Fig. 7 Percentage correct Grade 3 and 4 student translations: English-Zulu
The variation and accuracy of the translations give insight into teachers and students knowledge of what could be called the ‘standardised’ vocabulary of patterns.
The finding is clear—teachers’ knowledge of the vocabulary is far from perfect and student knowledge is extremely poor (see Figs.6 and7). Overall (more so in the student sample) many variations in spelling and several synonyms were found. The synonyms (especially in the indigenous languages) should be incorporated into the Department of Arts and Culture (DAC) dictionary, since translators tend to restrict themselves to using the words in the DAC dictionary. The translation activity revealed issues could arise in regard to language use, especially in written texts if the texts use only the more ‘pure’ word forms recommended in the DAC. For example, the DAC recommended word for number pattern is the more formalpopegopalowhile the less formal word for pattern viz. diphetheneng tse tsa dipalowhich is used in student print material might be more familiar to some. Our findings support that the DAC list is not adequate as a standard for translations of school learning material particularly since many dialects exist which do not all use the same words (Mojela, 2008). All possible alternatives for words should be included in general word lists so that they are more representative of the spoken languages. This and other research in South Africa indicates that language is not highly standardised (Mojela, 2008;
Bokamba,2014) although the CAPS policy has assumed that it is.
multilingual population they serve. As evidenced in the findings there is a poor relationship between teacher home language and LoLT in the sample schools and the correspondence between teacher and student home language was even lower.
This means that some teachers are teaching and many students are learning in a language that is not their main language. The literature has shown that in multilingual contexts, opportunities that provide for multilingual learning promote understanding (Makalela,2015; Planas,2018). Hence we argue that the purist ideology driving the CAPS policy which maintains that one exclusive LoLT should be used in a class may favour language use that could compromise mathematics learning and teaching since given the context in South African schools, particularly in urban areas, this would result in a LoLT that does not align with the student population.
There are two key findings that mitigate against meaningful implementation of CAPS policy. The first is that the LoLTs of the sample schools do not correspond well with the home languages of the teachers and students and the second is the evidence of a poor working knowledge of the mathematical vocabulary, more so in the two indigenous languages (IsiZulu and Setswana) that were the focus of this study. This chapter used a three-part dataset to shed light on the extent to which multilingualism is being enacted in schools in a context where it should be plain to see but findings showed teachers and students using more pure language than mixed languages. This is not surprising in the context of a policy that promotes the use of pure language. Added to this, we found that language use did not align well with the chosen LoLTs of the schools. What was seen is that English is being used in favour of other languages, most likely because there is a commonly held belief that English should be used for the teaching of mathematics (Setati,2008). Although English is the home language of a very small percentage of the participants in the study it was reported as a second (or other) spoken language by 74% of the teachers and 68% of the students in the sample. Since language proficiency in any one of the languages is not guaranteed, as was shown in the translation activity, the use of a single language (the current endorsement of the South African CAPS) for the teaching of mathematics might not offer the optimal learning opportunity. This study shows that in multilingual contexts there is evidence of speakers drawing on more than one language of expression (even when they are not meant to be doing so) and translanguaging (García & Wei,2014) for the learning and teaching of mathematics needs to be considered. Most teachers in this study reported that they speak at least four languages and it is common practice for teachers to teach in a language that is not their HL. In such a rich multilingual context, teachers and students should be allowed to draw on their multilingual resources and the evidence found in this study shows that they already do, despite policy constraints.
If teachers’ language use could be used to infer their language ideologies, in rela- tion to flexibility of language use, there is evidence of both monoglossic (purist) and/or heteroglossic (pluralist) ideologies. Purist language use requires standardisa- tion of the lexicon and broad knowledge and use of this lexicon. The main arguments on the two sides of the purist/pluralist debate are: purists would say that there is a need to know all the precise words and definitions in order for conceptual discussions to be meaningful while pluralists would say that language mixing is acceptable as
long as there are meaning and understanding of concepts under discussion. The study suggests that standardisation of terminology is not in place and this would indicate that the implementation of a purist monoglossic policy could be problematic.
Although this research clearly paints the picture of language use in multilingual schools, and the tragedy of the policy/practice mismatch, it did not investigate the impact of language use in these schools. Further research in this area is needed in order to inform best practices for mathematics teaching at the FP level in multilingual contexts.
References
Bamgbose, A. (1999). African language development and language planning—Language and development in Africa.Social Dynamics, 25(1), 13–30.
Barwell, R. (2018). From language as a resource to sources of meaning in multilingual mathematics classrooms.Journal of Mathematical Behavior, 50,155–168.
Barwell, R., Barton, B., & Setati, M. (2007). Multilingual issues in mathematics education:
Introduction.Educational Studies in Mathematics, 64,113–119.
Bokamba, E. G. (2014). The politics of language planning in Africa: Critical choices for the 21st century. InDiscrimination through language in Africa?: Perspectives on the Namibian experience (pp. 11–27). De Gruyter.https://doi.org/10.1515/9783110906677.11.
Cai, J., Kaiser, G., Perry, B., & Wong, N.-Y. (Eds.). (2009).Effective mathematics teaching from teachers’ perspectives. Rotterdam: Sense Publ.
Clarkson, P. (2016). The intertwining of politics and mathematics teaching in Papua New Guinea. In A. Anjum & P. Clarkson (Eds.),Teaching and learning mathematics in multilingual classrooms:
Issues for policy, practice and teacher education(pp. 25–39). Rotterdam: Sense Publishers.
Cummins, J. (1979). Linguistic interdependence and the educational development of bilingual children.Review of Educational Research, 49(2), 222–251.
Department of Basic Education. (2010).The status of the language of learning and teaching (LoLT) in South African public schools: A quantitative review. DBE: Pretoria.
