They share the idea that ...

Teaching Statistics in Middle School Mathematics Classrooms: Making Links with Mathematics but Avoiding Statistical Reasoning

Science.gov (United States)

Savard, Annie; Manuel, Dominic

2015-01-01

Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school…

Reconstruction of abstract quantum theory

International Nuclear Information System (INIS)

Drieschner, M.; Goernitz, T.; von Weizsaecker, C.F.

1988-01-01

Understanding quantum theory as a general theory of prediction, we reconstruct abstract quantum theory. Abstract means the general frame of quantum theory, without reference to a three-dimensional position space, to concepts like particle or field, or to special laws of dynamics. Reconstruction is the attempt to do this by formulating simple and plausible postulates on prediction in order to derive the basic concepts of quantum theory from them. Thereby no law of classical physics is presupposed which would then have to be quantized. We briefly discuss the relationship of theory and interpretation in physics and the fundamental role of time as a basic concept for physics. Then a number of assertions are given, formulated as succinctly as possible in order to make them easily quotable and comparable. The assertations are arranged in four groups: heuristic principles, verbal definitions of some terms, three basic postulates, and consequences. The three postulates of separable alternatives, indeterminism, and kinematics are the central points of this work. These brief assertions are commented upon, and their relationship with the interpretation of quantum theory is discussed. Also given are an outlook on the further development into concrete quantum theory and some philosophical reflections

The tools of mathematical reasoning

CERN Document Server

Lakins, Tamara J

2016-01-01

This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

Mathematical Model for the Control of measles 1*PETER, OJ ...

African Journals Online (AJOL)

PROF HORSFALL

2018-04-16

Apr 16, 2018 ... 5Department of Mathematics/Statistics, Federal University of Technology, Minna, Nigeria ... ABSTRACT: We proposed a mathematical model of measles disease dynamics with vaccination by ...... Equation with application.

Addressing Priorities for Elementary School Mathematics

Science.gov (United States)

Venenciano, Linda; Dougherty, Barbara

2014-01-01

Findings from international assessments present an opportunity to reconsider mathematics education across the grades. If concepts taught in elementary grades lay the foundation for continued study, then children's introduction to school mathematics deserves particular attention. We consider Davydov's theory (1966), which sequences…

K-12 Mathematics and the Web

Science.gov (United States)

Glazer, Evan

2005-01-01

The Web offers numerous learning resources and opportunities for K-12 mathematics education. This paper discusses those resources and opportunities. Discussion includes (a) asynchronous and synchronous communication tools, (b) the use of data sets to make connections between mathematics concepts and real-world applications, and (c) interactive…

The Philosophy of Mathematics Education

DEFF Research Database (Denmark)

mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards......This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical...... research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also...

Diffusion, quantum theory, and radically elementary mathematics (MN-47)

CERN Document Server

Faris, William G

2014-01-01

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein''s work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book''s inspiration is Princeton University mathematics professor Edward Nelson''s influential work in

Research in collegiate mathematics education VI

CERN Document Server

Selden, Annie; Harel, Guershon; Hauk, Shandy

2006-01-01

The sixth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the postsecondary level. The articles advance our understanding of collegiate mathematics education while being readable by a wide audience of mathematicians interested in issues affecting their own students. This is a collection of useful and informative research regarding the ways our students think about and learn mathematics. The volume opens with studies on students' experiences with calculus reform and on the effects of concept-based

A First Course in Applied Mathematics

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Rebaza, Jorge

2012-01-01

Explore real-world applications of selected mathematical theory, concepts, and methods Exploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation

Probability theory and mathematical statistics for engineers

CERN Document Server

Pugachev, V S

1984-01-01

Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Basudeb Datta. Articles written in Proceedings – Mathematical Sciences. Volume 112 Issue 2 May 2002 pp 257-281. Two-Dimensional Weak Pseudomanifolds on Eight Vertices · Basudeb Datta Nandini Nilakantan · More Details Abstract Fulltext PDF. We explicitly ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Forthcoming articles. Forthcoming articles. Proceedings – Mathematical Sciences. PMSC-D-14-00136. Combinatorics of tenth order mock theta functions. J K SAREEN M RANA. Abstract. In this paper we are providing the combinatorial interpretations of two tenth ...

