Articulo Ingles

Journal for Research in Mathematics Education

2005, Vol. 36, No. 5, 447–466

Teaching Mathematics in a Primary

Multilingual Classroom

Mamokgethi Setati

University of the Witwatersrand

This article explores the complex relationship between language and mathematics education in multilingual settings by presenting an analysis of one lesson from a multi- lingual primary mathematics classroom in South Africa taught by an appropriately qualified and experienced teacher. English emerged as a dominant language in this classroom, and this dominance was accompanied by procedural mathematics discourse. The learners’ home language functioned mainly as the language of soli- darity, whereas English functioned as the language of mathematics, authority, and assessment. The article argues for the need to recognize and acknowledge the polit- ical role of language when conducting research into the relationship between language and mathematics education in multilingual classrooms. The article draws implications for making critical, influential decisions about curriculum, assessment, and teacher education.

Key words: Bilingual issues; Discourse analysis; Elementary, K–8; English language learners; Language and mathematics; Multiculturalism; Race/ethnicity/SES; Teaching (role, style, methods)

This article explores the complex relationship between language and the teaching of mathematics in multilingual settings where the teacher shares a home language with the learners and the home language is not the language of learning and teaching (LoLT).1 The complex relationship between multilingualism and mathematics learning has long been recognized and has been described in detail elsewhere (e.g., Adler, 2001; Clarkson, 1991; Dawe, 1983; Setati, 1998; Setati & Adler, 2001; Stephens, Waywood, Clarke, & Izard, 1993; Zepp, 1989). All have argued that multilingualism per se does not impede mathematics learning.

1 I use the term language of learning and teaching (LoLT) rather than medium of instruction or language of instruction to refer to the language used for both learning and teaching. It is also used to refer to the language(s) used in textbooks and other classroom materials and the language(s) used for examination papers and answers across the curriculum.

The time to develop this article was supported by the National Research Foundation (NRF) under Grant Number GUN 2053954. Any ideas expressed are, however, those of the author and therefore the NRF does not accept any liability. My thanks to Kuki and her Grade 4 class for allowing me to learn from and with them.

Copyright © 2005 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.

This material may not be copied or distributed electronically or in any other format without written permission from NCTM.

Part of learning mathematics is acquiring fluency in the language of mathematics, which includes words; phrases; symbols; abbreviations; and ways of speaking, reading, writing, and arguing that are specific to mathematics. Learning to commu- nicate mathematically is now generally seen by research (Adler, 2001; Moschkovich, 1996, 1999, 2002; Pimm, 1987, 1991; Sfard, Nesher, Streefland, Cobb, & Mason, 1998), curriculum (Department of Education, 1996, 1997b) and the NCTM Standards documents (1991, 2000) as a central aspect of what it means to learn school mathematics. This focus on communicating mathematically, together with encouraging multilingualism, as the language-in-education policy in South Africa stipulates, raises concerns about the use of language(s) in multilingual class- rooms and about how mathematics teachers find a balance between making language choices in their multilingual classrooms, encouraging multilingualism, and initi- ating learners into ways of communicating mathematically.

Previously I have argued that, although the language-in-education policy of South Africa, which recognizes 11 official languages, is intended to address the over- valuing of English and the undervaluing of African languages, in practice English still dominates (Setati, 2002; Setati & Adler, 2001; Setati, Adler, Reed, & Bapoo,

2002). Although English is the home language of a minority, it is a dominant symbolic resource in the linguistic market (Bourdieu, 1991) in South Africa. The linguistic market is embodied by and enacted in the many key situations (e.g., educa- tional settings, job situations) in which symbolic resources, like certain types of linguistic skills, are demanded of social actors if they want to gain access to valu- able social, educational, and eventually material resources (Bourdieu, 1991). This article draws on a larger research project that focused on language practices in multi- lingual primary mathematics classrooms in South Africa and was guided by the following research questions: What language practices do teachers in multilingual primary mathematics classrooms use? Which languages do teachers use for what purposes? What kinds of mathematical Discourses are privileged? How do teachers use these languages and mathematical Discourses?

