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MATHS - LEARNING

TEACHING

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MATHS THROUGH

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INTRODUCTION In this short paper various aspects of the multilingual situation in London are described which have particular implications for mathematics. The SMILE project (Secondary Mathematics Individualised Learning Experiment), The Smile Centre, Middle Row School, Kensal Road, London WI0 5DB., which was started in 1972 has been developing some specific approaches to multilingualism in London Schools and these are also presented. SMILE has become a fully-fledged teaching and learning programme now. A useful starting point is the Inner London Education Authority's Language Census for 1982 (ILEA, 1983). In 1982, 50353 pupils (16% of the school population) used a language other than or in addition to English in the home. 147 different languages were recorded in the 1982 census. Some of these languages have oral traditions only but most of the others have their own scripts, literature and a history of education. Twelve languages had more than 1000 speakers each and between them accounted for 83% of pupils speaking a language other than or in addition to English. These languages were (in order of numbers of speakers): Bengali, Turkish, Gujrati, Spanish, Greek, Urdu, Punjabi, Chinese, Italian, Arabic, French and Portuguese. Many of these languages were concentrated in different divisions of the ILEA. For example, 60% of Bengali speakers were in Division 5, although substantial numbers were also recorded in Divisions 2, 3 and 4. The situation in the ILEA schools gives us an idea of the diversity of language use and language needs in the inner city schools of Britain today. So far, the practice has been of separating second language learners, extracting them from mainstream classes and giving them 'intensive teaching in English'. Thus, a situation of a s u b m e r s i o n p r o g r a m m e is created for these learners. In a submersion programme, the target language is that of the school and the inability of the learners to communicate in the school language is seen as a sign of limited intellectual and academic ability. There may be problems of communication with the teachers because of the lack of knowledge of the child's language on the part of the teacher and different culturally determined expectations of appropriate behaviour. The child's language may be seen as a cause Educational Studies in Mathematics 16 (1985) 215-219. 9 1985 by D. Reidel Publishing Company.

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o f academic deficiency and an impediment to learning the school language. A child's identity, which is intimately connected with home language and culture, is not reinforced or recognised in the school environment. In an immersion programme, where learners from a dominant language group are immersed into a second language learning environment (as is the case with English speaking learners immersed into the French learning environment in Canada) the situation is very different. They may have no competence in the target language but are praised and rewarded for any attempt they may make to use it. The teachers are familiar with the learners' language and culture. Moreover, their language and culture are never devalued at school and by society at large. The target language is introduced in the school after several grades and is taught in the higher grades so its importance is recognised implicitly or explicitly. As Cummins (1976) puts it: In general, what is communicated to children in an immersion programme is their success, whereas in a submersion programme children are often made to feel acutely aware of their failure. It is only recently that schools in Britain are beginning to retain second language learners in the mainstream classes so that they may learn English through peer group support and school subjects. Although this is still a situation of 'submersion', it is an improvement on the 'extraction' method in which second language learners miss out on a range of academic and social experience that takes place in a mainstream school.

THE S M I L E P R O G R A M M E Increasing numbers of schools are beginning to use the SMILE individualised learning programme in Britain. The SMILE programme is used here to illusstrate how strategies can be devised to meet the diverse needs of pupils in a multicultural and multilingual classroom. The programme was devised by maths teachers and understandably, they concentrated on mathematical concepts and assumed a certain level of linguistic competence and cultural familiarity from the learners. At the moment, the SMILE programme which consists o f more than 1300 worksheets and tasks covering a wide range of mathematical activities, is being reviewed so that imbalances from the point o f view of race, gender and class may be put right. From the point of view of language needs, translating instructions for teaching maths, giving elementary maths to second language learners, trying to avoid use of all language and concentrating on the 'language of mathematics' are very simplistic solutions. These solutions may be attractive to some maths teachers who are faced with the very real problem of teaching maths

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to learners with a variety of linguistic diversity and competence but from the point of view of language development, language needs and positive language support, these solutions on their own are of limited use when we consider the diverse needs of different language groups. An individualised learning programme like SMILE can be an immense language and multicultural teaching resource if the following considerations are kept in mind.

C O N S I D E R A T I O N S FROM A M U L T I C U L T U R A L PERSPECTIVE In most cases, second language learners have the conceptual competence in maths but fail to perform satisfactorily because traditional maths teaching and problem solving are invariably mediated through language and culturally determined content. For obvious reasons, second language learners are at a disadvantage from the start. However, the solutions do not lie in either translating worksheets into the first language, eliminating all language or reducing the language to infantile levels. With appropriate modifications, SMILE worksheets provide a challenging and worthwhile area of knowledge which second language learners can tackle. An individualised programme like this can introduce new and relevant language, generate talk in the classroom, provide opportunities for tackling problems in groups or in pairs, teach reading strategies (anticipating, intelligent guessing, reviewing, contextual reading, using pictorial support and cues, and so on) through meaningful work. Moreover, it gives reality to ideas of teacher expectations that are commensurate with the age and conceptual levels of the learners; making use of the knowledge that the second language learners bring with them to the classroom; collaborative learning; and giving learners confidence through setting them work which they know is on level with the work given to their peers in the mainstream classes. A programme like this does not treat second language learners as academically and intellectually inferior but it boosts their confidence and self-respect. T h e SMILE programme is therefore being updated with the following considerations in mind:

