Our findings suggest that both translanguaging moves and conversion moves that go beyond simple restatement are particularly important for broadening access to math- ematical ideas. However, in thinking about the implications for policy and prac- tice of this finding, key contextual factors need to be taken into account. Firstly, we acknowledge that richer networks are possible than seen in the translanguaging excerpts presented in this chapter. Specifically, there is limited inclusion of diagram- matic or concrete resources that can help to illustrate relative magnitudes across place values in the base ten system, for example Dienes blocks or place value coun- ters. This absence though, is typical of the limited range of resources that continues to be the norm in many South African classrooms as discussed in Spaull’s (2013) work. In our work in schools, we have seen that 100-square type number charts are the most commonly available representation relating to base ten structure. Dienes blocks and place value cards are much rarer. The paucity of resources makes the move between oral and symbolic representations more common in such contexts than in more advantaged contexts where the availability of a range of resources can commonly be taken for granted.
The second point follows, in many ways, from the first. With limited access to physical resources, the burden on language to do the explanatory work, to incorpo- rate reasoning and justification, is greater. This makes small and subtle differences in the ways in which moves between languages and between mathematical registers are used. This chapter shows that in mathematics classrooms, translanguaging and translation moves cannot be placed on the same level when debating the access to meaning-making. Translanguaging moves involve deeper understanding than transla- tion as translanguaging moves go beyond substitution of words or phrases. Translan- guaging involves more intentional and/or more elaborated processing and meaning- making as shown in the four classroom examples presented earlier in this chapter.
This observation is supported by the work of García and Wei (2014) who argue that translanguaging carries greater potential for meaning-making.
We have found these insights useful to share in our work in pre- and in-service teacher education. The kinds of contrastive examples that we have presented in this paper provide useful exemplars for discussion in pre-service teacher education. We are in the process of adding in excerpts that include the richer networks of resources such as place value cards which are relatively easy and cheap to create alongside translanguaging in our pre-service teacher education programme materials. These contrastive exemplars are intended to help teachers to think about their own instruc- tion in ways that allow a focus on language use in classrooms in instructional terms, as well as in political terms. Simultaneously, it helps us to address some of the gaps identified in primary teachers’ mathematical content and pedagogic content knowl- edge. Our hope is that through this kind of feeding into teacher education, we can support student teachers in the teaching of mathematics in the early grades to adopt and use translanguaging moves as a resource that enables a broadened and increased access to fundamental mathematics ideas. We are feeding in our examples of the
range of mathematical work that is possible in the context of translanguaging into discussions with other universities and with curriculum writers and policy makers.
Through this, we hope to feed into policy development that can include attention to and enhance teachers’ use of translanguaging approaches and multimodal languaging in the Language and Education policy in ways that deliver better on the promise of language as a resource in multilingual mathematics classrooms that can support more equitable attainment outcomes in the subject.
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Manono Pooholds a Ph.D. from the University of the Witwatersrand. Her Ph.D. focused on Primary Mathematics Education. She trained as a Foundation Phase teacher and practiced teaching for five years prior to undertaking tertiary education in Bachelor of Arts with Education as a major.
She holds a postgraduate degree in Personal and Professional Leadership and a Master’s degree in educational management which she obtained from the University of Johannesburg, South Africa.
She has coauthored some articles with colleagues within the Wits School of Education and has published a book chapter on her own.
Hamsa Venkatis a Professor of Mathematics Education and holds the South African Numeracy Chair at the University of the Witwatersrand in Johannesburg—now in its second 5-year phase of research and development in primary mathematics. She leads a team of academics and post- doctoral and postgraduate students, all involved in studying and improving primary mathematics teaching and learning in government primary schools serving disadvantaged students. Her work in South Africa has been in the areas of Mathematical Literacy and Primary Mathematics. Prior to this, Hamsa was based in England, working initially as a high-school mathematics teacher in London comprehensive schools, before moving into teacher education at the Institute of Educa- tion and research in mathematics education at King’s College London. She has published widely, across articles and books, and her research work continues to feed into provincial and national policy initiatives.