Mathematical Epistemology And Psychology
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Mathematical Epistemology And Psychology
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Author : E.W. Beth
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Mathematical Epistemology And Psychology written by E.W. Beth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Language Arts & Disciplines categories.
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.
Mathematical Epistemology And Psychology
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Author : Evert Willem Beth
language : en
Publisher:
Release Date : 1966
Mathematical Epistemology And Psychology written by Evert Willem Beth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Knowledge, Theory of categories.
Mathematical Epistemology And Psychology
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Author : Evert W. Beth
language : nl
Publisher:
Release Date : 1966
Mathematical Epistemology And Psychology written by Evert W. Beth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Naturalizing Logico Mathematical Knowledge
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Author : Sorin Bangu
language : en
Publisher: Routledge
Release Date : 2018-02-01
Naturalizing Logico Mathematical Knowledge written by Sorin Bangu and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-01 with Mathematics categories.
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.
Epistemological Foundations Of Mathematical Experience
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Author : Leslie P. Steffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Epistemological Foundations Of Mathematical Experience written by Leslie P. Steffe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Psychology categories.
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.
Mathematical Epistemology And Psychology Transl From The French By W Mays
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Author :
language : nl
Publisher:
Release Date : 1966
Mathematical Epistemology And Psychology Transl From The French By W Mays written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Epistemological Foundations Of Mathematical Experience
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Author : Leslie P Steffe
language : en
Publisher:
Release Date : 1991-09-17
Epistemological Foundations Of Mathematical Experience written by Leslie P Steffe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-17 with categories.
The Psychology Of Mathematics
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Author : Anderson Norton
language : en
Publisher: Routledge
Release Date : 2022-03-22
The Psychology Of Mathematics written by Anderson Norton and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-22 with Education categories.
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.
A Fractal Epistemology For A Scientific Psychology
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Author : Terry Marks-Tarlow
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2020-01-06
A Fractal Epistemology For A Scientific Psychology written by Terry Marks-Tarlow and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-06 with Psychology categories.
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.
Mathematical Knowledge
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Author : Mary Leng
language : en
Publisher: OUP Oxford
Release Date : 2007-11-15
Mathematical Knowledge written by Mary Leng and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-15 with Philosophy categories.
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.