Back in the summer (somewhat overshadowed by Olympic excitements), The Times carried a lively debate about the teaching of mathematics in English schools.
One correspondent told of his experience teaching ‘A-level standard calculus’ to primary school children, all in an afternoon. This brought an immediate query as to how he had coped without first giving them the advanced algebra & trigonometry needed.
This is the kind of attitude which infuriates me – the one that views education as necessarily entailing a journey through a funnel of ever-increasing specialisation, following the trail of the past, never able to 'start from here'.
While it is undoubtedly true that we need more people to be trained in maths to the kind of level needed in the modern world, it is also true that most of us need an appreciation of the kind of thing that maths can do, even if we baulk at detailed understanding.
Once upon a time the ability to decipher the hieroglyphs which encoded the language of words was far from common to all of us. Maybe one day numerical facility will be as widespread as is literacy today, or maybe the ability to decipher the formal logical code of maths will remain the province of something well short of a majority.
Nevertheless we all use intuitive mathematics every day – how many, more than, less than, addition, subtraction, multiplication, sharing (division), one-to-one correspondence, money, time, making things … albeit in much the same way that Moliere’s M Jourdain spoke prose.
Most people cannot ‘read’ musical notation, but can recognise a tune, make insightful comments on different styles of music, & even produce it themselves, whether reproducing a familiar tune ‘by ear’ or something of their own, instinctive, composition. And we can be taught much about what used to be called ‘musical appreciation’ without being troubled at all to learn the notation & formal rules of harmony.
I had less than one half term of A level maths, & though I was able to make up some of the deficiency at university, my grasp is nowhere near as secure as it should be, or would be if I had been able to get in the practice when I was younger. I retain the outrage I felt when I realised that, in 13 years of formal mathematical education had not even introduced the ideas of differential & integral calculus which had been known for centuries (compare & contrast how much the modern school child learns of genetics & DNA). I find it absolutely iniquitous that some very large proportion (possibly a majority) of the population has no idea even of what calculus is ‘for’
I do think however that if I were challenged to teach the basics to primary schoolchildren in an afternoon I might make a decent fist of it.
I would start with a song:
The square on the hypotenuse of a right tri-angle
Is equal to the sum of the squares on the two adjacent sides
Next step would be to talk about calculating the area of triangles, squares & rectangles (practically & arithmetically)
Then move on to finding the area of a triangle with a wiggly or curved hypotenuse.
I would have to give more thought to whether we could squeeze in the area of a circle & the magic of π.
Just because mathematicians arrived at calculus by one particular route does not mean that we all have to start from there.
