Mathematical Epistemology And Psychology

Author : E.W. Beth,J. Piaget
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Language Arts & Disciplines
ISBN : 9789401721936

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Mathematical Epistemology and Psychology by E.W. Beth,J. Piaget Pdf

One of the controversial philosophical issues of recent years has been the question of the nature of logical and mathematical entities. Platonist or linguistic modes of explanation have become fashionable, whilst abstrac tionist and constructionist theories have ceased to be so. Beth and Piaget approach this problem in their book from two somewhat different points of view. Beth's approach is largely historico-critical, although he discusses the nature of heuristic thinking in mathematics, whilst that of Piaget is psycho-genetic. The major purpose of this introduction is to summarise some of the main points of their respective arguments. In the first part of this book Beth makes a detailed study of the history of philosophical thinking about mathematics, and draws our attention to the important role played by the Aristotelian methodology of the demon strative sciences. This, he tells us, is characterised by three postulates: (a) deductivity, (b) self-evidence, and (c) reality. The last postulate asserts that the primitive notions of a demonstrative science must have reference to a domain of real entities in order to have significance. On the Aristote lian view discursive reasoning plays a major role in mathematics, whilst pure intuition plays a somewhat subordinate one.

Author : Evert Willem Beth,Jean Piaget
Publisher : Unknown
Page : 326 pages
File Size : 54,7 Mb
Release : 1966
Category : Knowledge, Theory of
ISBN : OCLC:440277775

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Mathematical Epistemology and Psychology by Evert Willem Beth,Jean Piaget Pdf

Author : Sorin Bangu
Publisher : Routledge
Page : 319 pages
File Size : 42,5 Mb
Release : 2018-02-01
Category : Mathematics
ISBN : 9781351998444

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Naturalizing Logico-Mathematical Knowledge by Sorin Bangu Pdf

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

Author : Leslie P. Steffe
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Psychology
ISBN : 9781461231783

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Epistemological Foundations of Mathematical Experience by Leslie P. Steffe Pdf

On the 26th, 27th, and 28th of February of 1988, a conference was held on the epistemological foundations of mathematical experience as part of the activities of NSF Grant No. MDR-8550463, Child Generated Multiplying and Dividing Algorithms: A Teaching Experiment. I had just completed work on the book Construction of Arithmetical Meanings and Strategies with Paul Cobb and Ernst von Glasersfeld and felt that substantial progress had been made in understanding the early numerical experiences of the six children who were the subjects of study in that book. While the book was in preparation, I was also engaged in the teaching experiment on mUltiplying and dividing algorithms. My focus in this teaching experiment was on investigating the mathematical experiences of the involved children and on developing a language through which those experiences might be expressed. However, prior to immersing myself in the conceptual analysis of the mathematical experiences of the children, I felt that it was crucial to critically evaluate the progress that we felt we had made in our earlier work. It was toward achieving this goal that I organized the conference. When trying to understand the mathematical experiences of a child, one can do no better than to interact with the child in a mathematical context guided by the intention to specify the child's current knowledge and the progress the child might make.

Author : Leslie P Steffe
Publisher : Unknown
Page : 332 pages
File Size : 46,9 Mb
Release : 1991-09-17
Category : Electronic
ISBN : 1461231795

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Epistemological Foundations of Mathematical Experience by Leslie P Steffe Pdf

Author : Jacques Hadamard
Publisher : Read Books Ltd
Page : 164 pages
File Size : 40,8 Mb
Release : 2013-04-16
Category : Mathematics
ISBN : 9781447493273

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An Essay on the Psychology of Invention in the Mathematical Field by Jacques Hadamard Pdf

Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

Author : Paul Christian Dawkins,Amy J. Hackenberg,Anderson Norton
Publisher : Springer Nature
Page : 620 pages
File Size : 52,8 Mb
Release : 2024-01-22
Category : Education
ISBN : 9783031473869

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Piaget’s Genetic Epistemology for Mathematics Education Research by Paul Christian Dawkins,Amy J. Hackenberg,Anderson Norton Pdf

The book provides an entry point for graduate students and other scholars interested in using the constructs of Piaget’s genetic epistemology in mathematics education research. Constructs comprising genetic epistemology form the basis for some of the most well-developed theoretical frameworks available for characterizing learning, particularly in mathematics. The depth and complexity of Piaget’s work can make it challenging to find adequate entry points for learners, not least because it requires a reorientation regarding the nature of mathematical knowledge itself. This volume gathers leading scholars to help address that challenge. The main section of the book presents key Piagetian constructs for mathematics education research such as schemes and operations, figurative and operative thought, images and meanings, and decentering. The chapters that discuss these constructs include examples from research and address how these constructs can be used in research. There are two chapters on various types of reflective abstraction, because this construct is Piaget’s primary tool for characterizing the advancement of knowledge. The later sections of the book contain commentaries reflecting on the contributions of the body of theory developed in the first section. They connect genetic epistemology to current research domains such as equity and the latest in educational psychology. Finally, the book closes with short chapters portraying how scholars are using these tools in specific arenas of mathematics education research, including in special education, early childhood education, and statistics education.

Author : Pearla Nesher,Jeremy Kilpatrick
Publisher : CUP Archive
Page : 234 pages
File Size : 51,6 Mb
Release : 1990-02-23
Category : Education
ISBN : 0521367875

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Mathematics and Cognition by Pearla Nesher,Jeremy Kilpatrick Pdf

This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.

