Download or read book Mathematical Epistemology and Psychology written by E.W. Beth and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Epistemology and Psychology written by Evert Willem Beth and published by . This book was released on 1966 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Naturalizing Logico Mathematical Knowledge written by Sorin Bangu and published by Routledge. This book was released on 2018-02-01 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Constructing Mathematical Knowledge written by Paul Ernest and published by Routledge. This book was released on 2012-10-12 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical epistemology and psychology written by Evert W. Beth and published by . This book was released on 1966 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Epistemological Foundations of Mathematical Experience written by Leslie P. Steffe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical epistemology and psychology Transl from the French by W Mays written by and published by . This book was released on 1966 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Personal Epistemology written by Barbara K. Hofer and published by Routledge. This book was released on 2012-08-21 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Epistemological Foundations of Mathematical Experience written by Leslie P Steffe and published by . This book was released on 1991-09-17 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Essay on the Psychology of Invention in the Mathematical Field written by Jacques Hadamard and published by Read Books Ltd. This book was released on 2011-10-25 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics and Cognition written by Pearla Nesher and published by CUP Archive. This book was released on 1990-02-23 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.
Download or read book The Oxford Handbook of Computational and Mathematical Psychology written by Jerome R. Busemeyer and published by . This book was released on 2015 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Oxford Handbook offers a comprehensive and authoritative review of important developments in computational and mathematical psychology. With chapters written by leading scientists across a variety of subdisciplines, it examines the field's influence on related research areas such as cognitive psychology, developmental psychology, clinical psychology, and neuroscience. The Handbook emphasizes examples and applications of the latest research, and will appeal to readers possessing various levels of modeling experience. The Oxford Handbook of Computational and mathematical Psychology covers the key developments in elementary cognitive mechanisms (signal detection, information processing, reinforcement learning), basic cognitive skills (perceptual judgment, categorization, episodic memory), higher-level cognition (Bayesian cognition, decision making, semantic memory, shape perception), modeling tools (Bayesian estimation and other new model comparison methods), and emerging new directions in computation and mathematical psychology (neurocognitive modeling, applications to clinical psychology, quantum cognition). The Handbook would make an ideal graduate-level textbook for courses in computational and mathematical psychology. Readers ranging from advanced undergraduates to experienced faculty members and researchers in virtually any area of psychology--including cognitive science and related social and behavioral sciences such as consumer behavior and communication--will find the text useful.
Download or read book Mathematical Knowledge written by Mary Leng and published by OUP Oxford. This book was released on 2007-11-15 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Fractal Epistemology for a Scientific Psychology written by Terry Marks-Tarlow and published by Cambridge Scholars Publishing. This book was released on 2020-01-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal dynamics provide an unparalleled tool for understanding the evolution of natural complexity throughout physical, biological, and psychological realms. This book’s conceptual framework helps to reconcile several persistent dichotomies in the natural sciences, including mind-brain, linear-nonlinear, subjective-objective, and even personal-transpersonal processes. A fractal approach is especially useful when applied to recursive processes of consciousness, both within their ordinary and anomalous manifestations. This novel way to study the interconnection of seemingly divided wholes encompasses multiple dimensions of experience and being. It brings together experts in diverse fields—neuropsychologists, psychiatrists, physicists, physiologists, psychoanalysts, mathematicians, and professors of religion and music composition—to demonstrate the value of fractals as model, method, and metaphor within psychology and related social and physical sciences. The result is a new perspective for understanding what has often been dismissed as too subjective, idiosyncratic, and ineffably beyond the scope of science, bringing these areas back into a natural-scientific framework.
Download or read book The Mathematical Psychology of Gratry and Boole written by Mary Everest Boole and published by . This book was released on 1897 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Psychology and Epistemology written by Jean Piaget and published by . This book was released on 1972 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Visual Thinking in Mathematics written by Marcus Giaquinto and published by Oxford University Press. This book was released on 2007-07-05 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
