The Language of Mathematics: Telling Mathematical Tales

ISBN-13: 9780387728582 / Angielski / Twarda / 2007 / 186 str.

Barton, Bill

Opis

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.

Spis treści

Speaking Mathematics Differently.- Space: Points of Reference.- Space: Static and Dynamic World Views.- Quantity: Trapping Numbers in Grammatical Nets.- Language and Mathematics.- The Evidence from Language.- Mumbling, Metaphors, & Mindlocks: The Origins of Mathematics.- A Never-Ending Braid: the Development of Mathematics.- What is Mathematics? Philosophical Comments.- Implications for Mathematics Education.- Learning Mathematics.- Multilingual and Indigenous Mathematics Education.

Blurb

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.