The Big Fish-Little Pond Effect on Affective Factors Based on PISA 2012 Mathematics Achievement

Directory of Open Access Journals (Sweden)

Dilara BAKAN KALAYCIOĞLU

2017-03-01

Full Text Available In this study, the 2012 PISA Turkey student questionnaire data is considered to determine the big fish-little pond effect. The mathematics self-efficacy, self-concept and anxiety affective factors are examined to explain the relation of each of them with the school type, gender, socioeconomic status, student’s mathematics achievement and school’s mathematics achievement covariates. A total number of 771 students from 88 high schools are in the sample. Factor analyses’ results support the construct validity of the Student Questionnaire’s mathematics self-efficacy, anxiety and self-concept items. Data set is analyzed with Multiple Indicator Multiple Cause Model and the patterns of association with covariates and affective factors were tested simultaneously. According to the results, Anatolian high school students have a higher mathematics self-efficacy and lower mathematics anxiety than do the general high school students. However, when the student mathematics achievement and school mathematics achievement variables were inserted to the model, school type was not associated with mathematics self-efficacy. Moreover, Anatolian high school student’s mathematics anxiety was higher than that of the general high school students. Student’s mathematics achievement was the most significant predictor of the mathematics self-efficacy, anxiety and self-concept factors. Finally, school’s mathematics achievement was a significant predictor of only mathematics self-concept. The identification of increase in school’s mathematics achievement yields a decrease in the student’s mathematics self-concept may be considered as the most important result of this study. These results provide evidence about the Anatolian high schools’ students experience big fish-little pond effect.

A mathematics sampler topics for the liberal arts

CERN Document Server

Berlinghoff, William P; Skrien, Dale

2001-01-01

Now in its fifth edition, A Mathematics Sampler presents mathematics as both science and art, focusing on the historical role of mathematics in our culture. It uses selected topics from modern mathematics-including computers, perfect numbers, and four-dimensional geometry-to exemplify the distinctive features of mathematics as an intellectual endeavor, a problem-solving tool, and a way of thinking about the rapidly changing world in which we live. A Mathematics Sampler also includes unique LINK sections throughout the book, each of which connects mathematical concepts with areas of interest th

The Language of Mathematics Utilizing Math in Practice

CERN Document Server

Baber, Robert L

2011-01-01

A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process-not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and i

A case study of analyzing student teachers' concept images of the ...

African Journals Online (AJOL)

Administrator

Key words: Definite integral, concept images, process conceptions, object .... led me to conceive a three dimensional matrix with process-object layers in rows, ...... Conference on Psychology of Mathematics Education, Norwich. ... On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as.

Basic abstract algebra for graduate students and advanced undergraduates

CERN Document Server

Ash, Robert B

2006-01-01

Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible.The early chapters provide students with background by investigating the basic properties of groups

NCTM Principles and Standards for Mathematically Talented Students

Science.gov (United States)

Deal, Linda J.; Wismer, Michael G.

2010-01-01

The "Principles and Standards for School Mathematics" published in 2000 by the National Council of Teachers of Mathematics (NCTM) created a vision of mathematical concepts and processes to establish core educational guidelines for instruction from grades K to 12. The overall plan does emphasize higher level thinking, problem solving, and…

Converging modalities ground abstract categories: the case of politics.

Science.gov (United States)

Farias, Ana Rita; Garrido, Margarida V; Semin, Gün R

2013-01-01

Three studies are reported examining the grounding of abstract concepts across two modalities (visual and auditory) and their symbolic representation. A comparison of the outcomes across these studies reveals that the symbolic representation of political concepts and their visual and auditory modalities is convergent. In other words, the spatial relationships between specific instances of the political categories are highly overlapping across the symbolic, visual and auditory modalities. These findings suggest that abstract categories display redundancy across modal and amodal representations, and are multimodal.

How we understand mathematics conceptual integration in the language of mathematical description

CERN Document Server

Woźny, Jacek

2018-01-01

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested...

Using Google Apps to Develop the Mathematical Practices

Science.gov (United States)

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…

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. CHANCHAL KUMAR. Articles written in Proceedings – Mathematical Sciences. Volume 120 Issue 2 April 2010 pp 163-168. Deficiently Extremal Cohen-Macaulay Algebras · Chanchal Kumar Pavinder Singh · More Details Abstract Fulltext PDF. The aim of this paper is ...

