The Language of Mathematics

1. Front Matter

   Pages i-xxi

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2. Speaking Mathematics Differently

   1. Space: Points of Reference

      Pages 15-26

   2. Space: Static and Dynamic World Views

      Pages 27-39

   3. Quantity: Trapping Numbers in Grammatical Nets

      Pages 41-53

3. Language and Mathematics

   1. The Evidence from Language

      Pages 57-64

   2. Mumbling, Metaphors, & Mindlocks: The Origins of Mathematics

      Pages 65-97

   3. A Never-Ending Braid: the Development of Mathematics

      Pages 99-119

   4. What is Mathematics? Philosophical Comments

      Pages 121-138

4. Implications for Mathematics Education

   1. Learning Mathematics

      Pages 141-159

   2. Multilingual and Indigenous Mathematics Education

      Pages 161-171

5. Back Matter

   Pages 173-188

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Abstract: An outline of the structure of the book is presented, making the argument that the language we use for everyday mathematical ideas presents us with valuable evidence and insights into the nature of mathematics. Keywords: mathematical discourse, nature of mathematics I begin the book by looking at the way people speaking different languages talk about mathematical ideas in their everyday conversation. I end up questioning some common beliefs about mathematics, its history, and its pedagogy. The way we (English speakers) use numbers, the way we give directions, the way we express relationships, are all so commonplace that it is hard to imagine any other way of expressing these ideas. We take for granted the structures of the following sentences: There are four people in the room. The book costs forty-five dollars. Two and three are five. Turn left. Go straight on. The sun rises in the east. A dog is a mammal. He is not my father. I will either go shopping or read my book this afternoon.

• Development of Mathematics
• Implications for Mathematics Education
• Language and Mathematics
• Learning Mathematics
• Multilingual and Indigenous Maths Education
• Origins of Mathematics
• Points of Reference
• Space
• Speaking Mathematic
• mathematics education

• University of Auckland, Auckland, New Zealand

  Bill Barton

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