Curricula

[jsburbidge]

 In the aftermath of last night's leaders' debate, Metro Morning had a discussion regarding the two elements of the elementary school curriculum which Doug Ford has announced an intention to change.  Unfortunately, the discussion was shallow and unenlightening.

 

On the sex ed. front, the interviewee mainly kept repeating the (entirely true, but unhelpful) point that there had been many years of consultation on the curriculum (in fact, there were two phases: once when it was being developed and once when the government got cold feet about introducing it in the wake of pushback from (mainly religious) minorities). The problem is that, regardless of whether Ford uses it as an excuse or not, "consultation" is not the issue with the curriculum.  The issue is that although the updated curriculum has moderate support from a majority of the population – and many people feel it does not really go far enough in responding to the context of the present day (Internet, changing mores, etc.) – there is a minority of people who will not accept it regardless of how much consultation is done.

 

These are small-c conservatives, almost entirely belonging to conservative religious groups (Roman Catholic, Eastern Orthodox, Evangelical Christian, Islamic, Orthodox Jewish, at a minimum). In general, Canadians tend to keep religion out of the public square, and in this case the compromise was to allow parents to withdraw their children from the relevant classes if they object to them.  This, of course, begged the question of the public policy objectives in having such a curriculum (a matter which the radio show also did not address) and the question of whether those aims effectively demand that the education should be universal. (There is some evidence that, on average, parents are much worse at providing this sort of education to their children than third parties are; there is also the aim of ensuring that everyone has a basis of the same common knowledge on matters of general importance in daily life; finally, there is the relation between this sort of education and anti-discrimination goals with regard to GLBTQIA individuals.)

 

None of this level of substantive analysis was provided, or even gestured towards. Nor was there any discussion of the politics of the matter. (Patrick Brown had avoided taking this kind of position on the entirely rational basis that the people who are opposed to the curriculum changes are almost all committed Conservative Party supporters in any case. It won't gain votes, and it may scare some away.)

 

On the other side, the person addressing the math curriculum issues was, if anything, less helpful still.  Again, they failed to address the (divergent) aims being served by the current math curriculum, and in particular why none of those aims matches, any longer, the drill to which Ford wishes to return. Or, indeed, why extensive drill has gone from being a desirable part of the math curriculum to a largely irrelevant one

 

In my day, almost all of grades four to eight was taken up in repeated drill with arithmetic and "word problems", frequently involving converting between Imperial measurements which we had never otherwise heard of. This was genuinely important because, at the time, it was (justifiably, based on knowledge then) assumed that any arithmetic anyone did for the rest of their lives would be done with pencil and paper (the fringe exceptions – slide rules and room-sized computers – were irrelevant, as they would be used only by math whizzes (engineers and scientists) in any case).  Really solid drill was one of the core components in a curriculum aimed at providing basic literacy and numeracy in a world where these were literally life-critical skills.

 

Then calculators came along.

 

Then they became so cheap they were given away like cereal toys.

 

By the time I reached the end of high school, my chemistry teacher was telling us that we needed to make an order of magnitude approximation on the back of an envelope before using a calculator (or slide rule - some of us still had them) to ensure that we hadn't made any stupid mistakes and were in the right ballpark. 

 

I'll grant that the primary school math curriculum is a mess. Having spent years assisting my daughter with her homework (which was not, pace the commenter on Metro Morning, at all difficult to do) I consider it to be very poorly structured. It flits from one topic to the next, never providing enough of a continued development of a topic to get interesting, or indeed to provide students having difficulty with an extended period of connected work.  On the other hand, it isn't any better at giving an idea of what really doing math is like than the old curriculum. (A mathematician is not particularly concerned about whether 7x8=56.  The concern is rather (1) with defining the operation of multiplication (2) showing it's commutative, associative, and distributive over addition, (3) showing that you can even get to a number like 56 generally on the number system using mathematical induction…)

 

From the point of view of learning real math it would be more sensible to give kids a term of working with quaternion or vector spaces rather than a term of drill in arithmetic.  On the other hand, very few people become real mathematicians, and only a relatively few more become physicists or other scientists who have to have a clear sense of, say, sophisticated symmetry groups.

 

A few more percent of the population become engineers, accountants, and others who, frankly, apply recipes and can normally rely heavily on computers to do the grunt work for them. (The engineers still need to learn analysis and Fourier series and the like in order to know how to solve certain sorts of problems numerically. But they don't need to be able to multiply.) They're not interested in number theory, abstract algebra, or foundations, though, except maybe as hobbies.

 

Almost everybody needs good education in doing things like back-of-the-envelope risk assessment, because humans are really bad at it, and it's important in everyday life. They need to have a gut sense of what compound interest does in order to make their way through the commercial financing world. They need a basic ability to structure simple calculations to feed to a calculator to determine things like how much paint you need to paint a room. They need some basic geometry to do certain kinds of practical handiwork.

 

This suggests that there should be three different math curricula, with only one subset being universal. How you stream or switch between them is another problem. (It wouldn't matter very much if a significant chunk of the population weren't demonstrably poor at thinkingabstractly, which makes them far more likely to struggle at math.) 

 

In none of these cases is a great deal more drill useful. 

 

As an aside, and while on the topic of small-c conservatism and curricula, I'd think that the obvious place to focus is very different: it's the humane letters curriculum, that is, in school, mainly English and History. Not only is it a quintessentially conservative concern to have the school curriculum inculcate solid cultural values but it is also traditional to inculcate those values by means of attention to European and particularly English literature and history. The recent decision to drop mandatory Shakespeare studies as part of the high school curriculum would, I would think, be a scandal to a well grounded traditional conservative. In addition the focus of the current curriculum on exclusively Canadian history and principally Canadian authors departs in its aims from the Conservative pattern of going to the "classics" for education: if not Homer, Sophocles, Virgil, and Horace, than at least Shakespeare, Milton, Pope, and Wordsworth. And a solid argument can be made for expanding the scope of a student's view so that it takes in people who thought and acted very differently, as shown by either their writings or their deeds. I could get behind a pledge to bring back Classics, and give the curriculum a larger spine of world literature and history. 

Comments

[ndrosen]

I largely agree with you, but I do wonder whether there was some real benefit to lots of math drill. Someone who has practice with multi-digit multiplication and division on paper, and who understands why the techniques work, is better equipped to understand algebraic multiplication and division, and to grasp whether figures being thrown at him make sense, or could not be even approximately true.

[graydon]

When the scope of career available to women stopped being "teacher or nurse or secretary", the teaching profession more or less lost everybody who likes math. There are individual exceptions, but statistically, every school teacher for a couple generations now is someone self-selected for not liking math. If you want kids to like arithmetic and learn it effectively, you have to make teaching pay as well as engineering or accounting as a necessary-but-not-sufficient precondition.

[jsburbidge]

There were exceptions. My high school calculus teacher was a male with an M.Sc. from Queen's who had presumably gone into teaching out of interest.

[graydon]

I hit some exceptions, too, but in general? And especially in early grades? Systemically, math is not something anyone likes or wants to teach.