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The Language of Mathematics : Telling Mathematical Tales :  Telling Mathematical Tales - Bill Barton

The Language of Mathematics : Telling Mathematical Tales

Telling Mathematical Tales

Hardcover Published: January 2008
ISBN: 9780387728582
Number Of Pages: 186

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The Language of Mathematics: Telling Mathematical Tales emerges from several contemporary concerns in mathematics, language, and mathematics education, but takes a different stance with respect to language. Rather than investigating the way language or culture impacts mathematics and how it is learned, this book begins by examining different languages and how they express mathematical ideas. The picture of mathematics that emerges is of a subject that is much more contingent, relative, and subject to human experience than is usually accepted. Barton's thesis takes the idea of mathematics as a human creation, and, using the evidence from language, comes to more radical conclusions than usual.

Everyday mathematical ideas are expressed quite differently in different languages. Variety occurs in the way languages express numbers, describe position, categorise patterns, as well as in the grammar of mathematical discourse. The first part of The Language of Mathematics: Telling Mathematical Tales explores these differences and thus illustrates the possibility of different mathematical worlds. This section both provides evidence of language difference with respect to mathematic talk and also demonstrates the congruence between mathematics as we know it and the English language. Other languages are not so congruent.

Part II discusses what this means for mathematics and argues for alternative answers to conventional questions about mathematics: where it comes from, how it develops, what it does and what it means. The notion that mathematics is the same for everyone, that it is an expression of universal human thought, is challenged. In addition, the relationship between language and mathematical thought is used to argue that the mathematical creativity embedded in minority languages should continue to be explored

The final section explores implications for mathematics education, discussing the consequences for the ways in which we learn and teach mathematics.

The Language of Mathematics: Telling Mathematical Tales will appeal to those interested in exploring the nature of mathematics, mathematics educators, researchers and graduate students of mathematics education.

Acknowledgementsp. vii
Prelude: Maori Mathematics Vocabularyp. 1
Introductionp. 7
Speaking Mathematics Differentlyp. 13
Space: Points of Referencep. 15
Ways of Locating: Linguistic Featuresp. 16
Ways of Locating: Mathematical Systemsp. 18
Linking the Linguistic and Mathematical Systemsp. 19
Space: Static and Dynamic World Viewsp. 27
What are Verbal Shapes?p. 28
Birds and Orbitsp. 30
European and Pacific Navigationp. 33
Linking the Linguistic and Mathematical Systemsp. 36
Quantity: Trapping Numbers in Grammatical Netsp. 41
Emerging Numbers: Polynesian Languagesp. 42
Numbers Trapped as Adjectives: Kankana-eyp. 43
Functioning Numbers: Dhivehip. 46
Congruence of Language with Mathematicsp. 50
Language and Mathematicsp. 55
The Evidence from Languagep. 57
Two Word Stories: Normal and Openp. 57
Reviewing the Evidencep. 61
Mumbling, Metaphors, & Mindlocks: The Origins of Mathematicsp. 65
Gossip & Mathematical Talkp. 65
Cognitive Science Contributionsp. 70
Fraction Systemsp. 73
Historical Evidencep. 78
Social Influence on Choicep. 80
The Role of Communicationp. 82
Metaphorsp. 88
Mindlocksp. 94
A Never-Ending Braid: The Development of Mathematicsp. 99
Pacific Navigation: Is It Mathematics?p. 101
A River or a Braid?p. 105
Snapping to Grid & Other Mechanismsp. 108
Rejection and Isolationp. 113
Mathematics, Society & Culturep. 115
What Is Mathematics? Philosophical Commentsp. 121
Middle Earthp. 121
Mathematical Worldsp. 124
Wittgensteinian Mathematical Worldsp. 127
Mathematics and Experiencep. 130
Recurrent History: Bachelardp. 132
Universal or Relativep. 134
Evidence, Reflections, & Consequencesp. 136
Implications for Mathematics Educationp. 139
Learning Mathematicsp. 141
Conclusions Through Educational Eyesp. 141
Becoming a Better Gossipp. 146
From 1 to 100: Playing & Exploringp. 149
Creating Mathematics Through Talkingp. 152
Some Thoughts About Teaching Mathematicsp. 154
Notes on Assessmentp. 157
Multilingual and Indigenous Mathematics Educationp. 161
Untold Richesp. 162
Mathematical Discoursep. 164
Mathematics Education for Indigenous Peoplesp. 166
End Wordsp. 173
Referencesp. 175
Index to Namesp. 183
Index to Subjectsp. 185
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780387728582
ISBN-10: 0387728589
Series: Mathematics Education Library
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 186
Published: January 2008
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.39 x 15.6  x 1.27
Weight (kg): 0.46

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