"Math Emergency"

[jsburbidge]

 The Globe and Mail thinks that Ontario is in the throes of a math emergency.

 

What I see elsewhere indicates that we aren't particularly out of the pack of the rest of the western polities regarding the maths performance of young people.

 

From where I stand we've always handled mathematics badly - and a return to the basics of drilled arithmetic seems to me a prescription which in no way suits the current situation.

 

I was in elementary school at the height of the New Math period, so we got some very, very early exposure to the idea of algebraic structures like groups (they then mainly went away again until university, with the odd few-week refresher along the way - modular arithmetic in Grade 6, for example, and maybe a bit of rings and fields at some point in Grade 13 Algebra). Other than that, grades 1-4 were largely taken up learning addition, subtraction, multiplication and division, and grades 5-8 solving problems using those operations. Only in high school did we progress to algebra (well, polynomials), functions, and the like.

 

In retrospect, it is clear that the driver of maths in school was not the subject in itself. In primary school, everything was really focussed on giving everyone the practical skills they needed to survive - make change, go over home accounts, estimate work to be done, handle recipes - which explains the otherwise insane emphasis not only on word problems but on problems using the more obscure relics of the Imperial system (I don't think we had to deal with hides) to encourage fluency through arduous practice. In high school, it was the subset of math useful if you were going to be a chemist, engineer, or possibly (at the low end) a sociologist or an accountant.

 

Ghosts of this sort of thing remain - the current Grade 9 science curriculum wants to talk about energy in kWh rather than joules (or, worse, electron volts) because the bulk of the students will have to deal with appliances and few will become physicists or chemists.

 

The high school maths curriculum in Ontario was driven by what was required for science and engineering (whence the choice of Cartesian rather than Apollonian conic sections) or for accounting (Grade 13 Relations and Functions, the course people took even if they didn't want to be scientists, engineers, or mathematicians, had a large block of calculating annuities and present value, which is still there in Grade 12 functions). A systematic treatment driven by what a mathematician would see as important or even interesting was brushed aside.

 

To a close approximation we have never taught mathematics as a discipline in our schools. (And if we had, few would have prospered at it, though possibly more than currently become serious mathematicians.)

 

Of course, much of this has been blown away by the prevalence of calculators and Excel (and now by AI which can do your factorization homework for you, albeit unreliably), and I don't think that the Ministry or OISE worked out how to respond, looking at my daughter's curriculum of a few years ago. My own advice would be to have long units covering things systematically, with more (real) algebra and geometry, as I think that that's the best way of bringing out the appeal of mathematical systems; and even slow students would be aided by longer treatments of connected ideas rather than the flitting from topic to topic they now get in elementary school.

 

Except for one thing. Some significant chunk of the population has a nearly complete inability to think abstractly, and true mathematics is almost as abstract as it gets. (Not quite; there is always philosophy. For real abstraction, go to Duns Scotus.) The old curriculum's math was entirely concrete: here are mechanisms for multiplication and long division: memorize the times tables by brute force and you can mechanically apply the rules whether you understand them or not.

 

Concrete math is now considerably lightened as a burden. You still have to understand some things - back of the envelope estimates to know when you're wildly wrong, and what the various Excel functions actually do so that you can deploy them intelligently - but most actual work is carried out by, essentially, moving around building blocks.

 

It's not that we can simply dispense with classical arithmetic. It's the most generally useful part of mathematics, and having a basic understanding of it is basic to some skills we really could benefit from having the broad population know. (Decent evaluations of risk, for example. Humans are crap at risk evaluation and have to learn it carefully, beginning with Bayesian probabilities.) But accepting the fact that about half the population isn't likely to get beyond that, and maybe deciding, once and for all, not to hold back the competent students in favour of Deweyan group promotions might be a more important step than panicking about a "math emergency" we share with most of the rest of the developed world.

Comments

[graydon]

I have a supposition about this.

Time was, women could not get jobs other than teacher or nurse. (On the whole and by and large, and maybe I should say "respectable" jobs, there.)

Once that restriction goes away, a lot of women who like math go become engineers and accountants; the pay is better and the prestige higher and the working conditions better.

Primary school math education becomes something universally taught by people who don't like it and who very often think it is unnecessary and otherwise fear it. Run that for a few generations and liking math is a rare thing that marks you as not quite the thing, socially, and which really depends on having the luck to have parents who will drill your times tables with you.

(The solution is not to remove women from the other profession jobs, though I wouldn't put it past this Ontario government to go there.)

The other thing that sticks with me is that two hundred and fifty years ago, people made money running schools to teach high-school age children enough spherical trig to navigate a ship. I think seeing the immediate material use matters a lot, and there's a lot of room to put that into the math curriculum. Abstract is all very well but no one learns things that are too many conceptual jumps away from their experience.