Waste management research abstracts no. 21

International Nuclear Information System (INIS)

1992-12-01

The 21th issue of this publication contains over 700 abstracts from 35 IAEA Member Countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed. Many programs involve cooperation among several countries and further international cooperation is expected to be promoted through availability of compiled information on research programs, institutions and scientists engaged in waste management

Waste management research abstracts. No. 20

International Nuclear Information System (INIS)

1990-10-01

The 20th issue of this publication contains over 700 abstracts from 32 IAEA Member Countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed. Many programs involve cooperation among several countries and further international cooperation is expected to be promoted through availability of compiled information on research programs, institutions and scientists engaged in waste management

Mathematical foundations of image processing and analysis

CERN Document Server

Pinoli, Jean-Charles

2014-01-01

Mathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overview of the key mathematical concepts, notions, tools and frameworks involved in the various fields of gray-tone and binary image processing and analysis, by proposing a large, but coherent, set of symbols and notations, a complete list of subjects and a detailed bibliography. It establishes a bridg

Ancient Indian Leaps into Mathematics

CERN Document Server

Yadav, B S

2011-01-01

This book presents contributions of mathematicians covering topics from ancient India, placing them in the broader context of the history of mathematics. Although the translations of some Sanskrit mathematical texts are available in the literature, Indian contributions are rarely presented in major Western historical works. Yet some of the well-known and universally-accepted discoveries from India, including the concept of zero and the decimal representation of numbers, have made lasting contributions to the foundation of modern mathematics. Through a systematic approach, this book examines th

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

Science.gov (United States)

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

Science.gov (United States)

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Elements of abstract harmonic analysis

CERN Document Server

Bachman, George

2013-01-01

Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give

The Semantic Isomorphism Theorem in Abstract Algebraic Logic

Czech Academy of Sciences Publication Activity Database

Moraschini, Tommaso

2016-01-01

Roč. 167, č. 12 (2016), s. 1298-1331 ISSN 0168-0072 R&D Projects: GA ČR GA13-14654S Institutional support: RVO:67985807 Keywords : algebra izable logics * abstract algebra ic logic * structural closure operators * semantic isomorphism theorem * evaluational frames * compositional lattice Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016

Mathematical foundations of event trees

International Nuclear Information System (INIS)

Papazoglou, Ioannis A.

1998-01-01

A mathematical foundation from first principles of event trees is presented. The main objective of this formulation is to offer a formal basis for developing automated computer assisted construction techniques for event trees. The mathematical theory of event trees is based on the correspondence between the paths of the tree and the elements of the outcome space of a joint event. The concept of a basic cylinder set is introduced to describe joint event outcomes conditional on specific outcomes of basic events or unconditional on the outcome of basic events. The concept of outcome space partition is used to describe the minimum amount of information intended to be preserved by the event tree representation. These concepts form the basis for an algorithm for systematic search for and generation of the most compact (reduced) form of an event tree consistent with the minimum amount of information the tree should preserve. This mathematical foundation allows for the development of techniques for automated generation of event trees corresponding to joint events which are formally described through other types of graphical models. Such a technique has been developed for complex systems described by functional blocks and it is reported elsewhere. On the quantification issue of event trees, a formal definition of a probability space corresponding to the event tree outcomes is provided. Finally, a short discussion is offered on the relationship of the presented mathematical theory with the more general use of event trees in reliability analysis of dynamic systems

Connecting mathematics learning through spatial reasoning

Science.gov (United States)

Mulligan, Joanne; Woolcott, Geoffrey; Mitchelmore, Michael; Davis, Brent

2018-03-01

Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new pathways for mathematics learning, pedagogy and curriculum. Novel analytical tools will map the unknown complex systems linking spatial and mathematical concepts. It will involve the design, implementation and evaluation of a Spatial Reasoning Mathematics Program (SRMP) in Grades 3 to 5. Benefits will be seen through development of critical spatial skills for students, increased teacher capability and informed policy and curriculum across STEM education.