Appropriate language. Quite often, second language learners are faced with vocabulary items and sentence constructions in worksheets which make it impossible for them to even attempt to solve a mathematical task. A lot of these hurdles are unnecessary and can be eliminated by using language that is appropriate for both first and second language learners. Content review. Some vocabulary items may be obscure, archaic or out of

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the ordinary. Such items can be replaced without great loss to the overall language content of an individualised learning network. Vocabulary support. Items of vocabulary that may present problems to second language learners can be explained at the back ofworksheets. At the moment, most worksheets are blank at the back. It is hoped that a tradition will be established in the SMILE network in which all learners can expect to find supporting explanations or picture cues on the backs of worksheets. Pictorial support. Many worksheets can be made more interesting and also aid learners to understand a message with help of pictures and other similar cues. The backs of worksheets can also be used for this type of support. Layout. Some worksheets have information clutter, instructions in language and format that the mainstream learners may be familiar with but present problems to second language learners, or pictures that are not suitable from the point of view of representation of culture, gender or social class. Assumptions of cultural familiarity. The suggestion here is not to eliminate all culturally determined concepts but to include ideas and concepts with which second language learners may be familiar. This would lead to a genuine exchange of cultures between all learners in the school system. Second language learners have to learn about the British and European cultures but other learners in the school system also have to learn about the universality of maths. A linguistically and culturally suitable learning programme, which recognises the needs of the learners at various levels of linguistic and conceptual stages, the wealth of knowledge they bring to school, and the contribution that other cultures (including their own) have made to the development of science and mathematics would make learning a more meaningful, relevant, valid and supportive process. An adapted SMILE programme has been tried out at a language centre in Division 5 of the ILEA in Britain. The majority of the learners were speakers of Bengali and were of Bangladeshi origin. With their limited English they tackled a range of mathematical tasks with enthusiasm. The learners knew they were doing maths that their peers were doing in the mainstream school. The mathematically gifted learners progressed fast and were able to take leading roles in explaining tasks to their peers in the mainstream schools a remarkable reversal in their normal role! Finally, it should be noted here that one cannot ignore the very unhealthy racial climate that exists in many British schools today. If this factor is lost sight of, ideas of peer group support and classroom interaction would become very unrealistic. Teachers of SMILE mathematics have produced the SMILE Anti-racist Policy which has direct relevance to developments in multicultural teaching content and the needs of the second language learners in the mainstream schools in Britain.

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As teachers we aim to encourage an active multi-cultural teaching approach. Against what background do we do this? We live in a racist society. One result of colonialism and imperialism has been the suppression of the culture and science of the Third World peoples and the creation of the myth of 'European Science' as a seamless body of truth. In this way it promotes the inferiority of black people and encourages white chauvinism. Too much of the way we teach mathematics shares in this. We do little to show that mathematics is the product of the thinking and achievements of all the people in the world. We must not allow the universality of mathematics to be lost. Anti-racist mathematics teaching, therefore, must mean at a minimum: (1) Teaching mathematics with a strong emphasis on its historical development, showing how at each stage mathematical developments have arisen as the response of different peoples to the problems they had to solve - be they Indian astronomers, Egyptian farmers, Spanish navigators or whoever. (2) Deliberately seeking out knowledge of the mathematics of the Third World peoples and making it easily accessible to all children learning mathematics. (3) Making deliberate use of the different mathematical methods brought by children to the classroom - e.g. different counting systems. (4) Critically assessing the content of present mathematics from the point of view of its relevance to living in a multi-cultural society. Such an approach may involve a number of different methods - ease study materials (e.g., development of number systems), or study of particular civilisations - or it may require the deliberate inclusion of more historical background material with existing activities. So far as possible, such work should be linked to other progressive cross-curricular material. The recruitment of a more culturally representative teaching staff will contribute immeasurably to such work. Whatever the method, the aim is to promote the dignity of all peoples and to understand that mathematics has a vital role to play in this.

REFERENCES Cummins J: 1976, The Influence of Bilingualism on Cognitive Growth: A Synthesis of Research b~ndings and Explanatory Hypotheses, Educational Research Centre, Saint Patrick's College, Dublin, Ireland. ILEA; 1983, 1983 Language Census, Research and Statistics 916/83, Inner London Education Authority, London, 1983.

Centre for Multi-Cultural Education, University o f London Institute o f Education, 20 Bedford Way, London WC1H OAL, England

SAFDER ALLADINA