Awards, and the problem with maths in my school

I had a pleasant surprise on Monday, when I opened our mail box to find an A4-sized letter from the OU.

Tearing it open on my way over the road to buy a drink, I caught sight of a cheque. Curiouser and curiouser. Well, I assumed at first that I'd overpaid something; maybe the financing for my course last year had been miscalculated. Actually, after reading the accompanying letter, I found out I'd been presented the 'Leslie Walshaw Award' for M208...for getting the best results in the course for my region! The fifty pound cheque was my prize! Wow!

So now I have an excuse for putting up my scores, as I've generally refrained from doing so, worried that it was a bit big-headed. I got OCAS: 96 (after substitution and rounding) and OES: 96. This means I actually did better in my exam than the coursework, which is quite unexpected! I was pleased enough with my marks already, but the award was such a great bonus, and it's definitely going on my C.V. As it turns out from reading the forum CC-Maths and Computing, if I'd lived in Region 8 instead (of 7), I'd not have won it, as the man who got it there's marks were more like 98 and 100. But I'm in Region 7, and well, my result was apparently the best here!

Changing the subject completely, I remembered something about my school maths education that looking back, was completely stupid. Maybe things have changed now, as I left secondary in 1994, but I wouldn't be surprised if it's the same. The thing is, they never told me what pi was! They'd tell us to use pi r squared to find out the area of a circle, or 2 pi r for the circumference, they'd tell us how ancient civilisations already knew about pi, that various approximations had been used like 22/7, and that recently computers had worked it out to thousands or millions of places, but they never told me what it was! I think I even asked... well Neil, it's a number, approximately 3.14, that you can use to calculate the area of a circle. Yes, so you said, but what is it!? What were people trying work it out to greater and greater accuracy? And also, how'd they know they were getting closer? What were they trying to get closer to? Well of course the answer is simply that pi is the ratio between the diameter of a circle and its circumference. Straighten out the circumference of a circle and you get 3.14... diameters. Why'd they never say that? Instantly, the relation 2 pi r makes perfect sense (2r being equal to the diameter). And while the other relations are not as instantly obvious, it is blatantly clear why pi is involved in all these equations relating to circle-related things.

I've just finished reading Surely You're Joking, Mr. Feynman, and I'm convinced Richard Feynman would have had issues with this too; it's simply not the right way to teach (in fact it resembles his story about his cousin learning algebra, in the Horizon interview). They should be teaching maths, not teaching processes. Unless you have an understanding of what you're doing, unless you can anchor it to some relevant fact, you're going to find it harder to learn.

I give you the example of pi (again). A few summers ago, I learnt pi up to fifty decimal places (and e but I've since forgotten that back to 32 places), my plan was to get them to 100, but I eventually fizzled out. Anyway, while it only took a few days, it was hard. This is because it was just a meaningless string of unrelated numbers. For comparison, think of how easy is it to learn a song with fifty words? Well that's what, ten lines!? Easy. Because the words are related. They form full sentences, and make a narrative. And don't forget, while each of the numbers to memorise in pi is just a 0-9, each of the words in the song can be drawn from thousands of choices (okay okay, so certain words have to go together, verbs might follow nouns and so on. But, I think this hardly counteracts the fact that there are so many words compared to just 10 numbers). The first time they introduce pi, they should tell you what it is. Learning what you can do with it would follow logically.