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The Language of Mathematics: Telling Mathematical Tales

Overview

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 ...

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Overview

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.

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Product Details

  • ISBN-13: 9780387929378
  • Publisher: Springer US
  • Publication date: 2/23/2009
  • Series: Mathematics Education Library Series , #44
  • Edition description: 2008
  • Edition number: 1
  • Pages: 186
  • Sales rank: 1,015,050
  • Product dimensions: 6.00 (w) x 9.20 (h) x 0.60 (d)

Table of Contents


Acknowledgements     vii
Prelude: Maori Mathematics Vocabulary     1
Introduction     7
Speaking Mathematics Differently     13
Space: Points of Reference     15
Ways of Locating: Linguistic Features     16
Ways of Locating: Mathematical Systems     18
Linking the Linguistic and Mathematical Systems     19
Space: Static and Dynamic World Views     27
What are Verbal Shapes?     28
Birds and Orbits     30
European and Pacific Navigation     33
Linking the Linguistic and Mathematical Systems     36
Quantity: Trapping Numbers in Grammatical Nets     41
Emerging Numbers: Polynesian Languages     42
Numbers Trapped as Adjectives: Kankana-ey     43
Functioning Numbers: Dhivehi     46
Congruence of Language with Mathematics     50
Language and Mathematics     55
The Evidence from Language     57
Two Word Stories: Normal and Open     57
Reviewing the Evidence     61
Mumbling, Metaphors, & Mindlocks: The Origins of Mathematics     65
Gossip & Mathematical Talk     65
Cognitive Science Contributions     70
Fraction Systems     73
Historical Evidence     78
Social Influence on Choice     80
The Role of Communication     82
Metaphors     88
Mindlocks     94
A Never-Ending Braid: The Development of Mathematics     99
Pacific Navigation: Is It Mathematics?     101
A River or a Braid?     105
Snapping to Grid & Other Mechanisms     108
Rejection and Isolation     113
Mathematics, Society & Culture     115
What Is Mathematics? Philosophical Comments     121
Middle Earth     121
Mathematical Worlds     124
Wittgensteinian Mathematical Worlds     127
Mathematics and Experience     130
Recurrent History: Bachelard     132
Universal or Relative     134
Evidence, Reflections, & Consequences     136
Implications for Mathematics Education     139
Learning Mathematics     141
Conclusions Through Educational Eyes     141
Becoming a Better Gossip     146
From 1 to 100: Playing & Exploring     149
Creating Mathematics Through Talking     152
Some Thoughts About Teaching Mathematics      154
Notes on Assessment     157
Multilingual and Indigenous Mathematics Education     161
Untold Riches     162
Mathematical Discourse     164
Mathematics Education for Indigenous Peoples     166
End Words     173
References     175
Index to Names     183
Index to Subjects     185
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