It sounds funny, all these years later, but when I went to Tamatea High School my maths teacher, universally known to classes (but not to his face) as ‘Cod’, tried to teach calculus without revealing either how it worked or what it was for.
Cod’s lessons were typically: ‘if you have these letters, which stand for things I haven’t explained, and do this and this, you can rearrange them to this.’ Then he’d write some problems on the board and walk out, never to be seen until next class. If he’d said: ‘it’s a way of calculating the area under a curve, and you can do that from different points if you understand tangents, though I didn’t teach you about those last year, and I’m sorry you failed the exam’, it would have helped. But Cod didn’t. Nor did he make himself available in class to ask.
The fact that half of us used to make ‘Cod noises’, whether he was there or not, was very funny, but the barrage of ‘blips’ and ‘bloops’ didn’t help any of us understand the maths. When my parents confronted Cod at a ‘meet the teacher’ evening, my mother asked him whether he’d taught senior maths before. She told me, way later, that he burst into tears.
The problem was that none of us were going to pass the externally-set finals exam. A friend of mine took action, and the upshot was that the entire senior maths class ended up being taught privately, after school, by the deputy principal. It turned out he was a maths teacher, and had written the national textbook. Woah! His assessment of the issue we faced was simple: calculus made up half the finals, and you needed fifty percent to pass – so although there wasn’t time to catch us up on the rest, he’d make sure we knew calculus. And he did. Damn, he was good.
Curiously, my physics teacher (who rode a chopper-modded Triumph and was uber-cool) was also a maths teacher. So why the senior maths class ended up with Cod, given all the talent to hand in the school, is a mystery, although it was under control of Tamatea High School‘s headmaster of the day. Of course, it made sense if you assumed this headmaster was dedicated to making every kid into worthless failures, and hiring incompetent teachers was one of his techniques. On my experience of that headmaster’s conduct with writing and English teaching, his assignation of Cod to the senior maths class wasn’t the only evidence for this apparent agenda. But hey – I was just a pupil who was sent elsewhere to actually learn, against the explicit efforts of that headmaster to block me, so how can I be sure? (Ask me for details in the comments).
The outcome of the extra-class maths tuition from the DP – who, as I say, was really good, and determined that we would be uplifted – was that I did end up being able to do calculus for the exam. And today, especially after a quick Google search, I can tell you that +C added at the end of an integration stands for ‘plus anti-Cod’ (an infinite number of them).
What Cod should have said was: ‘if you have a pot of boiling water and turn the element off, you’ll notice the drop in temperature can be plotted as a curve. What counts for cooking is the total energy, represented by the area under the line on a graph. If it was a straight line, you could work it out using geometry. But it isn’t. It’s a curve, and to calculate that, you need to know calculus. So if you want to save power costs, you can use calculus to figure out when to turn the power off – and end up with perfectly cooked spuds.’*
All this underscores one point. Wads of raw data are one thing; but without an organising principle they are meaningless. That’s what was missing from Cod’s maths lessons. And the point is true of more than mathematics. It works for history. More soon.
Copyright © Matthew Wright 2017