#### 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*

So, of course details, Matthew!

Learning math is one thing, but I suspect good math teachers are jewels to be treasured and guarded and fawned upon. A quick example.

My calculus for math major course. Day One. August in North Carolina is a HOT month even without global warming, so most of us in class wore light cotton short sleeved shirts. Our professor walks in, shuts the door, and we see he is wearing a long-sleeved, flannel shirt, no tie, but buttoned all the way up. He looked at us and announced, “Good morning, class. Today we’re going to discuss the differentiable area under a curve.” Prof proceeds to draw an X-Y coordinate system and a squiggly curve. Fortunately for me, I had a little calculus in high school, saw the curve was (technically) a differentiable curve, so I knew what he was about to do, i.e., draw a series of rectangles under the curve to illustrate how, as “delta x” (x dimension of the rectangle) approaches zero, the area under the curve may be more closely approximated. I think I have that right, but it’s been a few (!) years. When I looked around at the other 35 members of the class, a universal glaze crept over their eyes. Our 36-member class was down to twenty-four by the end of the week, sixteen after the first quiz, twelve until Thanksgiving break. Eight people came back after Thanksgiving. Six people took the final exam. Four people passed. When my Dad asked why I got a “C” I explained I was third in my class, and surely that counted for something.

Don’t even get me started on my high school geometry teacher, or the prof I had for group theory (or the textbook for group theory!)

Math textbooks are part of the problem, at least here in the States. It wasn’t until I took group theory that I understood some of the things the people who wrote my Calculus II textbook were trying to do, that weren’t explained in the book. Sometimes, if I needed a straightforward, comprehensible explanation I’d go to my Dad’s textbooks from the 1950s. Those actually made sense to me, and I could usually go back to my contemporary textbook and figure out what they were trying to get across.

I don’t think math has to be mysterious, but it seems like a lot of math teachers/professors want to render it mysteriously impenetrable.

Very interesting. I struggled with math in high school and university and never liked it. My father, however, could do it easily and I’m told his father (who died eons before I was born, could do calculus and helped his kids with it even though he’d left school when he was 13.

When I was in junior high my father used to try to help me with my homework and remembered algebra effortlessly. Unfortunately it seemed the method we were being taught for everything was not as straightforward as the one he’d learned, leaving me fairly lost. Looking back I don’t really know if I’m just poor at math (although I made it through Calc 3 in university or my teachers weren’t all that effective at teaching it, or something in between. While I can do a lot of math and ratios and whatnot in my head, I’d was hard pressed to remember much algebra or geometry when my own kids were taking it.

It was thanks to Cod, basically, that I swung from physics to softer science and history at university. I’d have needed to catch up on too much maths – he’d been my teacher right through from early on and the result was generally disastrous. As it stands I’ve since made sure I have enough to back up the physics that interests me, but there are a lot of gaps. The guy responsible for the debacle was the headmaster – he was so poor at hiring competent teachers, and so bad at leadership, that at one point there was serious talk among the senior class of leaving en masse for a rival high school. I have to thank him for being able to write though – the English teacher he hired for senior class was as useless as the maths teacher, causing my parents to send me off to tertiary courses in the local polytechnic, which included specifically how to write (and how to write fiction). I never looked back. I guess I could say that my high school set me up for life… just not by intention…

This reminds me an awful lot of a Calculus teacher I had in university. It was for the first semester of calculus and I’m not entirely certain he actually knew calculus. He’d basically write an equation out on the board and then call on somebody in the class to finish it, and of course there was always somebody who could. I didn’t learn a thing, although he was otherwise a nice guy.

Calculus was necessary for my major (geology) and I had to have three semesters of it. Fortunately the next two I had a calculus teacher (both were TAs, not professors) who really knew it, was a good teacher, and who was dedicated to teaching it. If you did poorly on an exam you could come into his office and he’d go over the problems you missed and give you an exam on those sorts of problems.

Sounds a bit like the deputy principal at my senior high school – he knew his stuff and was very approachable on it.

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Wow that’s really awesome to have the person that wrote the national textbook for a headteacher!!