Symbols and Meanings in School Mathematics

by Pimm,David

• ISBN13: 9780415113854
• ISBN10: 0415113857
• Format: Nonspecific Binding
• Copyright: 1995-05-26
• Publisher: Routledge

Summary

Symbols and Meanings in School Mathematicsexplores the various uses and aspects of symbols in school mathematics and also examines the notion of mathematical meaning. It is concerned with the power of language which enables us to do mathematics, giving us the ability to name and rename, to transform names and to use names and description to conjure, communicate and control our images. It is in the interplay between language, image and object that mathematics is created and can be communicated to others. One theme which runs throughout the book is the core metaphor of manipulation. Practical apparatus is known as manipulatives, some recent computer software is called symbolic manipulators, and we are taught to manipulate numbers, algebraic expressions and geometric figures and images. The book also addresses a set of questions of particular relevance to the last decade of the twentieth century, which arise due to the proliferation of machines offering mathematicalfunctioning.

Table of Contents

In Acknowledgement: Naming Names	p. ix
An Idiosyncratic Preface	p. xi
Introduction	p. 1
Manipulatives as Symbols	p. 12
Geometric Images and Symbols	p. 32
What Counts as a Number?	p. 60
Algebra Transforming	p. 88
Making Representations and Interpretations	p. 118
Symbols and Measures	p. 135
Living in the Material World: Symbols in Contexts	p. 153
On Fluency and Understanding	p. 170
On Manipulation	p. 184
Notes	p. 192
References	p. 206
Name Index	p. 214
Subject Index	p. 216
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