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The common discourse practice in multilingual classrooms is the use of the IRE (Pimm, 1987). Pimm (1987) explains that, in a mathematics classroom, the oral communication tends to be strictly controlled and one of the difficulties with the teaching and learning

of mathematics is the emphasis on a quiet, controlled, individual atmosphere as being appropriate. He further argues that the most familiar situation in a mathematics classroom is that of a teacher initiated question and the response is then evaluated. In this type of communication a teacher retains control of the conversation. Colleman (1996) reports that, in the classroom in Brunei where he conducted his study, it was observed that the class was the orchestration of choral responses (p. 17). Colleman referred to this as the ‘completion chorus phenomenon’. Prophet & Rowell (1993, p. 204) in their study also reported that this phenomenon was common in a junior secondary school in Botswana. They referred to this strategy as ‘the most commonly used question and answer technique’.

Investigating secondary school mathematics teaching strategies in Lesotho, Polaki (1996) reports how the teachers’ strong desire to attain high pass rates in the public examinations led teachers to adopt the largely teacher-centered strategies such as teach, give an example and then learners do the exercise, question-and-answer, and exposition, consolidation and practice. Primary school teachers in Lesotho were also reported to have a preference for ‘teach-example-exercise’ as it was believed to be very effective in preparing learners for the examination (Polaki, 1996). In such situations mathematics teaching and learning are viewed as processes involving nothing more than the attainment of correct answers by using correct procedures. Writing about mathematics elementary classrooms in which the LoLT was the mother tongue, Burton (1992) echoes the same observation. She further observes that lessons are more often characterized by teacher presentations and independent silent work than by group discussion.

Chick (1996) conducted a micro-ethnographic study of a mathematics lesson in Kwa- Zulu Natal classrooms in apartheid RSA. He argues that the ‘rhythmic manner in which ... participants synchronize the chorusing sequences ... serve social rather than academic functions’ (Chick, 1996, p. 30). He outlines these functions on page 36, which include reducing the possibility of loss of face, giving classroom participants a sense of accomplishment, and allowing them to hide their poor command of English, to obscure their inadequate understanding of academic content, and to maintain the facade of

effective learning taking place. Johnson (1992, p. 169) reports that the last three functions are typical of the situation in Hong Kong multilingual classrooms. He reports that teachers resort to code-switching as ‘the best solution to the problems’.

More relevant to my study is that this literature makes explicit claims as to what is considered as the most common teacher-pupil talk in a mathematics classroom. It shows the heavy reliance upon the IRE pattern of interaction. Classrooms need to be places where teachers assist learners to perform/act in many different ways using tools of different kinds, but particularly discourse. The traditional, easily recognized classroom discourse of the IRE variety tells a story in which children are constrained socially, cognitively and linguistically.

Krashen (1982) and Long (1983), report that, even though classroom discussions were being observed in their study, the effectiveness of those classroom discussions, was doubtful because it was the teacher who initiated what is to be discussed, decides who must provide a response, which the teacher either commends or condemns, and decides when to put an end to the discussion. According to Sinclair & Coulthard (1975) such classroom talk is characterized by a predictable sequence, which they call the initiate- response-feedback (IRF) sequence. As Le Roux (1996) noted, the IRF framework, which is very common in many less affluent African classrooms, places the learner in a responding role. The learners’ opportunities for participating productively in the classroom in a multilingual classroom are very limited and constrained.

Apart from the IRE pattern in multilingual classrooms, it is also observed that, this IRE goes together with the procedural discourse. Procedural discourse is where the emphasis in teaching mathematics is aimed at establishing the steps that should be taken to solve a problem with little or no development of concepts. Khisty (1993) observed a pattern of discourse in a bilingual classroom, which she characterized as being procedural. This discourse introduces a learner to traditionally accepted procedures. Even though doing mathematics requires some knowledge of algorithms, it also requires a good deal of conceptual understanding in order to know why and how the steps should be

undertaken. When the emphasis is on following procedures, much of what the teachers say is in the form of directions that learners have to memorize.

Setati (1998) argues that switching between the learner’s home language and English enhanced the quality of mathematical interactions in the classroom. She demonstrates that conceptual discourse (where the emphasis is on knowing why and how the steps should be undertaken) dominated in classrooms where the home language was being used. Thus the home language of the learners is being used to clarify the concepts and so enhance the conceptual understanding of the mathematics. Similarly, in Brunei, use of Malay allowed a greater freedom of expression and provided more meaningful opportunities for real communication which enhanced the conceptual understanding. This reflects that, when teachers in a mathematics classroom do not resort to the use of home languages, in most cases, their lessons are characterized by the IRE pattern of interaction accompanied by a procedural discourse. At this point, one wonders where these patterns of interactions come from. Can there be a link between what the teachers do in a mathematics classroom and what mathematics teacher educators do in a college mathematics classroom?

