Discourse, Mathematics and Mathematics Education

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DISCOURSE, MATHEMATICS AND MATHEMATICS EDUCATION

INTRODUCTION

Mathematics has long had a curious relationship with language. For some, mathematics is a language; for others mathematics is beyond language, a mode of thinking that escapes the ambiguities of human beings or the languages they use. The teaching and learning of mathematics is, however, a process that, perhaps more than any other subject, depends on language. Abstract mathematical ideas are brought into being through classroom talk or writing. It is perhaps for this reason that mathematics teachers and educators have always been interested in the language of mathematics and the role of language in the teaching and learning of mathematics. In this chapter, I give an overview of some of the key issues, ideas and findings of research in this area. I discuss, in particular, research on mathematical discourse or mathematics classroom discourse, by which I mean research that focuses on language in use in social context in mathematics or mathematics classrooms. Much of the work I refer to draws explicitly on theories of discourse. Some of these theories merge with theories of learning or cognition, however, so the boundaries are not clearly defined. In general, then, I will refer to research that has a central concern with the social, ideological or political nature and use of language as part of the process of doing, teaching and learning mathematics. E A R LY D E V E L O P M E N T S

Research on discourse in mathematics and mathematics education dates back little more than 25 years. Austin and Howson’s (1979) survey of research on ‘Language and mathematical education’, for example, contains little that could be said to concern discourse in the sense I have indicated earlier. There was a recognition, however, that mathematics involves a distinctive form of language use. Halliday (1978), for example, defined the mathematics register as: the meanings that belong to the language of mathematics (the mathematical use of natural language, that is: not mathematics itself ), and that a language must express if it is being used for mathematical purposes ( p. 195). M. Martin-Jones, A. M. de Mejia and N. H. Hornberger (eds), Encyclopedia of Language and Education, 2nd Edition, Volume 3: Discourse and Education, 317–328. #2008 Springer Science+Business Media LLC.

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R I C H A R D B A RW E L L

This definition maintains a separation between language and mathematics, or rather, between linguistic meaning and mathematical meaning. Halliday makes a number of important observations about mathematics registers. First, all languages are equally capable of developing mathematics registers, although there is variation in the extent to which this has happened. Second, different languages, through their semantic structure, stress some meanings more than others. The mathematics registers of different languages, therefore, stress different mathematical meanings. This may mean that students of mathematics in different languages develop differing awareness of a given aspect of mathema

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