Professor Anthony Essien, Associate Professor in Mathematics Education and Interim Numeracy Chair, Wits School of Education used a rainfall chart to show his audience how the word ‘least’ – in the context of nothingness – does not make sense in African languages.
He was addressing the first joint colloquium of three Universities South Africa’s Communities of Practice held in Stellenbosch where over 50 delegates from all public universities met to explore Multilingualism in the teaching and learning of Mathematics in Higher Education – Enhancing Success. The participating groups included the CoP for the Teaching and Learning of African Languages (CoPAL), the CoP for the Teaching and Learning of Mathematics (CoP TLM) and the Education Deans’ Forum (EDF).
Professor Essien told how he took three pens, put them on table, then asked his students to translate this into isiZulu as he took away one pen at a time: “I give my ‘Language and Communication in Mathematics Education’ masters class a task: I take three columns with dots indicating rainfall. January has five dots. February none. March one dot. I ask them which month has the least rainfall. The majority of my monolingual students will say February. African students mostly say March.
“Using the three pens, I ask students to translate to any of the African languages present in the class the following: ‘there are 3 pens on the table’. Students are often able to translate this easily. But when it comes to ‘there is zero pen on the table’, the students translate this as ‘there is no pen on the table’. When pressed to use the term ‘zero’, they are unable to. At the end, we agree that, in fact, the correct answer is February because zero is a number”.
“The movement of zero as absence, to zero as a number, is always a difficult concept to teach, especially when someone comes with linguistic baggage that comes from their home language. In any African language, I challenge you to think of the word least in the context of nothingness. I speak three African languages; the word does not exist in the context of nothingness. In African languages, ‘least’ means that a quantity is involved, and this quantity is the smallest, and as such, it is nonsensical to think about least in the context of nothingness. This is one instance where meaning making can be constrained by a natural language in multilingual classrooms.” (See Essien, Sapire & Moleko, 2024 – forthcoming).
During last week’s Colloquium, Professor Essien spoke to the topic Teaching for meaning making in mathematics teacher education multilingual contexts: What does it entail?
He asked his academics audience: “What does it take to teach mathematics with meaning within multilingual contexts? I’m a teacher educator like most of us here, and so, for me, teacher education comes into play. In the words of (Canadian education author) Michael Fullan: “Teacher education has the honour of simultaneously being the worst problem and the best solution in education.”
Professor Essien also referred to Canadian academic, Richard Barwell’s triple challenge, where teachers have to pay attention to the mathematics, the English and then the mathematical language, saying he had added to that, the interaction between languages.
Factors that influence how students make sense of the mathematics taught in class included the language structure, an understanding of the everyday use of concepts, and how that interfered with their mathematical knowledge.
“I’ve been visiting KwaZulu-Natal schools seeking permission to conduct a multilingualism study, with specific focus on the transition phase. We want to understand what the challenges are when learners transition from home language to English, but more importantly, we want to find solutions to bring to the challenge transition poses.”
He said teachers asked him why the government wanted them to teach in isiZulu for the first three years of schooling, adding that “Research shows that the more learners are grounded in their home language, the better able they are at mathematics.”
He cited the South African researcher, Kathleen Heugh’s work on Ethiopia where different regions have different language education policies. Some regions immediately teach in English; others teach in the home language for the first three years with the switch coming in the fourth year; yet others teach for six years in the home language, switching to English in the seventh year.
“Her research showed that those who have studied mathematics and science in their home language for longer performed better than those who switched very quickly.”
Similarly, Australian researcher Philip Clarkson’s study of English proficiency and student maths performance found that those who were good in both home language and English fared better – even against English speakers in a monolingual environment.
English proficiency as a predictor
South African researcher Sarah Howie’s work found that student’s proficiency of English was a strong predictor of their success in mathematics.
Said Professor Essien: “But proficiency is not enough. I argue that the ability to teach or understand mathematical concepts goes beyond mere proficiency in either English or the home language. When we talk about teaching and learning in multilingual classrooms, we talk about what is visible. What lurks behind the visible is taken for granted.
