The Ontario Government is getting into a frazzle about the failure rate of public school students in mathematics, offering bonuses for teachers doing skills upgrading. Fingers have been pointed at the teachers' math skills, their math teaching skills, the curriculum, and other possible culprits.
There is, of course, a long-term issue with teachers and math skills, in that someone with good math skills coming out of university can find more attractive areas to specialize in than teaching.
However, I have spent the past several years watching my daughter deal with the curriculum, and I do think that there is a problem with it: it fits the needs of almost no children. It flits from topic to topic in such a way that students who have difficulty do not get enough drill to master the issues; but it also allows for no real exploration of the issues by students who are good at math, for the same reason.
They will have a two or three week unit on series, for example, which could be extended to any number of
interesting things to explore; but then there will be a sharp break and they'll move on to an equally short unit on, say, geometry.
And while we're on the topic of math skills in the general population, maybe we should ask: what skills?
A few weeks ago I was on public transit and saw an ad designed to popularize the idea of a need for math skills. The example problem it gave was a simple word problem of the sort which requires conversion from words to a simple polynomial and then solving for x. It was soluble by someone with high-school math trivially. But I thought: for someone who does not work in the sciences or engineering, where is that type of skill necessary? Certainly not in everyday life; nor, I think, in accountancy or other similar fields, where numbers tend to be delivered and manipulated in quite a different way. So for a student with an interest in (say) history and languages, there's no obvious reason for this sort of skill to be considered a critical one: yet the provincial curriculum makes it important. In contrast, estimating probabilities and risk in a back-of-the-envelope manner is probably more important in day-to-day life; humans are notoriously bad at it. Understanding some of the underlying issues around encryption (such as the difficulty of factoring large primes, or the ease of doing frequency analysis) is becoming a generally useful skill set (not the ability to do it, but the understanding of what is hard and what is easy).
Students who have the potential to be good scientists, mathematicians, engineers, and the like need a far more challenging, ambitious, and interesting curriculum than we are giving them. (A genuinely competent 17-year-old should be able to handle
Hardy's Course of Pure Mathematics if properly prepared.) Students who are not going there need only a fraction of what we are shoving down their throats. (When was the last time I really needed, say, trigonometry at the high-school level? I don't have to measure very many things by angle-and-one-side mechanisms; either I need more -- Fourier analysis, full-blown trigonometric functions, etc., or I need none.) And the relatively rare students who have the ability but are interested in everything -- literature, history, philosophy, and languages as well as maths and sciences -- can handle the more difficult stream and benefit from it.
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