Author : Paul Ernest
Publisher : Routledge
Page : 295 pages
File Size : 47,8 Mb
Release : 2012-10-12
Category : Education
ISBN : 9781136364723

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Constructing Mathematical Knowledge by Paul Ernest Pdf

First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.

Author : Mary Leng,Alexander Paseau,Michael Potter
Publisher : OUP Oxford
Page : 236 pages
File Size : 47,5 Mb
Release : 2007-11-15
Category : Philosophy
ISBN : 9780191527890

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Mathematical Knowledge by Mary Leng,Alexander Paseau,Michael Potter Pdf

What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field.

Author : Jean Piaget
Publisher : Unknown
Page : 128 pages
File Size : 46,9 Mb
Release : 1972
Category : Psychology
ISBN : NWU:35556001270289

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Psychology and Epistemology by Jean Piaget Pdf

In the past knowledge was considered static, but epistemologists now take that as soon as an entity of knowledge crystallizes it must dissolve again in the current of new developments of understanding. Here Piaget brings scientific analysis, without philosophical presuppositions, to bear on the understanding of knowledge as a process. This approach to knowledge underlines the benefits of interdisciplinary studies; and Piaget puts forward specific proposals for cooperation between philosophy, linguistics, cybernetics, political economy, demography, logic, epistemology and experimental teaching methods. It is the contention of this great theoretician that such interdisciplinary work could lead to a whole "circle of sciences", in which wide-ranging disciplines would link hands in a general theory of knowledge. -- Back cover.

Author : Anderson Norton
Publisher : Routledge
Page : 238 pages
File Size : 54,7 Mb
Release : 2022-03-22
Category : Education
ISBN : 9781000547016

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The Psychology of Mathematics by Anderson Norton Pdf

This book offers an innovative introduction to the psychological basis of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. Through accessible and engaging writing, award-winning mathematician and educator Anderson Norton reframes mathematics as something that exists first in the minds of students, rather than something that exists first in a textbook. By exploring the psychological basis for mathematics at every level—including geometry, algebra, calculus, complex analysis, and more—Norton unlocks students’ personal power to construct mathematical objects based on their own mental activity and illustrates the power of mathematics in organizing the world as we know it. Including reflections and activities designed to inspire awareness of the mental actions and processes coordinated in practicing mathematics, the book is geared toward current and future secondary and elementary mathematics teachers who will empower the next generation of mathematicians and STEM majors. Those interested in the history and philosophy that underpins mathematics will also benefit from this book, as well as those informed and curious minds attentive to the human experience more generally.

Author : Marcus Giaquinto
Publisher : Oxford University Press
Page : 298 pages
File Size : 53,7 Mb
Release : 2007-07-05
Category : Mathematics
ISBN : 9780199285945

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Visual Thinking in Mathematics by Marcus Giaquinto Pdf

Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.

Author : Barbara K. Hofer,Paul R. Pintrich
Publisher : Routledge
Page : 429 pages
File Size : 45,8 Mb
Release : 2012-08-21
Category : Education
ISBN : 9781136608636

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Personal Epistemology by Barbara K. Hofer,Paul R. Pintrich Pdf

This is the first book to provide a comprehensive overview of the theoretical and methodological approaches to the study of personal epistemology from a psychological and educational perspective. Both theory building and empirical research have grown dramatically in the past decade but, until now, this work has not been pulled together in a single volume. That is the mission of this volume whose state-of-the-art theory and research are likely to define the field for the next 20 years. Key features of this important new book include: *Pioneering Contributors--The book provides current perspectives of each of the major theoreticians and researchers who pioneered this growing field, as well as contributions from new researchers. *Diverse Perspectives--The contributors represent a variety of perspectives, including education, educational psychology, developmental psychology, higher education, and science and mathematics education. *Editorial Integration--Opening and closing chapters by the editors set out key issues confronting the field.

Author : Jean Lave
Publisher : Cambridge University Press
Page : 236 pages
File Size : 54,9 Mb
Release : 1988-07-29
Category : Psychology
ISBN : 9781107268319

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Cognition in Practice by Jean Lave Pdf

Most previous research on human cognition has focused on problem-solving, and has confined its investigations to the laboratory. As a result, it has been difficult to account for complex mental processes and their place in culture and history. In this startling - indeed, disco in forting - study, Jean Lave moves the analysis of one particular form of cognitive activity, - arithmetic problem-solving - out of the laboratory into the domain of everyday life. In so doing, she shows how mathematics in the 'real world', like all thinking, is shaped by the dynamic encounter between the culturally endowed mind and its total context, a subtle interaction that shapes 1) Both tile human subject and the world within which it acts. The study is focused on mundane daily, activities, such as grocery shopping for 'best buys' in the supermarket, dieting, and so on. Innovative in its method, fascinating in its findings, the research is above all significant in its theoretical contributions. Have offers a cogent critique of conventional cognitive theory, turning for an alternative to recent social theory, and weaving a compelling synthesis from elements of culture theory, theories of practice, and Marxist discourse. The result is a new way of understanding human thought processes, a vision of cognition as the dialectic between persons-acting, and the settings in which their activity is constituted. The book will appeal to anthropologists, for its novel theory of the relation of cognition to culture and context; to cognitive scientists and educational theorists; and to the 'plain folks' who form its subject, and who will recognize themselves in it, a rare accomplishment in the modern social sciences.