Most research on mathematics education in bi/multilingual classrooms has argued for the use of the learners’ home language(s) as resources for learning and teaching mathematics (e.g., Adendorff, 1993; Adler, 1998, 2001; Arthur, 1994; Khisty,

1995; Merritt, Cleghorn, Abagi, & Bunyi, 1992; Moschkovich, 1996, 1999, 2002; Ncedo, Peires, & Morar, 2002; Rakgokong, 1994; Setati, 1998; Setati & Adler, 2001; Setati et al., 2002). These authors have argued for the use of the learners’ home language(s) in learning and teaching mathematics as a necessary support as learners seek to develop proficiency in both the LoLT (e.g., English) and the learning of mathematics. Such studies have been framed by a conception of mediated learning, wherein language is seen as a tool for thinking and communicating. In this article, language is also seen as always “political,” having implications for how social goods are or ought to be distributed.

WHAT DO I MEAN BY DISCOURSE?

The notion of Discourse is used in this article as defined by Gee (1996, 1999). According to Gee (1999, p. 7), “discourse” using a lowercase “d” refers to how language is used “on site” to enact activities and identities. However, “Discourse” using an uppercase “D” involves much more than words:

A Discourse is a socially accepted association among ways of using language, other symbolic expressions, and ‘artifacts’, of thinking, feeling, believing, valuing and acting that can be used to identify oneself as a member of a socially meaningful group or ‘social network’, or to signal (that one is playing) a socially meaningful ‘role’. (Gee,

1996, p. 131)

In her recent work, Moschkovich (2002) drew on Gee (1996, 1999) to offer an insightful discussion on mathematical Discourses. She highlights the fact that, like Discourses in other contexts, mathematical Discourses create “social positions” (perspectives) from which learners are “invited” to speak, listen, act, read, write, think, feel, believe, and value. Furthermore, as Moschkovich (2002) emphasized, “there is no one mathematical Discourse” (p.199). There is a range of mathemat- ical Discourses, and the ability to communicate mathematically requires fluency in this range.

Two categories of mathematical Discourses emerged in the study discussed in this article: procedural and conceptual Discourses. Procedural Discourses are Discourses that focus on the procedural steps taken to solve a problem. Procedural Discourse is consistent with what Thompson, Philipp, Thompson, and Boyd (1994, p. 86) described as a computational orientation in teaching, where mathematics is viewed as composed of procedural steps and doing mathematics as computing or following a set of procedures in the absence of any reason for the computation.

Conceptual Discourses are Discourses in which the reasons for calculating in particular ways and using particular procedures to solve a mathematical problem become explicit topics of conversations (Sfard et al., 1998, p. 46). In conceptual Discourses, learners articulate, share, discuss, reflect upon, and refine their under- standing of the mathematics that is the focus of the interaction. It is the responsi- bility of the teacher to create a classroom environment in which these kinds of inter- actions are possible—classroom situations where conceptual Discourse is not only encouraged but valued. This Discourse is recognizable in reform classrooms. As Thompson et al. (1994) argued, to create a conceptual orientation, the teacher must reflect long and deeply on her goals for, and images of, mathematics and mathe- matics teaching. To be able to communicate mathematically, a learner needs to be able to engage in both procedural and conceptual Discourses.

In addition to these mathematical Discourses, there are also nonmathematical Discourses at play during mathematics teaching. Regulatory and contextual Discourses are the two nonmathematical Discourses that emerged from the data discussed in this article. Regulatory Discourse is mainly used by the teacher and refers to interactions that focus on regulating the learners’ behavior. This Discourse is used mainly to call for the learners’ attention, to request them to listen to the

teacher or to each other or to get them ready for a specific task during the lesson. Contextual Discourse focuses

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