Tuesday, 2 April 2013

The difference between theory and practice is...

...that in theory there is no difference and in practice there is!

In about an hour I'm heading off to Seapoint to register for the 7th Mathematics Education in Society conference where I'll be presenting my Masters work and getting the opportunity to gather opinions and insights from people whose work I've been following for 5 years now. I'm rather excited!

More importantly, I've just reread the (very short! damn word count limits!) summary of my work I submitted ages ago as my conference application. I can't say I'm happy with it, but it was a furious click-send-at-23:59 submission so I shouldn't be surprised.

For those unaware, my Masters thesis is about teachers beliefs about mathematics teaching and language and how these things interact in the classroom. I'll do a follow up post about why very few South African children learn in their mother tongue and what implications research is showing from this (I'll delve into some of Neville Alexander's writing on language and political and educational emancipation to illustrate the point in said forth-coming blog. The topic deserves tomes of its own). Suffice to say for now, there is a very strong correlation between mathematics attainment and language of teaching and learning in SA. Of course, language of teaching and learning also proxies for many other variables that are known to have an effect on students' mathematical attainment, such as socio-economic circumstances, access to physical resources such as solid schools, textbooks and ICT equipment, access to human resources such as well-trained teachers etc. and this all comes saddled with the moribund gamut that is South African political and social history. But there's definitely something to the language variable on its own: across the world, students who learn in their home language learn better. It seems an obvious thing to say, but you'd be surprised at how controversial it is.

So I spent a month in a very rural school up in the Eastern Cape observing teachers and chatting to them about their thoughts about the role of language in their classrooms. Unsurprisingly, they didn't think it mattered much, and this is not an uncommon response. People think mathematics is symbols and numbers... the least language-dependent of the subjects. Not at all. Firstly mathematics is often described as a language itself. Choose a random textbook off the shelf and turn to the introduction. 10:1 says the first paragraph mentions something like "Mathematics is a language that... " or "Mathematics is the language which...". And like all languages, you learn what the NEW word/symbol/signifier means IN YOUR OWN LANGUAGE so that you can translate: attach meaning to the new squiggle on the page in terms you already know. What does "<" mean? What does "!" mean? How do we use the word "any" in mathematics and how is it different to the way we use it in the super market? Never mind overloaded terms such as "element" or "power". And then there's the discourse: how we talk mathematics. The way we rationalize our responses, structure logical arguments. A lovely example is Goldbach's conjecture (I had to look that one up because I always get it confused with Riemann's hypothesis. Oh well...). Goldbach's conjecture is still unsolved and is very easily stated. Something like this:

Every even integer greater than 2 can be expressed as the sum of two primes.

Simple huh? But every word is used in a mathematical way. The word "every". The word "expressed". The word "prime". Mastering such overloaded lexica AS WELL AS the style/register of mathematics is difficult enough in your own language, never mind a second language, and certainly not in a language that is--for all intensive purposes--foreign. 

So when our children are learning mathematics in English but they speak isiXhosa 90% of the time, well, making real meaning is very difficult. This combines with rote learning, teachers who are unconfident of their subject content knowledge and little linguistic resources to use to acquire English in order to acquire mathematics. The textbooks are in English. The exams are in English. And a kid who gets a question like "b) Hence, determine the roots of the new equation if p=0" ... well, you can guess what happens.

But I'm not happy with my conference submission for a couple of reasons:

In particular, the crappy word count doesn't give space to unpack and explore problematic terms such as "rural" or "poorly trained" teachers. When I describe the village as "homogenously isiXhosa speaking", well, it doesn't feel quite right: such a whopping big generalization is not au fait in academia. Grr... now I'll have to waste 5 of my 10 minutes of presentation time sounding defensive while I qualify what I meant when I wrote that near-midnight-rushed-submission. I promise the quality of the work is better than the submission! Promise!

Meantime, here's hoping I'll get to really chew the fat over some of the things troubling me about the research. Like validity issues around measuring and studying beliefs (ouch!).

One positive thing though. My work in my new school over the last 3 months has confirmed the major trajectory of the research. What teachers believe about their work is one of the core fundamental variables in determining what they are willing to try and how they are willing to change their practice. And effecting change in teacher practice is probably the single biggest thing we can do to improve our rather defunct education system. Connecting theory with practice! Here's hoping that comes through in the conference...

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