The Role of Reasoning in the Australian Curriculum: Mathematics

Science.gov (United States)

McCluskey, Catherine; Mulligan, Joanne; Mitchelmore, Mike

2016-01-01

The mathematical proficiencies in the "Australian Curriculum: Mathematics" of understanding, problem solving, reasoning, and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in…

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

Science.gov (United States)

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Science and mathematics teaching through local games in preschools of Botswana

Directory of Open Access Journals (Sweden)

Kabita Bose

2016-11-01

Full Text Available This article presents a study regarding preschool teachers’ skills and competencies in teaching science and mathematics. The aim of the project was twofold; one to find out the preschool teachers’ knowledge about mathematics and science concepts and then to develop support material to empower them with skills and competencies to teach these concepts in preschools. A qualitative approach was adopted, and a case study method was used. Data were collected through two workshops and focus group discussions with preschool teachers. The study revealed that the preschool teachers had content knowledge, but lacked pedagogical knowledge that is crucial in teaching of preschool children, and they provided science and mathematics experiences in preschools scarcely. A resource book of 33 local games and rhymes thus was developed as a support material to empower the teachers with skills and competencies to use play to teach science and mathematics in preschools. The resource book developed consists of 33 local games/rhymes and is packaged with the games’ illustrations, steps and rules followed in the games, science and mathematics concepts and competencies that could be taught to children, along with probing questions that would help in teaching of science and mathematics concepts to children.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Rémi Léandre. Articles written in Proceedings – Mathematical Sciences. Volume 116 Issue 4 November 2006 pp 507-518 Non-commutative Probability Theory. Malliavin Calculus of Bismut Type without Probability · Rémi Léandre · More Details Abstract Fulltext PDF.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. MEGHA GOYAL. Articles written in Proceedings – Mathematical Sciences. Volume 128 Issue 1 March 2018 pp 2 Research Article. On 3-way combinatorial identities · A K AGARWAL MEGHA GOYAL · More Details Abstract Fulltext PDF. In this paper, we provide ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Pravir Dutt. Articles written in Proceedings – Mathematical Sciences. Volume 112 Issue 4 November 2002 pp 601-639. Stability Estimates for ℎ- Spectral Element Methods for Elliptic Problems · Pravir Dutt Satyendra Tomar B V Rathish Kumar · More Details Abstract ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. B V Rao. Articles written in Proceedings – Mathematical Sciences. Volume 116 Issue 1 February 2006 pp 83-96. On Characterisation of Markov Processes Via Martingale Problems · Abhay G Bhatt Rajeeva L Karandikar B V Rao · More Details Abstract Fulltext PDF.

Mathematical modeling of dissolved oxygen in fish ponds ...

African Journals Online (AJOL)

Mathematical modeling of dissolved oxygen in fish ponds. WJS Mwegoha, ME Kaseva, SMM Sabai. Abstract. A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide and chemical oxygen demand (COD) on Dissolved Oxygen (DO) in fish ponds. The effects ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Suprio Bhar. Articles written in Proceedings – Mathematical Sciences. Volume 125 Issue 1 February 2015 pp 113-125. Differential operators on Hermite Sobolev spaces · Suprio Bhar B Rajeev · More Details Abstract Fulltext PDF. In this paper, we compute the Hilbert ...

The Image of Mathematics Held by Irish Post-Primary Students

Science.gov (United States)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2014-01-01

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for "image of mathematics" was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research…

Converging modalities ground abstract categories: the case of politics.

Directory of Open Access Journals (Sweden)

Ana Rita Farias

Full Text Available Three studies are reported examining the grounding of abstract concepts across two modalities (visual and auditory and their symbolic representation. A comparison of the outcomes across these studies reveals that the symbolic representation of political concepts and their visual and auditory modalities is convergent. In other words, the spatial relationships between specific instances of the political categories are highly overlapping across the symbolic, visual and auditory modalities. These findings suggest that abstract categories display redundancy across modal and amodal representations, and are multimodal.

Rethinking Mathematics Teaching in Liberia: Realistic Mathematics Education

Science.gov (United States)

Stemn, Blidi S.

2017-01-01

In some African cultures, the concept of division does not necessarily mean sharing money or an item equally. How an item is shared might depend on the ages of the individuals involved. This article describes the use of the Realistic Mathematics Education (RME) approach to teach division word problems involving money in a 3rd-grade class in…

An abstract approach to music.

Energy Technology Data Exchange (ETDEWEB)

Kaper, H. G.; Tipei, S.

