Epistemological Foundations of Mathematical Experience
Epistemological Foundations of Mathematical Experience

Author: Leslie P. Steffe

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 257

ISBN-13: 1461231787

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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.

Experience and Prediction
Experience and Prediction

Author: Hans Reichenbach

Publisher: Forgotten Books

Published: 2017-09-12

Total Pages: 420

ISBN-13: 9781528150422

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Excerpt from Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge The conviction that the key to an understanding of sci entific method is contained within the probability problem grew stronger and stronger with me in the face of such basic mistakes. This is the reason why, for a long time, I renounced a comprehensive report of my epistemological views, although my special investigations into different problems of epistemology demanded a construction of foundations different from those constructed by some of my philosophical friends. I concentrated my inquiry on the problem of probability which demanded at the same time a mathematical and a logical analysis. It is only after having traced out a logistic theory of probability, includ ing a solution of the problem of induction, that I turn now to an application of these ideas to questions of a more gen eral epistemological character. As my theory of probabil ity has been published for some years, it was not necessary to present it with all mathematical details once more in the present book; the fifth chapter, however, gives an ah breviated report of this theory - a report which seemed necessary as the probability book has been published in German only. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

The Mathematical Experience
The Mathematical Experience

Author: Philip J. Davis

Publisher: Houghton Mifflin Harcourt

Published: 1998

Total Pages: 470

ISBN-13: 9780395929681

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Explores the foundations of mathematics, looking at the history and philosophy of the field, and includes biographical sketches of people who have made mathematics their life's work

Doing Management Research
Doing Management Research

Author:

Publisher: SAGE

Published: 2001-07-12

Total Pages: 446

ISBN-13: 9780761965176

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Doing Management Research, a major new textbook, provides answers to questions and problems which researchers invariably encounter when embarking on management research, be it quantitative or qualitative. This book will carefully guide the reader through the research process from beginning to end. An excellent tool for academics and students, it enables the reader to acquire and build upon empirical evidence, and to decide what tools to use to understand and describe what is being observed, and then, which methods of analysis to adopt. There is an entire section dedicated to writing up and communicating the research findings. Written in an accessible and easy-to-use style, this book can be read from cover to cover or dipped

Constructing Mathematical Knowledge
Constructing Mathematical Knowledge

Author: Paul Ernest

Publisher: Routledge

Published: 2012-10-12

Total Pages: 295

ISBN-13: 1136364722

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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.

Mathematical Epistemology and Psychology
Mathematical Epistemology and Psychology

Author: E.W. Beth

Publisher: Springer

Published: 1966

Total Pages: 356

ISBN-13:

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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.

Mathematics, Science and Epistemology: Volume 2, Philosophical Papers
Mathematics, Science and Epistemology: Volume 2, Philosophical Papers

Author: Imre Lakatos

Publisher: Cambridge University Press

Published: 1980-10-16

Total Pages: 302

ISBN-13: 9780521280303

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Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics together with some critical essays on contemporary philosophers of science.

Learning Mathematics
Learning Mathematics

Author: Paul Cobb

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 204

ISBN-13: 9401720576

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This volume emphasizes students' inferred mathematical experiences as the starting point in the theory-building process. The book addresses conceptual constructions, including multiplicative notions, fractions, algebra, and the fundamental theorem of calculus, and theoretical constructs such as the crucial role of language and symbols, and the importance of dynamic imagery.