Africa is endowed with works of art available for classroom illustration of various mathematical concepts from elementary schooling, all the way to university instruction — Professor Kakoma Luneta (below) of the Faculty of Education at the University of Johannesburg, told senior academics at Stellenbosch University (SU) last week.
He was delivering a keynote address titled Mathematics teacher trainers’ critical views of training mathematics teachers for multilingual classrooms in South Africa at thefirst-ever joint colloquium of Universities South Africa’s three communities of practice that was hosted at SU’s Institute for Advanced Study (STIAS).
The Colloquium had gathered over 50 members of the Community of Practice for the Teaching and Learning of African Languages (CoPAL), the Community of Practice for the Teaching and Learning of Mathematics (TLM CoP) and the Education Deans’ Forum (EDF). The senior academics were exploring ways to make Multilingualism in the teaching and learning of Mathematics in Higher Education a reality, especially as public universities gear themselves up to implement the Language Policy Framework for Higher Education Institutions, which was gazetted in 2020 and came into effect from January 2022.
A business case for multilingual teaching and learning
Professor Luneta said in looking for literature on multilingual classrooms in South Africa, he had discovered over 14, 890 articles, conference presentations, masters and doctoral studies published on this subject since 1994 – yet South Africa was still debating this subject, close to 30 years after democratisation.
In making a case for multilingual classrooms, he summarised key findings of some of those studies, first defining a multilingual classroom in the South African context as one in which there are three or more different home languages spoken by the children in that classroom while the language of learning and teaching (LOLT) of the school is English.
He cited a Donald et al (2006) study that showed that children learning in a language other than their mother tongue often suffer negative consequences concerning their psychological, social and educational development. Another scholar, Heugh (2005) had found that mainstream education succeeds less when based on languages other than the child’s mother tongue. Yet another study, by Edwards & Ngwaru (2011), had found that learners with a solid mother-tongue foundation participate with higher confidence in their learning and outperform peers who only operate from a second language.
A more recent study (University Research Co., 2019) had demonstrated that mismatches between the language of instruction (LOI) and the language that students and teachers speak and understand best, can hamper effective teaching and learning.
On the benefits of multilingualism in teaching, Professor Luneta said classrooms embracing multiple languages enable code-switching (Albertyne and Guzula 2020), the process of alternating from one language to another in one conversation. He said this encouraged active learning of an alternative language while keeping the learner grounded in their home language. He added that learners allowed to code-switch in class tend to express their understanding of the subject matter better to teachers and to their peers. Professor Luneta cautioned, however, that teachers ought to know the principles of code-switching because if it is not monitored it can lead to misconceptions and errors especially in mathematics.
Turning back to South Africa, Professor Luneta expressed regret that none of the country’s 12 official languages (including Sign Language) feature in classrooms beyond Grade 3, apart from English. He said from Grade 4, English takes over as the sole medium of instruction in most schools, and it does so to the detriment of learners’ home languages. He said it did not help that “parents and members of school governing bodies have biased language attitudes, beliefs and values that mostly favour English.”
He said that, notwithstanding, a solution was available to turn the situation around.
Multilingual illustrations using place-based mathematics
Advocating for the use of African artefacts to illustrate mathematical concepts, Professor Luneta upheld that teachers ought to have a deep understanding of mathematics content and the language context in which the artwork is embedded, to be able to make the necessary connections, extract and extrapolate the mathematics in artefacts in their communities and the land. Such a teacher would be able to refer to those images in multilingual teaching to create meaning and enhance conceptual understanding among their learners, because the images or artefacts are unilingual and appeal to all the learners in their own mother tongues.
Mrs Mhlanga showing her knowledge of shapes and measurements in the making of baskets and mats (from Luneta 2022).
One appropriate example lies in basket weaving. Professor Luneta explained that by weaving reeds in a spiral fashion from the centre outwardly, Mrs Mhlanga (pictured above) displays innate mathematical knowledge of equiangular spiral parametric equation, without being aware of it at all. He said Zulu, Xhosa or any other children from South Africa’s 12 official language groups would easily relate to such artwork as these illustrations are unilingual.
