Chapter 1 Th1is Stu•dy
2.3. Teaching mathematics to second language learners
MacGr,egor and Price (19'99:449) ,investigated language proficiency and algebra .learning .and condude that if learners are proficient in 1language it enables them to "use language as an or,ganizer of knowledge and a tool for reasoning." These authors point out ( 1999:450) that it has been shown "that students who
performed poorly in mathematics tended to have low 'levels of competence in their mother tongues. A level of language proficiency in at least one language is a necessary foundation for academic leaming." These authors investigated three components of metahnguistic awareness - awareness of symbol, syntax, and ambiguity - to ascertain students' success 'in learning the notation of algebra.
They found that very few students with low metalinguistic scores achieved high a,lgebra scores. Hence, it would be necessary to ascertain mother-tongue language proficiency of learners when embarking on ascertaining possible reasons for inadequacies in mathematics when learners are taught mathematics.
Furthermore, learners being taught in a second langu.ag,e would have to cope with the mastery of an additional language before this new language may be used as a composer of iknow,ledge and as an instrument for thinking.
81ishop (1992: 176) refe:rs to research with second-lang,uage :learners where problems of learning mathematics through a second !language are described as
"formidable, and do not just relate to the linguistic aspect." Language is
characterised as be1ing a product of, and a carrier of, cultural and societal
assumptions and history, and ·"what" it describes •can be just as incomprehensible to a non-speaker as "how" it describes. He suggests that bilingual learners
should not ,have to do everything in the "official" 1langua,ge and small-group work allows use of more familiar language.
Laridon (1993:42) points to studies that indicate that thorough bilingualism is fundamental to enhance cognitive ability to cope with the learning of mathematics through a non-mother tongue medium. Furthermore, constructivism relies
heavily on efficient communication among learners and between learners and their teacher. IHe thus considers the language issue fundamental to the
development of reformed learner-centred curr.icuila.
Setati (1999: 179) points out that there are benefits that result from alternating between two or more languages (code-switching) in the mathematics classroom.
This author h1igh'/ighted other studies that have shown that the use of the learners' first language in mathematics teaching and 1learning provides the support needed while the learners cont,inue to develop proficiency in the second language. Setati (1998:40) considers ,that the extensive use of the first language is not really permissibl,e in South African classrooms but it is the "best means available to teachers to foster mathematical understanding ... " She is of the opinion that it is an educational resource and the use of the learners' first language is "also a key to the world and culture of the learners involved. It enables the participants to ma:k,e relevant connections with their lives beyond the school."
Moschkovich (1999) a1Iso suggests strategies for supporting a mathematical discussion among English second langruage learners. A teacher could introduce students to concepts and terms in the famihar language and later conduct
lessons in English. The learners would, however, a'lso need to be surrounded by materials in both 1\anguages. Moschkovich indicates that communication
amongst learners also needs to be fostered so that learners should be grouped in mathematics lessons. Strategies she suggests to support student participation in mathematical discussions included "establishing and modeling consistent norms for discussions, revoicing student contributions, building on what students say and probing what students mean" (Moschkovich 1999:18). She adds that a teacher should not focus primarily on vocabulary development but instead on mathematical content and arguments whilst interpreting, clarifying and rephrasing what students say. She also advocates a discourse approach to learning
mathematics. By this she means considering the different ways of talking about mathematical objects and points of view of mathematical situations that students bring to classroom discussions. According to Moschkovich a discourse approach to learning mathematics can also help to shift the focus of mathematics
instruction for English language learners from language development to mathematical content. So instead of requiring learners to chorus technical, mathematical words, they should rather be given the opportunity to participate in discussions. Students would need to clarify, accept and build on their responses and there should also be revoicing of student statements. After all, in a
mathematics classroom, the mathematics content is more important than the
"correct" pronunciation of the English words of mathematical terminology.
Brodie ( 1991: 17) points to research which showed that students learning
mathematics in a language, which is not their mother tongue, may be faced with difficulties such as:
• differences between ordinary English and mathematical English
• the Greek or Latin roots of mathematical terms
• the lack of accessibility of "logical connectives in the mathematical reasoning process"
• the absence of context in many algebraic problems.
However, these obstacles mentioned by Brodie may not be limited to second
language learners. All these problems may be equally pertinent to first-language
learners of mathematks. She sugg,ests the foilllowing techniques and activities to try to integrate I1ang1uage and mathematks:
• ho1lding mathematics discussions
•• explicitly teaching mathematical 'language ,. deve'loping concepts before naming them
• encouraging students' questions
• asking open-et11ded questions
,. teaching the history ,of mathematics
• encouraging students to verbaHse their sense of pattern and generality before using symbols.
Perhaps not only second-language learners, but a'l:I mathematics learners, would benefit from these suggestions.
Adler (1998:25) interviewed six teachers in thr,ee different urban multilingual contexts 1in South Africa and she found that some mathematics teachers who teach mathematics in a language that is ne.ither the teacher's nor the pupils' first la:nguag,e, consider that this prlaces additiona1I and complex demands on the teaching and ,learning of mathematics. Other teachers believed that English as the language of instruction is not the problem but that mathematics is difficult for everyone, irrespective of their main language. She found that some teachers considered that both the medium of instruction and the fact that mathematics is a difficult subject is of concern in the mathematics classroom. Adler refers to the
"thr·ee-dimensional dynamic at play in the teaching and learning of mathematics in multilingual classrooms". This po.ints to the access to the language of learning, (English), the access to the ,language of mathematics and to "classroom cultural processes". It would appear that teachers who teach mathematics through the medium of Engliish to Zulu speaking learners, with !limited knowledge of English, have a chaUenging situation at hand.