Perspectives on Mathematical Practices: Bringing Together Philosophy of Mathematics, Sociology of Mathematics, and Mathematics Education / Edition 1

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Overview

Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next.

The editors of this book felt the urge, first of all, to bring together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.

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Product Details

Table of Contents


Introduction     1
How to Deal with Mathematical Practice?
How and Why Mathematics is Unique as a Social Practice   Jody Azzouni     3
Mathematics as Objective Knowledge and as Human Practice   Eduard Glas     25
The Comparison of Mathematics with Narrative   R. S. D. Thomas     43
Theory of Mind, Social Science, and Mathematical Practice   Sal Restivo     61
Taking Mathematical Practice Seriously
Incommensurability in Mathematics   Otavio Bueno     83
Mathematical Progress as Increased Scope   Madeline Muntersbjorn     107
Proof in C17 Algebra   Brendan Larvor     119
The Informal Logic of Mathematical Proof   Andrew Aberdein     135
The Special Case of Mathematics Education
Mathematicians' Narratives about Mathematics   Leone Burton     155
Philosophy of Mathematics and Mathematics Education   Anthony Peressini   Dominic Peressini     175
Mathematical Practices in and Across School Contexts   Jill Adler     191
The Importance of a Journal for Mathematics Teachers   Ad Meskens     215
On the Interdisciplinary Study of Mathematical Practice, with a Real Live Case Study   Reuben Hersh     231
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