math education

[cellio]

Being of a certain age, I learned arithmetic the conventional way and neatly dodged New Math. I knew things had changed since then -- at least in the ability of high-school graduates to do arithmetic unassisted -- but I didn't realize just how strange things had gotten. amergina posted a link to this (longish) news story broadcast: math education: an inconvenient truth. Sigh.

To summarize, some (apparently-big-name) published curricula are now skipping conventional methods to teach new ways of doing arithmetic. Some are different ways of breaking down the problems; others are primarily notational differences. All of them seem, on average, slower and more error-prone.

Now granted, I sometimes do arithmetic by the "reason through it" process the reporter dislikes (what did they call that, clusters?), but it's kind of specialized. For example, a 15% tip reduces to a 10% tip and half again; that's fast and easy. If I'm multiplying by a number ending in 9 or 1, it's often easier to reduce to another problem and then deal with the leftovers. If I need the square root of 4862 (I just pulled that number out of thin air), I can't tell you exactly what it is but I know it's a bit less than 70. Sometimes I think in patterns like that. I think this is a fine thing to teach people after they have mastered conventional write-it-down-and-work-it-out methods. Not before, and certainly not instead of. (And I think it's better if you can give them an educational environment in which they figure out these "tricks" for themselves, like I did.)

I assume these new teaching methods (which include "use calculators") are largely responsible for many people being unable to get order of magnitude right. Those of the previous generation undoubtedly said that about the move away from slide-rules, but I never used a slide-rule (except as a novelty) and I can approximate... I once had a calculator-armed teenage clerk at a produce stand insist that my bag of vegetables came to over $200. Even if he had no instincts about what vegetables cost, he should have been able to tell that the price codes he'd read off the list didn't add up to that and maybe he'd mistyped something.

(When shopping I tend to keep rough a mental tally, so when I get to the check-out I know approximately what the total should be. I gather that this is unusual. It's just the way I learned to shop, probably from a time when you had to make sure you didn't exceed cash on hand. Now I use plastic for everything, but the habit remained.)

Well, I guess I can take comfort in one thing: if what they say about mental exercise is correct, I should be pretty close to immune to Alzheimer's. :-)

Comments

Re: teachers and administrations have a part in this

[cellio]

Hi Valorie!

To clarify, my school experience involved a lot of rote memorization and timed drills. But there was other stuff on top of it; we did do area, and I remember the number line pretty early, and of course word problems (don't know if that's "new" or "old"). I don't remember precisely how I learned that, say, multiplication is commutative, but I have a sense of it being "show, not tell". I don't remember any unconventional notation (like lattices).

If parents and, especially, teachers and administrators don't do their jobs, none of the rest of it matters. I guess I was lucky there; while I don't remember my father the math fan teaching me (and he explicitly refused to teach me "tricks" or rules, because I should learn those on my own in due time), he was certainly available to review homework and answer questions. (My mother is not so mathematically inclined, but she indirectly supported my math education: when we went grocery shopping it was my job to tell her which package to buy for the best price, from a pretty early age, long before stores started posting the price per ounce.)

I'm rambling; sorry. :-)

Your story about teachers unable or unwilling to learn the material saddens me, and you're right that in that case the curriculum doesn't matter. I suppose I have an unsupportes sense that if that's the situation in your school, you're probably still better off sticking with the basics just because it's the most common approach and, maybe, some future teacher will be able to fix your students (and that that would be harder if you used techniquest that future teacher might not know). But talk about playing to the lowest common denominator... :-(

How practical is it to get parents (= voters) to go along with an eight-year experiment?