1999-04-19

In this article we have outlined a formal framework for an abstract approach to music and music composition. The model is formulated in terms of objects that have attributes, obey relationships, and are subject to certain well-defined operations. The motivation for this approach uses traditional terms and concepts of music theory, but the approach itself is formal and uses the language of mathematics. The universal object is an audio wave; partials, sounds, and compositions are special objects, which are placed in a hierarchical order based on time scales. The objects have both static and dynamic attributes. When we realize a composition, we assign values to each of its attributes: a (scalar) value to a static attribute, an envelope and a size to a dynamic attribute. A composition is then a trajectory in the space of aural events, and the complex audio wave is its formal representation. Sounds are fibers in the space of aural events, from which the composer weaves the trajectory of a composition. Each sound object in turn is made up of partials, which are the elementary building blocks of any music composition. The partials evolve on the fastest time scale in the hierarchy of partials, sounds, and compositions. The ideas outlined in this article are being implemented in a digital instrument for additive sound synthesis and in software for music composition. A demonstration of some preliminary results has been submitted by the authors for presentation at the conference.

Drawing Space: Mathematicians' Kinetic Conceptions of Eigenvectors

Science.gov (United States)

Sinclair, Nathalie; Gol Tabaghi, Shiva

2010-01-01

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of…

The Mathematical Theory of Multifocal Lenses

Institute of Scientific and Technical Information of China (English)

Jacob RUBINSTEIN

2017-01-01

This paper presents the fundamental optical concepts of designing multifocal ophthalmic lenses and the mathematical methods associated with them.In particular,it is shown that the design methodology is heavily based on differential geometric ideas such as Willmore surfaces.A key role is played by Hamilton's eikonal functions.It is shown that these functions capture all the information on the local blur and distortion created by the lenses.Along the way,formulas for computing the eikonal functions are derived.Finally,the author lists a few intriguing mathematical problems and novel concepts in optics as future projects.

The Ellipse A Historical and Mathematical Journey

CERN Document Server

Mazer, Arthur

2011-01-01

Explores the development of the ellipse and presents mathematical concepts within a rich, historical context The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment. Incorporating illuminating historical background and examples, the author brings together basic concepts from geometry, algebra, trigonometry, and calculus to uncover the ellipse as the shape of a planet's orbit around the sun. The book begins with a discussion that tells the st

A course of higher mathematics

CERN Document Server

Smirnov, Vladimir Ivanovich; Lohwater, A J

1964-01-01

A Course of Higher Mathematics, I: Elementary Calculus is a five-volume course of higher mathematics used by mathematicians, physicists, and engineers in the U.S.S.R. This volume deals with calculus and principles of mathematical analysis including topics on functions of single and multiple variables. The functional relationships, theory of limits, and the concept of differentiation, whether as theories and applications, are discussed. This book also examines the applications of differential calculus to geometry. For example, the equations to determine the differential of arc or the parameter

Problem solving through recreational mathematics

CERN Document Server

Averbach, Bonnie

1999-01-01

Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics - problems, puzzles and games - to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire ga

Lakatos and Hersh on Mathematical Proof

Directory of Open Access Journals (Sweden)

Hossein Bayat

2015-12-01

Full Text Available The concept of Mathematical Proof has been controversial for the past few decades. Different philosophers have offered different theories about the nature of Mathematical Proof, among which theories presented by Lakatos and Hersh have had significant similarities and differences with each other. It seems that a comparison and critical review of these two theories will lead to a better understanding of the concept of mathematical proof and will be a big step towards solving many related problems. Lakatos and Hersh argue that, firstly, “mathematical proof” has two different meanings, formal and informal; and, secondly, informal proofs are affected by human factors, such as individual decisions and collective agreements. I call these two thesis, respectively, “proof dualism” and “humanism”. But on the other hand, their theories have significant dissimilarities and are by no means equivalent. Lakatos is committed to linear proof dualism and methodological humanism, while Hersh’s theory involves some sort of parallel proof dualism and sociological humanism. According to linear proof dualism, the two main types of proofs are provided in order to achieve a common goal: incarnation of mathematical concepts and methods and truth. However, according to the parallel proof dualism, two main types of proofs are provided in order to achieve two different types of purposes: production of a valid sequence of signs (the goal of the formal proof and persuasion of the audience (the goal of the informal proof. Hersh’s humanism is informative and indicates pluralism; whereas, Lakatos’ version of humanism is normative and monistic.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. OLIVIA X M YAO. Articles written in Proceedings – Mathematical Sciences. Volume 127 Issue 3 June 2017 pp 393-410 Research Article. New modular relations involving cubes of the Göllnitz–Gordon functions · OLIVIA X M YAO · More Details Abstract Fulltext PDF.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. K R Parthasarathy. Articles written in Proceedings – Mathematical Sciences. Volume 113 Issue 1 February 2003 pp 3-13. A Remark on the Unitary Group of a Tensor Product of Finite-Dimensional Hilbert Spaces · K R Parthasarathy · More Details Abstract Fulltext ...