Basketry showing the reeds woven in spiral and circular formats (From Luneta 2022).
Professor Luneta said at advanced cognitive levels, the spiral configuration of the traditional basket could also be used to explain the propeller concept in physics.
He also cited the triangles, trapeziums and parallel lines forming patterns of dodecagonal pyramids in the interior of a thatched roof, saying these were as applicable to primary school mathematics as they were to university advanced mathematics.
Thatched roofing and a higher-order cognitive level problem from the thatch patterns (from Luneta 2022, p.23).
Other examples were tubular baskets illustrating cylindrical concepts; colourful Ndebele beadwork which could be used to demonstrate symmetrical shapes (kites) and patterns, as well as artwork in Zulu huts and even more artefacts from Venda and Pedi cultures (See Luneta 2022).
Beadwork display of the knowledge of geometrical properties of a rhombus and a kite (from Luneta 2022).
His point was to demonstrate a theory published in Skovsmose (2012), that the grasp of mathematics in young learners in multilingual classrooms increases when teachers explain concepts using familiar features that the learners can identify with.
Professor Luneta called this model of teaching place-based mathematics education — an approach to mathematics education that engages students and teachers from their cultural contexts, using objects of importance to them and their communities (Nicol & Luneta, 2018).
A glimpse at Professor Luneta
In addition to his teaching experience in the United Kingdom and the United States, Professor Luneta has been involved in mathematics teaching and engagement with mathematics education researchers from eight countries in Sub-Saharan Africa (Botswana, ESwatini, Ethiopia, Kenya, Lesotho, Malawi, Namibia, Zambia and Zimbabwe), most of which are contending with multilingualism in classrooms, except Lesotho and ESwatini. He admitted that while it is not easy to teach one group in more than one language, the complexity increases with the kind of multiple language diversity that one finds in South Africa’s classrooms.
He said more of his articles and books on mathematics cognition can be found on his website: https://kluneta.com . He was open to sharing resources with those willing to delve deeper into the subject.
An NRF-rated researcher, Professor Luneta holds a PhD in Mathematics Teaching from the University of the Witwatersrand and a master’s in the same discipline from the University of Sussex in England. His research interest lies in Mathematics Teacher Education at elementary and secondary schooling levels, among other areas. He is a visiting Professor of Mathematics Education at Canada’s University of British Columbia; was recently a Visiting Scholar at the University of Cambridge’s Centre for Neuroscience Education. Specialising in both Mathematics and Physics, Professor Luneta has published five books, over 100 book chapters and articles in accredited journals.
Albertyn, L. and Guzula, X. (2020). Multilingual Classrooms Boost Learning. Unsplash UCT. Available https://www.news.uct.ac.za/article/-2020-03-03-multilingual-classroomsboost-learning.
Donald, D., Lazaras S. & Lotwana P. (2005). Educational psychology and social context. 2ed. Cape Town Oxford University Press
Edwards, V., & Ngwaru, J. M. (2011). Multilingual education in South Africa: The role of publishers. Journal of Multilingual and Multicultural Development, 32(5), 435-450.
Heugh, K. (2002). The case against bilingual and multilingual education in South Africa: laying bare the myths: Many languages in education: issues of implementation. Perspectives in education, 20(1), 171-196.
Luneta, K (2022). Can the Fourth Industrial Revolution resolve why the teaching of mathematics in the current paradigm continues to be decontextualised and ineffective?; Chapter 2 in Chirinda B., Luneta K. & Uworwabayeho A. Mathematics Education in Africa The Fourth Industrial Revolution Mathematics. Research in Mathematics Education Series. 978-3-031-13926-0 Springer Nature Switzerland AG
Nicol, C., & Luneta, K. (2018). Place-based mathematics education in the global north and global south. Paper presented at the World Educational Research Association (WERA 2018 world congress) conference, Cape Town Convention Centre, Cape Town, 3–5 August
Skovsmose, O. (2012). Towards a critical mathematics education research programme?. In Opening the cage (pp. 343-368). Brill.
‘Mateboho Green is Universities South Africa’s Manager: Corporate Communications.