voices from the beehive, part 3

and another thing

Another in the series of “buzzy little critters flying around within my bonnet”, I’m afraid. (There will be a more detailed response to some of the excellent and thought-provoking comments on the “AI and Accountancy” post from Wednesday, as time and energy permits. This time, I regret to inform you that I am off on my bullshit about mathematics education. Please don’t waste your valuable time and energy trying to find evidence that I am wrong; as I always warn in this series, these are not arguments or policies, they’re bees.

So … mathematics education, incredibly frustrating state of. The older I get, the more it annoys and worries me. Not just because of the extremely frightening consequences of widespread innumeracy in public life, but because I meet so very many people who could have been very good at mathematics and enjoyed it, but who believe themselves to be incapable of doing so. I’m very influenced in this by having done an MSc in Finance at the London Business School, where I discovered by observing my classmates that lawyers and advertising copywriters with a completely humanities background could learn stochastic calculus in six weeks if the motivation was there to teach them.

The problem is that education is hard to measure, but easy to mismeasure. It’s interesting that if you observe driving theory courses, regulatory certification courses and the like, you notice that whenever people are serious about teaching a set body of knowledge as efficiently as possible, they come up with something resembling Direct Instruction. If you want to get a classroom full of kids who can factor polynomials and solve trigonometry problems, you get a load of rote memorisation, a big book of problem sets and maybe make up a nursery rhyme for the quadratic formula.

Unfortunately, this tends to deliver a classroom full of kids that can pass the exam but can’t do maths. In the English system, half of them will completely stall at this level, and at least half of the remaining half might be able to struggle through calculus and elementary linear algebra taught in the same fashion, then absolutely fall apart the minute they see a textbook written in theorem/proof fashion. This was my story too; almost all the maths I ever learned, I had to teach myself for various projects, sustained only by the personality problems which made it slightly less painful to force myself through the bloody stuff than to admit I was wrong. I’ve actually learned some things three times, because as far as I can tell my brain interprets linear algebra as an injury and attempts to heal from it.

So what’s the solution? I think that if you want to heal maths, you need to look at English.

We don’t pretend that spelling is the same thing as poetry; we have “English language” and “English literature” exams. “Mathematics” and “Arithmetic” are also different things. You do actually need everybody in a modern country to be able to divide up a restaurant bill and order paving slabs, and there are some kinds of calculating algorithm that it would be good to just drill into everyone’s brain through rote learning.

But it’s also good to teach mathematics! Another whole subject could be made out of abstract reasoning and problem solving skills. And this would not necessarily be elitist or exclusive. At railway stations, they sell books of “Logic Problems”, and casual observation of the kind of people who buy them make me think they’re not mainly targeted at people to whom the name George Boole means much. On more than one occasion, I’ve had a puzzle fan express to me their surprise at finding out that “there’s no maths in sudoku”, because you don’t add or subtract the numbers. We might be surprised what we discovered if we spent a few million quid on drawing up a simple, Suzuki/Kodaly style method of instruction to get general principles of deduction and induction into people’s heads.

While I’m at it, let’s look at the English Language syllabus.If this is meant to teach skills of written communication in a modern environment, it ought to include a significant amount of training in data visualisation. Someone who can’t create a chart these days can’t write a memo. That would be significantly more useful than the regularly advocated “training in basic statistics”; as I regularly have occasion to reflect, when you look at the absolute doosies that professors of economics and evidence-based medicine come up with, it really doesn’t make you hopeful for the creation of an informed electorate.