“We say there is high language diversity, yes, but there is also the distinct nature of multilingualism that needs to be considered. In KZN, for example, there is a dominance of one language, isiZulu. A cosmopolitan city like Johannesburg has a multiplicity of languages in the class and what works in a context of one dominant language cannot be transferred to such a setting.”
He said the setting was very important, using, as an example, Nigeria, where languages are autonomous. “Here you have Nguni and Sotho languages where there is mutual intelligibility. Someone speaking Xhosa will understand someone speaking isiZulu and if I switched language in Johannesburg, I’d reach a lot of people. If I used my home language in Lagos nobody would understand me.”
Still engaging with what is visible and what lurks behind the visible, Professor Essien said: “We have a colonial history; English, a colonial language, versus indigenous languages. But there are also cross linguistic and cross translational issues.
Our learners come to the classroom with varying proficiencies, not only in English but in their home language. That plays into what we do in class.
“When we talk about teaching for meaning making, I like to draw on the discourse of decoloniality where we talk about the decolonisation of mathematics. What I see in literature is that decolonising mathematics is simply equated to recontextualization where instead of using Mount Everest, you use Table Mountain…
“That is not decolonising maths. If you want to decolonise maths, you need to consider critical issues, like curriculum design and the teaching and learning of mathematics. It’s about softening the boundaries between the languages that are present in the classroom and drawing on the full repertoire of the students. That implies metalinguistic awareness, pedagogical trans-languaging and cross linguistic comparisons between the languages.
“We keep coming to conferences and talking about questions around language issues and the teaching and learning of mathematics. But we are not making progress– simply researching the same things. Let’s stop asking if language is a resource. We need to move away from that and think about how we need to harness the epistemic potential of multiple languages in the context of language diversity.
“We need to ask questions: In terms of language policy, what would a full repertoire language policy look like, where it is officially mandated that learners use all languages available to them? The same question applies for teacher education, and for textbooks.”
Question One: The notion that language in the maths class is a type of soft skill… isn’t that a myth? The way maths is understood goes beyond problem solving techniques and the use of symbols to get to the correct answer.
Professor Essien: What do you mean by soft skill?
Response: The skill that is regarded as secondary in understanding a particular concept. Maths is about equations, symbols, formulas, calculations. Language is on the periphery. Maybe language should come to the centre.
Professor Essien: I agree with the last point. The issue of language cannot be a peripheral thing – it is central to understanding maths. Maths is not just algorithmic gymnastics. Part of understanding maths is being able to justify, explain and communicate… without language there is no mathematics.
Professor Stanley Madonsela (left), Associate Professor and Chair of the Department of African Languages at the University of South Africa’s College of Human Sciences, commented: Understanding core ideas and the ability to transfer them to new situations should be the twin goals of education today. But this would include the skills that they are actually showing, which would include the application of the knowledge that they have obtained. Most importantly, the self-acknowledge or their understanding of the metacognitive awareness will indicate the understanding of the meaning – even in the mathematics signatures that are there, or signs.
Professor Essien (right): It’s about meaning making for the students, involving those students. When I make a presentation on language issues, sceptics will tell me that what I am saying is that they, as teachers, would need to be proficient in the home language of the students and if they are not, they can’t use what I am saying.
I say no. If you understand the home language, it’s an advantage. But if you don’t, you can still make use of the languages that are present in the class. In Khayelitsha, a study was conducted with learners – who were asked a question by someone who didn’t understand isiXhosa: what do you call a turning point in your home language? They struggled to provide an answer. Think of turning point in English… it is turning but it’s at a point. It is an oxymoron in itself. Students could not translate that.
When they understood that it was a change of direction, they could coin a phrase in Xhosa. The learners then surmised that perhaps the English phrase should be the turning place rather than turning point.
Essien, A., Sapire, I., Moleko, M. (2024 – forthcoming). The Concept of Language-as-resource/Sources of Meaning from an African Perspective: Challenges and Opportunities in Mathematics Education. In Essien A. (Ed). Multilingualism in Mathematics Education in Africa. Bloomsbury: London. Pp 1-20
Charmain Naidoo is a contract writer for Universities South Africa.