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The role that language plays in the teaching and learning of mathematics is one of some of the important debates in the current literature in mathematics education. In this chapter, I review literatures related to this study, giving particular attention to the manner in which teachers engage students in the exploration of mathematical concepts and procedures, in order to explore different and existing kinds of patterns of interaction observed in multilingual mathematics classroom in South Africa.
Aspects reviewed include the following sub-headings: Linguistic situation in South Africa; Teaching and learning mathematics in multilingual classrooms in South Africa; Does language impact teaching and learning of mathematics? And the role of the teacher and Learner participation in classroom discourse.
Linguistic situation in South Africa
Post-apartheid South Africa's new constitution of 1993/1996 embraced language as a human right and multilingualism as a national resource, raising major African languages to national official status alongside, English and Afrikaans (Hornberger & Vaish, 2009). This has led to multicultural student populations in classrooms, schools and universities nationwide. The Language in education policy that was adopted in 1997 recognises all eleven official languages. According to this policy, learners have the right to study in any of the official languages of their choice (Department of Education, 1997). According to Hornberger & Vaish (2009), South African scholars have documented ideologies favouring English in Black African communities of South Africa. She further claims that Zulu, Xhosa or other Black parental demands for English-medium instruction for their children are fuelled by the perception and reality of English as language of power; parents are simultaneously drawn to English by it hegemonic status and away from mother tongue education by a deep suspicion born of apartheid. I have seen in my experience as a learner and a teacher, parents taking away their kids from townships schools to former Model C schools where English is the most dominant language. The study done by Setati (2008), revealed that learners and teachers preferred English as the language of learning and teaching (LolT) and that learner's and teacher's choice of language was informed by the fact that English provides access to social goods such as higher education, employment, etc.
Teaching and learning mathematics in multilingual classrooms in South Africa
Previous and current studies on teaching and leaning in multilingual classrooms have indicated that teaching and learning in multilingual classroom is very complex. Barwell (2009) describes multilingual classrooms by saying these classrooms are considered to be multilingual if two of more languages are used overtly in the conduct of classroom business. And mathematics classrooms are also considered to be multilingual if students use two or more languages to do mathematics.
There is a continuing debate regarding which language should be used for teaching mathematics in multilingual classrooms in which neither the teachers' nor the learners' main language is English which is the LoLT in their schools (Setati, Molefe & Langa, 2008). This is typical situation in South African classrooms; teachers and learners come to classrooms with different levels of proficiency in two or more languages other than English and yet are not proficient in English. The research done by Setati, Chitera & Essien (2009) shows that teachers in these classrooms face a major task of having to teach mathematics and English at the same time, while learners have to cope with learning mathematics, as a discipline of knowledge and also as a way of communicating, in English, a language that they are still learning. This research also claims that this places additional demands on mathematics teachers in multilingual classrooms and their learners who learn mathematics in a language that is not their home language.
Does language impact teaching and learning of mathematics?
The importance and the impact of language in learning and teaching of mathematics has long been acknowledged by the research literature (Howie 2002, 2003, 2004; Boulet 2007; Essien 2010; Barwell 2009; Setati 2008). Based on her analyses of the poor performance of South African learners in the mathematics component of the Third International Mathematics and Science Study (TIMSS), Howie (2002, 2003, 2004) suggested that the key factor responsible for the poor performance by South African learners was due to the low proficiency in English language and she suggested a solution to this could only be to develop the learners English language proficiency. Furthermore she argues that pupils who speak the language that is used in assessments more frequently, are likely to attain higher scores on mathematics. And if their language proficiency is higher, the learners are likely also to attain higher scores in Mathematics. Say more
The role of the teacher and Learner participation in classroom discourse
Current curriculum initiatives in mathematics call for the development of classroom communities that take communication about mathematics as a central focus. In these proposals, mathematical discourse involving explanation, argumentation, and defence of mathematical ideas becomes a defining feature of quality classroom experience (Anthony & Walshaw, 2008).
According to Boulet (2007) researchers in mathematics education agree and encourage teachers to involve learners in mathematical discussions, as communication is essential to the learning of mathematics. Specifically from the perspective of mathematics learning, by articulating the principles, concepts and rationale behind the steps of a particular problem solution, students have the opportunity to reinforce and deepen their understanding of higher-level knowledge structures in mathematical content.
