The other day I read an interesting interview with Freeman Dyson, renowned physicist and general ideas man. Despite being highly mathematically competent himself, he comments that maths as we know it shouldn’t really be taught in schools, as it is a specialist skill.
That is the kind of statement that gets the hackles up of people who work in, for example, engineering or coding. They talk about how indispensable maths is in their work and I don’t disagree. What isn’t being recognised is that these are specialist professions which require specialist skills. School teaching, for at least the first ten years, needs to be generalist in focus as we don’t know what destinies the students are bound for.
I think the question we need to answer is what mathematical skills are required for the general population. What do we need to live in the modern world, independent of the needs of our professional life? These are the skills that should be emphasised, and specialised skills taught in the last few years of school, if at all.
Basic arithmetic. No-one gets very far without a robust toolkit of basic skills in order to do everyday life activities such as buying and selling. Addition, subtraction, multiplication and division are the big ones. The emphasis here should be on a multiplicity of approaches – if a student has an idiosyncratic method which nevertheless gets the right answer, that is great.
Basic algebra. Most people get along just fine without calculus, but it’s really useful to be able to wrangle a few simple a + b = x problems.
Basic geometry. At some point in their life, everyone has to measure and build something, and needs to know how physical shapes interact. This might involve some very basic trigonometry, but not much more. If medieval people managed to build cathedrals with basic geometry, most modern adults will be fine.
Lots of probability and statistics. I think that training in probability is one of the most important things to be educated in. Our modern world relies on being able to determine which of two events is more likely, whether it’s in the casino, in elections, insurance, and all forms of planning for the future. In particular it is nearly impossible to be scientifically literate without being able to understand simple probability and statistics. This may sound like special pleading but for most of the wicked decisions we have to deal with as a civilisation the answers aren’t clear. We need probability and statistics to interpret the evidence.
So why do we continue to teach maths beyond the basics? Generations of kids have whined about how they’re going to use calculus in the future, and I think they’re right. Why do we teach it?
It seems to me that much of it is a hurdle requirement. Each time my local firefighting service hires professional firefighters, there are so many applicants that they have to thin the list some way in order to avoid conducting 3000 interviews. So they set the fitness requirements absurdly high, generally much higher than are required for the job itself. I suspect that late school maths is the same – it is being used as a way of separating out the clever kids from the less clever ones by teaching a skill that is only useful for very specific populations of student.
Apart from overhauling the curriculum, I feel that we need to put a lot more thought into how we separate the wheat from the chaff. Just as medical schools realised years ago that high marks are a poor proxy for whether someone will make a good doctor, maths-as-performance-art is the wrong fork in the road.