Friday 9 January 2009

Bad Mathematics? (part 1)

I'll tell you something about myself: I was a little horror at school. Looking back, for some years, I had no idea why the teachers hadn't strangled me. I constantly interrupted their lessons with questions and different angles and complications. It wasn't until I tried teaching myself that I realised how inspiring and indeed flattering it is if a pupil does this - because they're listening, and thinking! (A lot of other kids thought it was just because I "got away with everything".)

Except in Maths. My main interest in Maths lessons was imitating the teacher, who had a funny way of shaking her head, and passing notes. What I learnt, I learnt from daydreaming and looking around the room. We had a fantastic classroom - full of origami shapes and a row of Marmite pots of different sizes and brilliant graphs on the walls. (Then in year 10 they started expanding the school and knocking the good classrooms down, exiling us to a blank-walled Portakabin, where I passed even more notes.)

It simply made no sense to me. I didn't care. It was a bunch of rules to memorise, not logic, not intellectual satisfaction. And I couldn't memorise the rules, any more than I could memorise a novel in Mongolian. Oh, I might get a few sound sequences right, but I'd be as likely to muddle them up as not. I loved graphs, statistics and percentages, because those have always made sense. I can add up the shopping bill without any trouble at all, and I do well in multiple choice exams because I know what the answer should be - but proving it? No way. To this day I have no idea what "sine" and "cosine" mean. Although when I was 14 or 15, I discovered that "tan 89" is multiplied by 10 if you change it to "tan 89.9", and again at "tan 89.99" and so on . . . I asked my mother what "tan 90" would be and she said, "It's infinite". I realised that that meant two of the triangle's lines were parallel, so they never joined up. That was satisfaction.

Of course, I ended up with a C at GCSE, and that ended my prospects of studying physics. I accepted the evaluation of myself as someone who was fundamentally hopeless at maths, and resigned myself to eternal confusion and dissatisfaction with many concepts in Chemistry. What is a zero order reaction? Why, if you double the concentration of something, does the reaction rate square? That's illogical. My mind rebelled. "Don't worry. Just plug in the numbers!" kind friends reassured me. And a university lecturer said of calculus: "Don't try to understand it, just learn it, that's much easier."

Well, I memorised what I could, then forgot it as soon as the exam was over. In my first year, as we caught up with algebra, I sat next to a 25-year-old Chinese student. She said in horror, "We learnt all this in primary school!" and zipped her way down the page within a minute or so. Not only could she do it, but she could remember that far back! I had always been uncomfortable with mnemonics and memory techniques at school. I felt they were an insult to the fascinating world we live in. If you really know and understand something, you remember it without that kind of thing. And it also means you are simply learning it for the exam, not for its own worth, which is so infinitely greater - and therefore are free to forget it the minute the invigilator collects the papers.

I remember another experience I had: my boss asked me to imagine a fictional wind turbine, and told me its value fell by so many percent in such and such a time, so what would it cost in a year? I answered correctly immediately. He asked me what formula I had used. I said, "I don't know. Instinct." He was furious. "Instinct is bad. You must not use it," he told me many times, and summoned me to his desk for a lecture. He made me and my colleague apply a formula. Well, needless to say, I have no idea what that formula was and am not hugely interested!

Have I convinced you how much I hate maths yet?

I hope not, because I regard maths with the same sorrow and yearning as I regard an unrequited love, a forgotten beautiful book, a star I see in the sky that I long to reach out and touch. As one sometimes makes a fool of oneself in unrequited love, I made an utter prat of myself on Georgia's website last night, trying to use geometry to work out the number of jelly beans in a jar. I felt I had the answer at my fingertips. I was sure that by turning half the circumference of the jar into the jar's area, I should get a good estimate . . .

And I don't think I'm alone in this. People are interested in how many percent of people think this, in whether a drawing containing an illusion really measures the same as that. Logic problems, Sudoku, the Enigma challenge in New Scientist, comparisons such as how many times so many cars would stretch around the world . . . I think people are interested in numbers and patterns. But they don't admit it. (As Paul Sutherland reported, I said the same about science recently. But I think it is even truer of mathematics.) Why?

The BBC wrote an interesting take on popular culture and blamed "traditional education", as if tradition itself was a bad thing (anyone who automatically condemns all "tradition" should watch Holy Week processions in Spain). And a couple of years ago, a quantum physicist named Stefan Huber at Sussex University said to a few of us Chemistry teachers-to-be that mathematics is like learning a language or a musical instrument - there is no such thing as being fundamentally good or bad, it is simply a matter of practice. But schools and exam boards go by instant results, and if you don't instantly catch on, they direct you to study "arts" A levels and give up on you. That was very, very true, at least for me. (I was certainly expected to beat instant results out of the pupils I taught. There was no such thing as giving them time. If they didn't all achieve the two "learning objectives" by the end of the lesson, I was in big trouble!)

Since September, I have also devoted a surprising amount of time to drawing circles, rectangles and triangles. All of a sudden I am realising how much there is to find out about these objects and their relationships with each other. I just wish I knew where my compasses and a ruler had got to! This was invigorated the other day when I read in David and Judith Goodstein's "Feynman's Lost Lecture" that a circle outside an equilateral triangle will be twice the diameter of a circle inside it, and I was overcome with the need to check this out - and try it out on other shapes, too. But it is mostly because of a wonderful document Chris sent me in September, called "A Mathematician's Lament".

This is a 25-page pdf file so may take a few minutes to download. It is worth every second - one of the most thrilling and thought-provoking pieces of writing I have ever read, and the same kind of burst of light as the end of a Shakespeare tragedy. I seem to be writing an awful lot more than I'd actually planned, and my tabby-and-white-and-ginger monsterkin Izzy is licking the screen and walking on the keyboard and purring demandingly at me, so I'll split this post into two parts and write my take on the document tomorrow. Let me know what you think of it. It answered an awful lot for me.


Georgia said...

Hi Alice! Very interesting post! I just started reading the "Lament." I'll write more when I've finished it.

Anonymous said...

Hi Alice! I've just started reading "The Lament" too. I am actually enjoying it thoroughly (even though I just crawled away from a bloody battle with domains and radicals and exponents...)

I loved the view of an artist. Being one myself, I could hardly contain myslef at the thought of someone graduating with an art masters and never having touched a blank canvass!

Anyway, I'll let you know when I've finished (only on page 8 or 9 right now...)

Thanks for posting this!

-fellow zooite/maths hater