Pokémon Battles as a Context for Mathematical Modeling

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McGuffey, William

2017-01-01

In this article I explore some of the underlying mathematics of Poke´mon battles and describe ways that teachers at the secondary level could explore concepts of mathematical game theory in this context. I discuss various ways of representing and analyzing a Poke´mon battle using game theory and conclude with an example of applying concepts of…

Didactic use of cinema in Mathematics

Directory of Open Access Journals (Sweden)

Pablo BELTRÁN PELLICER

2014-10-01

Full Text Available The use of cinema as didactical resource in the Mathematics classroom has interested several authors and teachers during the last years, mainly because of its power to motivate students. On this point, suggestive compilations of scenes containing mathematical references, detailed analysis of movies closely related to Mathematics and even didactical materials to be used in the classroom have been developed. This article proposes a theoretical framework for designing classroom sequences based on the didactical situation which can arise from movies or fiction series scenes. In order to develop such a framework, we follow a didactical engineering process, taking into account some specific characteristics, as the one related to the didactical transposition, as it is required to consider the mathematic knowledge within the chosen scene, overall the way it appears. As well, a classroom experience is described, designed following the mentioned guidelines and implemented in the course of a collaborative project between two secondary education centers, where a significant motivation increase has been detected, due to using mathematical situations from the real world (or from fictional contexts but which can be easily assimilated by the students. There was also evidence about the fact that the designed didactical sequences allow to reduce the cognitive gap required to acquire certain mathematical concepts, because of the scenes provide additional information within an extra-mathematical context. Therefore, our proposal establishes some basic considerations in order to efficiently design didactical sequences using movie scenes as a resource, underlining its power to motivate as well as its facilitating ability when introducing new mathematical concepts to our students.

Mindset Matters: Supporting Student Persistence Through The Developmental Mathematics Pipeline

OpenAIRE

Kiser, Tracey Nicole

2016-01-01

Abstract of the DissertationMindset Matters: Supporting Student Persistence Through The Developmental Mathematics PipelinebyTracey Nicole KiserDoctor of Education in Teaching and LearningUniversity of California, San Diego, 2016Christopher P. Halter, ChairDevelopmental mathematics is one of the most challenging leaks in the mathematics K-20 pipeline. Few students enter two-year colleges prepared to successfully engage in college-level mathematics classes. Many of students who place into devel...

How Bob Barker Would (Probably) Teach Discrete Mathematics

Science.gov (United States)

Urness, Timothy

2010-01-01

This article proposes a discrete mathematics course in which games from "The Price Is Right" are used to engage students in a deeper, practical study of discrete mathematics. The games themselves are not the focus of the course; rather, the mathematical principles of the games give motivation for the concepts being taught. The game examples are…

Introducing geometry concept based on history of Islamic geometry

Science.gov (United States)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

The early emergence and puzzling decline of relational reasoning: Effects of knowledge and search on inferring abstract concepts.

Science.gov (United States)

Walker, Caren M; Bridgers, Sophie; Gopnik, Alison

2016-11-01

We explore the developmental trajectory and underlying mechanisms of abstract relational reasoning. We describe a surprising developmental pattern: Younger learners are better than older ones at inferring abstract causal relations. Walker and Gopnik (2014) demonstrated that toddlers are able to infer that an effect was caused by a relation between two objects (whether they are the same or different), rather than by individual kinds of objects. While these findings are consistent with evidence that infants recognize same-different relations, they contrast with a large literature suggesting that older children tend to have difficulty inferring these relations. Why might this be? In Experiment 1a, we demonstrate that while younger children (18-30-month-olds) have no difficulty learning these relational concepts, older children (36-48-month-olds) fail to draw this abstract inference. Experiment 1b replicates the finding with 18-30-month-olds using a more demanding intervention task. Experiment 2 tests whether this difference in performance might be because older children have developed the general hypothesis that individual kinds of objects are causal - the high initial probability of this alternative hypothesis might override the data that favors the relational hypothesis. Providing additional information falsifying the alternative hypothesis improves older children's performance. Finally, Experiment 3 demonstrates that prompting for explanations during learning also improves performance, even without any additional information. These findings are discussed in light of recent computational and algorithmic theories of learning. Copyright © 2016 Elsevier B.V. All rights reserved.