Furthermore, Moschokvich (1999) maintains that the important functions of productive classroom are uncovering the mathematical content in student contribution and bringing different ways of talking and point of views into contact. She further explains that in many mathematics classrooms, students are no longer primarily grappling with acquiring technical vocabulary, developing comprehension skills to read and understand mathematics textbooks or solving standard word problems. But students are now expected to participate in both verbal and written practice such as explaining solution process, describing conjectures, proving conclusions and presenting arguments.
However, there are difficulties or drawbacks that can make it difficult for communication to run smoothly in classrooms. This can definitely prevent learners from accessing important aspects and concepts of mathematics or voicing their ideas. Most of our learners are not speaking English as their first language, whereas English is used as a medium of instruction in our schools, therefore a focus on correction of vocabulary or grammatical errors in what students say and the variety of ways that students who are learning English do can become problematic in learners' mathematics acquisition.
Now, the question is what do teachers do or can do in situations like this, to ensure and encourage learner participation in classroom?
New curricula demands a lot from teachers. Worldwide, policy makers are placing increasing demands on schools and their teachers to use effective research-informed practices. The study done by Essien (2010) reveals that, in any classroom, the teacher plays a key role in the management of the communication in the classroom. He further argues that well-structured questions (unlike procedural questions requiring procedural answers) can provoke extended dialogue in the classroom, thereby creating opportunity for meaningful participation by learners. Furthermore, the study shows that the teacher's ability to draw on learners' linguistic resource: one of which is structuring questions to allow learners to sufficiently express their thinking, is therefore important in creating a classroom environment where learners are effectively participating in the creation of and fostering of their own knowledge. Walshaw & Anthony (2009) maintain this by arguing that effective teachers facilitate classroom dialogue that is focused towards mathematical argumentation. They elaborate more on this by saying that students need to be taught how to articulate sound mathematical explanations and how to justify their solutions. Furthermore, encouraging the use of oral, written and concrete representation, effective teachers model the process of explaining and justifying, guiding students into mathematical conventions.
In this study, I use the work of Jina and Bridie (2008) as a theoretical framework to take the work on patterns of interaction observed in South African classrooms further by explaining learner participation and teacher-learner interaction in classroom discourse. The motive behind the choice of this theoretical framework is that this study was done in South African schools on the topic: Teacher questions and patterns of interactions in the new and old curriculum. The study reveals that two patterns of interaction emerged, namely, "funnelling" and "leading through a method".
This study also expanded more on teacher questioning and how teacher questions can support learners' thinking. Chin (2006) supports this argument by saying that questioning is a prominent feature of classroom talk. Teacher questioning should be in such a way that elicit what learners think, to encourage them to elaborate on their previous answers and ideas, to help learners construct conceptual knowledge. Thus, questioning is used to diagnose and extend learners' ideas and to scaffold learners' thinking.
Campbell & Erdogan (2008) claim that teacher questions can disrupt the flow of what is going on in the learners' mind, so that the learners' attention can be focused on instructional objectives. However, they claim that if used appropriately, teachers' questions can engage learners in the vicinity of instructional objectives, help move instructional objects to the forefront of students' attention, and promote learner translation and processing of instructional objectives.
However, the deficiency of this study is that it does not take the forms of listening the teacher uses during classroom discourse. As I have discussed in chapter 1 of this study that, Davies (1997) outlines three forms of listening, and further argues that listening is a very powerful tool and should be used to foster teaching and learning of mathematics. Listening to others' explanations gives learners opportunities to develop their own understandings. By listening to others, learners can become aware of alternative perspectives and strategies.
In this study I have discussed the difficulties of learning and teaching mathematics in multilingual classrooms.
As Setati and Adler (2001) claim:
There are numerous, distinct mathematical discourses that require navigation at the same time. Moving between language and discourses in moments of practice is significant challenge for mathematics education research and practice. These arise out of the South African context and have specific relevance in the current educational debates in South Africa. Multilingual mathematics classrooms are, however, an increasing urban phenomenon in many other counries. (p.244)
Little is known about how educators experience and implement a new curriculum and instruction in contrast to what they used to know and apply. It remains uncertain what kinds of teacher knowledge are necessary to support and facilitate learning mathematics in a setting where main language of the teacher and pupils differs and where the language of instruction and teaching methods makes it difficult for mathematical discourses that promote conceptual understanding.