Alex Bellos has written a book about mathematics which I shall try to get hold of. Speaking about it on Start The Week he said something which really set me thinking: that Asians may have a head start in maths because of the language they use for numbers – for example a simple progression one, two … ten, one-one, one-two … two-one …
In my very brief teaching career I was given the job of trying to teach maths to girls who had couldn’t do maths – had failed miserably by the time they got to (in current usage) Year 10 or 11. This was in a country where dropping maths was simply not considered an option by their parents – unlike in good old England where to qualify for university you only needed an O level in maths OR a science – which meant that many, mostly girls, opted for the safer territory of biology, might even have been encouraged to drop what could still be seen as an unsuitable subject for a girl.
The school had decided to try to start them again using the innovative Cambridge New Mathematics Project, which introduced students to notions such as set theory. During my first week or two I had to deal with complaints about the homework I had assigned – including in one case an angry father who came in person to remonstrate that tea sets had nothing to do with his daughter being able to get her sums right.
But when we moved on to number bases the girls came to life, in a way which really took me by surprise. They really enjoyed being asked to do things like ‘Express the number 23 in Base 8’ and we had fun discussing whether 11 in Base 2 should be called eleven or whether we needed to invent a different name to avoid confusion.
The Laws of Algebra also went down very well, and when I explained that if A-B=C, then A=C+B and there was no need to do a subtraction in order to work out how much change you needed to give if someone gave you $1 for a purchase costing 73¢. I can still here the squeals of one girl: Oh Miss! Oh thank you Miss!! When she could speak through the embarrassment of having everybody stare at her, she explained that her ambition had always been to get a job in the large department store, go to work in make up & smart clothes, but she had expected to fail in her ambition because she had never before been able to understand how to make change.
The girls did very well in their first end of term exams – so well that I feared I had not set questions which were testing enough or my marking had been too lenient (those were the days – no special teacher training, a degree was enough, just get on with it). I sent the papers & my marks to a lecturer at the university, a specialist in maths education; he thought they were ok, so everyone was very pleased.
I am afraid that the girls were unable to keep up that rate of progress however – for one thing their teacher was very much less confident when it came to geometry which started from the unfamiliar territory of rotations & reflections – dangerous ground for one who always has to stop & think in order to distinguish between left & right, east & west.
But, if you find it hard to grasp the basic idea of how even our basic counting numbers are constructed with numerical symbols - & some children may permanently fail to grasp this from the very beginning just because of the confusion of irregular names, might it not be a good idea, just for fun (I hold out no hope of getting everyone to follow) to play games with small children, in which the number after ten is called onety-one, and so on. Or is this already a commonplace?
