izibalo (n.) -mathematics

OR more precisely ulwazi ngeziganga zezibalo. The knowledge about the magnitude of calculations (1).

This is the first of many posts which simply relate how different authors and dictionaries explain mathematical ideas in isiXhosa. All dictionaries will be cited, of course.

One of the reasons commonly given for not teaching mathematics and other technical subjects in indigenous languages is the lack of lexicon development in those languages. What is interesting, however, is how some seem to think that lexicon development is always natural and instinctive: not so. Linguists all over the world have spent lifetimes explicitly developing words to describe new phenomena that they cannot yet capture. Afrikaans is a good example of where this has happened as an explicit language development project in (almost) living memory*.

Some excellent dictionaries based on the work of South African linguists to develop mathematical register and words in isiXhosa are available. I will draw on these in this and future posts to share some of their work and hopefully get readers thinking about how we break down conceptual ideas behind rather opaque, non-self-explanatory words. Here is one example:

i-aljibra (Xhosalized spelling of ‘algebra’): uphicotho lobunto bamanani nezixa olwenziwa ngeempawu ezinjengoonobumba nezinye.(2)

Translation: an arrangement/weave of numbers and amounts which are made by means of  marks similar to other alphabetical letters.

There are two potential points of discussion with the above definition. The first is whether you think ‘i-aljibra’ is a genuine isiXhosa word. I would argue that it is. Languages borrow and appropriate from each other all the time. Besides: it is not as if the hegemonic language of the sciences, English, has not borrowed extensively from other languages in order to broaden its own expressive capacity. Many of our mathematical words are not English in their origin: algebra (Arabic), geometry (Greek), to name just a couple. So there is no good reason for our own African languages to not borrow… or, even better, claim, words from other languages to describe things that they don’t yet have a word for. Language purists might not feel comfortable with this idea, but it is how languages adapt, thrive and grow.

The second is the actual definition itself. As a mathematician, I am unsatisfied with that definition. That’s where you, reader, come in. Please do comment on these posts about the clarity and completeness of the definitions posted, today and hereafter. I would personally want a high school student, who picked up this definition, to get a sense of expressing relationships and patterns irrespective of particular numeric instantiations of that pattern: that is the essence of algebra to me. IsiXhosa speakers in particular, if you can help out with amendments and alternatives, that’d be great.

In summary, there’s no reason why well intentioned and committed linguists and technical experts cannot develop the vernacular they require to talk meaningfully about technical work and ideas. The potential benefits are enormous: the research about learning in your own language is voluminous and convincing. It would take an enormous pressure off our children in our schools to learn English as soon as possible: English can be mastered as English and not as a means to accessing content, mathematical foundations can be laid well. The improvement in maths and science attainment,  if students are learning in a dual medium classroom environment wherein they can understand a concept in the language they know best, would be fantastic!

(1) Mathematics Dictionary for Intermediate and Senior Phase: PRAESA, UCT.

(2) The Greater Dictionary of isiXhosa Volumes 1-3: Fort Hare University Press.

*it should be noted that language development is engaged in for a variety of political ends, whether they be nationalistic, reform-based or purely academic. The key ingredient is often the political will to commit resources to the project, and how said language development work fits in with the ideological agenda of those in power.