Department of Basic Education. (2014).Report on the annual national assessment of 2014 grades 1 to 6 & 9. Pretoria: DBE.
Department of Education. (1997).Language in education policy 14 July 1997.http://education.
pwv.gov.za/policies%20and%20Reports/Policies/Language.
Essien, A. (2018). The role of language in the teaching and learning of early grade Mathematics:
An 11-year account of research in Kenya, Malawi and South Africa.African Journal of Research in Mathematics, Science and Technology Education, 48–59.https://doi.org/10.1080/18117295.
2018.1434453.
García, O., & Wei, L. (2014). Translanguaging: Language, bilingualism and education.
Basingstoke, Hampshire; New York: Palgrave Macmillan.
Heugh, K. (2014). Dreams and realities: Developing countries and the English language.Current Issues in Language Planning, 15(1), 110–116.
Kajoro, P. (2016). Transition of the medium of instruction from English to Kiswahili in Tanzanian primary schools. In A. Anjum & P. Clarkson (Eds.),Teaching and learning mathematics in multi- lingual classrooms: Issues for policy, practice and teacher education(pp. 25–39). Rotterdam:
Sense Publishers.
Kroskrity, P. V. (2004). Language ieologies. In A. Duranti (Ed.), A companion to linguistic anthropology(pp. 496–515). Malden: Blackwell.
Lafon, M., & Webb, V. (2010). The standardisation of African languages. Michel Lafon; Vic Webb.
IFAS, pp. 141, 2008, Nouveaux Cahiers de l’Ifas, AureliaWa Kabwe Segatti. <halshs-00449090>.
Lyon, J. (1996).Becoming bilingual: Language acquisition in a bilingual community. Clevedon:
Multilingual Matters.
Macnamara, J. (1977). Language learning and thought: Perspectives in neurolinguistics and psycholinguistics economic theory and mathematical economics. New York: New York Academic Press.
Makalela, L. (2015). Translanguaging as a vehicle for epistemic access: Cases for reading comprehension and multilingual interactions.Per Linguam, 31(1), 15.https://doi.org/10.5785/
31-1-628.
Mojela, V. M. (2008). Standardization or stigmatization? Challenges confronting lexicography and terminography in Sesotho sa Leboa*.Lexikos18(AFRILEX-reeks/series), 119–130.
Phakeng, M. (2017).Mathematics education and language diversity: From language-as-problem to language-as-resource.Keynote address at the NSTF (National Science and Technology Forum) discussion on multilingualism in STEM subjects, Emperor’s Palace, Benoni.
Pimm, D. (1981). Mathematics? I speak it fluently. In A. Floyd (Ed.),Developing mathematical thinking. Workington: Addison Wesley.
Planas, N. (2018). Language as resource: A key notion for understanding the complexity of math- ematics learning.Educational Studies in Mathematics, 98,215–229.https://doi.org/10.1007/s10 649-018-9810-y.
Prediger, S., Kuzu, T., Schüler-Meyer, A., & Wagner, J. (2019). One mind, two languages—Separate conceptualisations? A case study of students’ bilingual modes for dealing with language-related conceptualisations of fractions.Research in Mathematics Education, 21(2), 188–207.https://doi.
org/10.1080/14794802.2019.1602561.
Robertson, S., & Graven, M. (2018). Exploratory mathematics talk in a second language: A soci- olinguistic perspective.Educational Studies in Mathematics, Online.https://doi.org/10.1007/s10 649-018-9840-5.
Ryan, U., & Parra, A. (2019). Epistemological aspects of multilingualism in mathematics education:
An inferentialist approach.Research in Mathematics Education, 21(2), 152–167.
Sapire, I. (2017). Researching multilingualism in early grade mathematics: Survey—Technical report. Johannesburg: University of the Witwatersrand.
Sapire, I. (2018).Researching multilingualism in early grade mathematics: Interviews—Technical report. Johannesburg: University of the Witwatersrand.
Sapire, I., & Roberts, G. (2017).The status of the language of learning and teaching (LoLT) in schools: A quantitative overview: 2008-2016(Draft report).
Setati, M. (2008). Access to mathematics versus access to the language of power: The struggle in multilingual mathematics classrooms.South African Journal of Education, 28(1), 103–116.
Trudell, B., & Piper, B. (2013). Whatever the law says: Language policy implementation and early- grade literacy achievement in Kenya.Current Issues in Language Planning.https://doi.org/10.
1080/14664208.2013.856985.
Ingrid Sapirehas been involved in mathematics teacher education for 27 years and is based at the University of the Witwatersrand. Since 2012 her focus has been on the development of materials at scale for Foundation Phase mathematics teachers and students both at a provincial and national level. All of her work in the Foundation Phase has had a focus on the multilingual project—how to best provide for students in the system, challenging the policy whenever necessary. In 2017–2018 she was the chairperson of a ministerial task team that developed a framework for the teaching of mathematics in South Africa schools. She is currently heading the multilingual Bala Wande (Calculating with Confidence) Foundation Phase mathematics programme and working on her Ph.D., in multilingualism in Mathematics in the Foundation Phase.
Anthony A. Essienis an Associate Professor and the Head of the Mathematics Education Divi- sion at the University of the Witwatersrand, South Africa. He is a series editor of the book series Studies on Mathematics Education and Society. His field of research is in mathematics teacher
education in contexts of language diversity. He is also a current member of the International Committee (Board of Trustees) for the International Group for the Psychology of Mathematics Education (IGPME). Anthony also served as an associate editor of Pythagoras, the academic journal of the Association for Mathematics Education of South Africa, for 11 years. In addition to his background in mathematics education, Anthony also has a background in Philosophy.