"Math Emergency"
Jan. 5th, 2026 07:43 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
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.
no subject
Date: 2026-01-06 03:43 am (UTC)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.
no subject
Date: 2026-01-09 02:45 am (UTC)I note, as sn addendum, but relevant to your comment: the author, who is at OISE, essentially argues that the difference between math achievement in the current set of students relates solely and only to the levels of explicit support the better-achieving students get - tutoring, patents who assist with math, etc.
This may be true for a chunk of the population, but I feel edited out. I recall no particular assistance from my parents when I was in elementary school learning math; what would have been the point? In high school, there were significant periods of "don't bother coming to class, just practice on old Junior Math tests". There are, and have always been, those of us with a natural aptitude for math. Teachers can certainly be of assistance, if leading through spherical trigonometry or integrating along a curve in complex space; but not at the level the author is dealing with.
A century or so ago, about 1% of the population went to university. A small subset of those people did mathematics (my grandfather, interestingly, among them, although he ended up as a Methodist minister after taking the graduating prize in Mathematics at Mount Allison). I'm not sure we're doing any worse than we used to do, when primary school math was all arithmetic drill. I think that overall we're still doing somewhat better.
no subject
Date: 2026-01-09 03:18 am (UTC)I think the drill did a lot of people somewhat better in terms of being reliably able to do something, even if it was very basic arithmetic, than we now do. (I took industrial woodworking; it had required remedial math, and it started with positional notation. It needed to.) In terms of overall transmission of knowledge, perhaps we are doing better.
And, yes, there are folks with a high aptitude, but (cynically) it's better for them if the system doesn't notice them at all, at least pre-University, and it's also not how you want to be designing the system generally. That has to have some measurable of success it doesn't make an objective, and perhaps that's much of the present trouble; no one agrees on what students should be able to do. (If there is agreement, things tend to work OK. Or at least that woodworking math course did produce people able to manage fractions and the other calculations required for furniture layout.)
no subject
Date: 2026-01-09 07:23 pm (UTC)More specifically, I am not familiar with Ontario's way of doing things, but I am familiar with US/Chicago and pre-1990 Romanian secondary education and there is one thing both got right: tracking. I received zero help from my parents with my science learning although I got some encouragement from my father, but I think I did as well as I did and did not get stuck with the general mediocrity because I got tracked starting with end of grade 8. Of course, I am but one atypical data point.
As to human's poor grasp of risk, I will always remember the Monty Hall vos Savant story as no better illustrator of the utter failure of even her more learned "peers" to grok such a deceptively simple probability problem.
PS: Here is the unpaywalled oped for those that don't have access to the Globe: https://archive.is/On1za
no subject
Date: 2026-01-10 11:12 pm (UTC)I was tracked - sort of - for one year. When my father was on sabbatical in France and I would have been in Grade 12 I was placed in Seconde based on my age, and, on the assumption that adjusting to math and science would be easier than adjusting to French Literature, I was placed in the C (Math/Science) stream; but because a couple of courses would have been recapitulation of what I would have done, they swapped them out for A Stream French Literature courses (A being the literature and humanities stream).
This actually ended up highlighting the problems an equivalent French student would have had with the streaming. I enjoyed the Maths - mainly, to my recollection, two-dimensional vector spaces, which I still think of as "espaces vectorielles" - but I also not only enjoyed but did well in the literature courses. (At one stage during the year our (C/2nde) French teacher looked at the Carnet de Notes and remarked "I see that the Canadian placed above you all again on your recent maths test." When someone had the temerity to object that that was probably because I'd had different and better prior schooling in mathematics, she responded: "Does that explain why he's doing better than the rest of you in French as well?")
A student who wants to do literature, and classical languages, and math or science, is not well served by a tracking system based on type of studies. (Tracking based purely in general skill is more like acceleration.) I managed to keep some involvement in all three areas, plus a bit of French Literature, as an undergraduate and had to specialize only in graduate school.
Tracking
Date: 2026-01-11 02:45 am (UTC)Early 90s, as I transferred to the Chicago public schools, I had the opportunity to be tested for placement in AP Calc, AP physics, Honours English and COBOL programming (as I was too late to register for Pascal language), all within three semesters only.
While the tracking in Romania was stricter (all 72 students in track A at my high school had the exact same curriculum for the four year program), and quite soft in US (more akin to a semi-tracking system known as ability grouping), I think there was enough wiggle room in both systems not to be typecast.
If most Ontario schools already have at least ability grouping opportunities, then IMO the problems are not so much with the education system, but with everything else around it: culture, family, peers, society, etc.