From the literature discussed in this section, in most multilingual classrooms, mathematics teaching is mostly done through the IRE interaction that focuses on procedural discourse. However, research on effective instruction for learners whose main language is not the LoLT emphasizes the importance of using a variety of methods (discourses) tailored to learners' needs (August & Pease-Alvarez, 1996). August and Pease-Alvarez explain that instructional methods (discourses) selected depend on the level (s) of English language proficiency and available resources, among other factors. Using multiple approaches (discourses), August & Pease-Alvarez (1996) and Reyhner & Davison (1993) argue that teachers can meet the needs of a wider variety of learners. Nystrand & Gamoran (1991, p. 257 - 258) argue that limiting classroom exchanges to the single traditional mode is at the heart of why life in schools is “emotionally flat”, that is, classrooms may be orderly but they are frequently “life less”.

Dufficy (2001) argues that different discourse practices encourage a child to practice constructing joint understandings of the world. Rather than the teacher’s assuming control of knowledge and testing the child’s “fit” to that conception, the options provide for the potential of knowledge sharing, and, crucially, life worlds are shared in classrooms, viewpoints are both expected and supported, class members summon the courage to pose questions, disagree and enter the wider social conversation on the issue, and patterns of discourse might come to be seen for the role they can play, including the IRE. One wonders about the extent to which mathematics teachers in multilingual classrooms can go with procedural discourse, the IRE or learner-centered discourse in order to help learners to learn and understand mathematics. I feel that, although teachers may provide instruction, the instruction should follow the learner's needs and interests rather than being prescribed in a predetermined manner.

Teaching and learning mathematics in multilingual classrooms is indeed complex. Teachers have their own strategies for dealing with the challenges that they meet as discussed above. A question that now needs to be answered is: What forms of classroom discourse practices in teacher training college mathematics classrooms would help the mathematics teachers develop strategies that would help them in dealing with these challenges? Beyond questions about the effectiveness of various classroom discourse practices are questions about who is able to engage in what discourse practices and language processes, when, and where. In other words, what constitutes college discourse practices for multilingual classrooms?

3.4 Conclusion

In the mathematics classrooms, the learners’ home languages can vary a great deal. Mathematics teachers would want to use instructional strategies that respect and build on these differences while helping all learners learn important mathematical concepts and skills. This literature review highlights some instructional approaches that are used by teachers in a mathematics classroom that is multilingual, such as the use of everyday language and integrating the home language of the learners with the LoLT in trying to

accommodate all the learners in the classroom. However, these practices come with a lot of challenges and dilemmas.

In chapter 2, I indicated that teacher training programmes in most African countries do not focus on training the student teachers for multilingual classrooms. In fact, in most African countries where the use of home languages as LoLT are encouraged, teacher training programmes still train their student teachers as before the local languages were introduced. I argued that to improve learners’ performance also entails training teachers for multilingual contexts. From the literature discussed in chapter 3, it shows that there is a gap between what the student teachers go through in a college mathematics classroom and what is experienced when they begin to teach. As indicated before, the question of what is being done in the teacher training programmes to help the mathematics teachers remains a mystery.

The next chapter develops a theoretical framework that will help in explaining the discourse practices of mathematics teacher educators in teacher training colleges in Malawi.

CHAPTER FOUR

THEORETICAL FRAMEWORK FOR INVESTIGATING

DISCOURSE PRACTICES

4.1 Introduction

The purpose of this chapter is to develop a framework that will describe and explain how mathematics teacher educators construct a multilingual classroom and the discourse practices being produced in a college mathematics classroom. It conceptualizes the discourse practices used by the mathematics teacher educators as they prepare student teachers to teach mathematics. The framework developed here is shaped by Critical Discourse Analysis (CDA) drawn from Fairclough (1989, 2001, 2003). This provides the theoretical and conceptual tools to examine the discourse practices of the mathematics teacher educators and how they make available these discourse practices for the student teachers to draw on.

In broad terms, this chapter examines how to study the discourse practices of the mathematics teacher educators and how they support the student teachers develop discourse practices relevant for teaching and learning school mathematics in multilingual classrooms. This chapter is broken down into several sections. The first section discusses what it means for student teachers to develop discourse practices for mathematics teaching. The second section provides an introduction to CDA, followed by its origins, key terms and elements of Fairclough’s CDA. Thereafter, I outline the strategies involved in doing CDA. The last section discusses why CDA is relevant to my study.