The hue of concepts.

Science.gov (United States)

Albertazzi, Liliana; Canal, Luisa; Malfatti, Michela; Micciolo, Rocco

2013-01-01

The study shows a systematic naturally biased association between percepts and concepts. Specifically, it shows that a series of terms pertaining to an abstract semantic field (related to the frame of ethics in social behaviour) has a nonrandom, highly significant, association with colours (hues). This is the first time that consistent associations between abstract terms and colours have been reported in the general population. The main hypothesis, ie that there appear to be 'hues of concepts', was borne out by the results: the abstract terms considered were coloured with blue/green (ie cool) colours as well as their synonyms, while their antonyms were coloured with red/yellow (ie warm) colours. The association provides information about the nature of abstract concepts and their relationship with perception. It also sheds light on the interrelations among words in semantic domains that, to date, have been studied from only a computational viewpoint.

Values in the Mathematics Classroom: Supporting Cognitive and Affective Pedagogical Ideas

Science.gov (United States)

Seah, Wee Tiong

2016-01-01

Values are the personal convictions which one finds important. Three different aspects which are associated with mathematics education differently are identified, namely, values through mathematics education, values of mathematics education, and values for mathematics. These are paired with Bishop's (1996) conceptions of general educational,…

Transformative Learning: Personal Empowerment in Learning Mathematics

Science.gov (United States)

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…

Abstract Cauchy problems three approaches

CERN Document Server

Melnikova, Irina V

2001-01-01

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches.Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, b...

21st Annual Conference of Ramanujan Mathematical Society

Indian Academy of Sciences (India)

Paper Presentation: Those who want to present papers should send an abstract of the paper along with a hard copy of the paper so as to reach the Local Secretary, 21st Annual. Conference of Ramanujan Mathematical Society, Department of Mathematics and Statis- tics, University of Hyderabad, Hyderabad 500046 on or ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Hongliang Yao. Articles written in Proceedings – Mathematical Sciences. Volume 120 Issue 2 April 2010 pp 199-207. A T -Algebras and Extensions of A T -Algebras · Hongliang Yao · More Details Abstract Fulltext PDF. Lin and Su classified A T -algebras of real rank ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Vijay Kodiyalam. Articles written in Proceedings – Mathematical Sciences. Volume 110 Issue 3 August 2000 pp 263-292. The Algebra of -relations · Vijay Kodiyalam R Srinivasan V S Sunder · More Details Abstract Fulltext PDF. In this paper, we study a tower { A n G ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Bülent Nafi Örnek. Articles written in Proceedings – Mathematical Sciences. Volume 126 Issue 1 February 2016 pp 69-78. Sharpened forms of the generalized Schwarz inequality on the boundary · Tuğba Akyel Bülent Nafi Örnek · More Details Abstract Fulltext PDF.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. K B Sinha. Articles written in Proceedings – Mathematical Sciences. Volume 111 Issue 2 May 2001 pp 179-201. Spectra of Anderson Type Models with Decaying Randomness · M Krishna K B Sinha · More Details Abstract Fulltext PDF. In this paper we consider some ...

Books for Professionals: Premathematical Concepts.

Science.gov (United States)

King, Margaret A.

1993-01-01

Reviews four books on teaching premathematical concepts to young children: (1) "Windows on Mathematics: Worktime Activities for Young Children" (Westley and Randolph); (2) "Hands-On Math: Manipulative Math for Young Children" (Stone); (3) "Books You Can Count On: Linking Mathematics and Literature" (Griffiths and Clyne); and (4) "Mathematics…

Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete-Representational-Abstract Sequence and Schema-Based Instruction

Science.gov (United States)

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)…

Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

Science.gov (United States)

Hitt, Fernando

2011-09-01

Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics teachers can be divided into three categories: those with a boundless overflow (enthusiasm) who want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher, by not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this article, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We also note that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future.

Academic and Nonacademic Validating Agents on Latinas' Mathematics and Science Self Concept: A Quantitative Study Utilizing the High School Longitudinal Study of 2009

Science.gov (United States)

Garza, Jennifer M.

2017-01-01

The purpose of this study is to inform and further the discussion of academic (i.e., teachers and school counselors) and non-academic (i.e., parents, family, friends, etc.) validating agents on Latina students' mathematics and science self-concepts. This study found a relationship between Latina students' interactions with academic and…

Putting Foundations Into Mathematics

Science.gov (United States)

Hubbard, G. L.

1972-01-01

For meaningful learning of mathematics, a learning set is required which demands that all things accepted as true should be demonstrable in terms of a paradigm appropriate to the child's cognitive development: preparatory, concrete-particular, concrete-general, formal-abstract. Future teachers should experience all paradigms to become aware that…

Mathematics Objectives and Measurement Specifications 1986-1990. Exit Level. Texas Educational Assessment of Minimum Skills (TEAMS).

Science.gov (United States)

Texas Education Agency, Austin. Div. of Educational Assessment.

This document lists the objectives for the Texas educational assessment program in mathematics. Eighteen objectives for exit level mathematics are listed, by category: number concepts (4); computation (3); applied computation (5); statistical concepts (3); geometric concepts (2); and algebraic concepts (1). Then general specifications are listed…

Lectures in the history of mathematics

CERN Document Server

Bos, Henk J M

1993-01-01

"[These lectures] are about themes of the history of mathematics which, for various reasons, are dear to me. The early differential and integral calculus, the work of Christiaan Huygens, and the concept of construction in seventeenth- and eighteenth-century mathematics are the three themes around which much of my research has concentrated and which continue to fascinate me by the insights they offer in the development of that special human activity called mathematics." -from the Introduction This volume contains eleven lectures ranging over a variety of topics in the history of mathematics. The lectures, presented between 1970 and 1987, were delivered in a variety of venues and appeared only in less accessible publications. Those who teach mathematics, as well as mathematics historians, will appreciate this insightful, wide-ranging book.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. José M Sigarreta. Articles written in Proceedings – Mathematical Sciences. Volume 120 Issue 5 November 2010 pp 593-609. Gromov Hyperbolicity in Cartesian Product Graphs · Junior Michel José M Rodríguez José M Sigarreta María Villeta · More Details Abstract ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Q X Yang. Articles written in Proceedings – Mathematical Sciences. Volume 115 Issue 2 May 2005 pp 191-200. L p -Continuity for Calderón–Zygmund Operator · Q X Yang · More Details Abstract Fulltext PDF. Given a Calderón–Zygmund (- for short) operator , ...

An introduction to mathematical modeling of infectious diseases

CERN Document Server

Li, Michael Y

2018-01-01

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies.  The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis.  Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases.  Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Mathematical foundations of thermodynamics

CERN Document Server

Giles, R; Stark, M; Ulam, S

2013-01-01

Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodyn

Mathematics for electronic technology

CERN Document Server

Howson, D P

1975-01-01

Mathematics for Electronic Technology is a nine-chapter book that begins with the elucidation of the introductory concepts related to use of mathematics in electronic engineering, including differentiation, integration, partial differentiation, infinite series, vectors, vector algebra, and surface, volume and line integrals. Subsequent chapters explore the determinants, differential equations, matrix analysis, complex variable, topography, graph theory, and numerical analysis used in this field. The use of Fourier method for harmonic analysis and the Laplace transform is also described. The ma

Reading and Reflecting: Elementary Preservice Teachers' Conceptions about Teaching Mathematics for Equity

Science.gov (United States)

Jackson, Christa; Jong, Cindy

2017-01-01

Teaching mathematics for equity is critical because it provides opportunities for all students, especially those who have been traditionally marginalised, to learn mathematics that is rigorous and relevant to their lives. This article reports on our work, as mathematics teacher educators, on exposing and engaging 60 elementary preservice teachers…

Functional Abstraction of Stochastic Hybrid Systems

NARCIS (Netherlands)

Bujorianu, L.M.; Blom, Henk A.P.; Hermanns, H.

2006-01-01

The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways

What do mathematics teachers and teacher trainees know about the history of mathematics?

Science.gov (United States)

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.

Remembering the hindu festivities mathematically by the balinese using integer operations and least common multiple

Science.gov (United States)

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.

Illustrating Mathematics using 3D Printers

OpenAIRE

Knill, Oliver; Slavkovsky, Elizabeth

2013-01-01

3D printing technology can help to visualize proofs in mathematics. In this document we aim to illustrate how 3D printing can help to visualize concepts and mathematical proofs. As already known to educators in ancient Greece, models allow to bring mathematics closer to the public. The new 3D printing technology makes the realization of such tools more accessible than ever. This is an updated version of a paper included in book Low-Cost 3D Printing for science, education and Sustainable Devel...

Introduction to the foundations of mathematics