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

tangent

[cellio]

But then, that leaves the question of what happens to the other 25%! What about the kids who are good at abstraction and weak on concrete operations?

This is, of course, a problem that goes well beyond math, and gets to the whole question of when it's ok to cater to the majority and what you owe the minority. I felt largely cheated by my school system because they had no accommodations for people near the tails of the bell curve; it was very much a "one size fits all" approach. I don't know what the answer is; even if it were practical for every student to have an individual, tailored experience, I don't think that would be ideal either. Somewhere in there you also have to learn about compromise and getting along in community, too.

Re: tangent

[siderea]

Yepyep! And that raises some very fundamental questions about (1) how a society allocates resources in general and (2) just what is universal education trying to achieve.

If we are educating kids to a certain standard.... why do we have (or try to have) all kids stay in school until 12th grade? And why do we then throw kids out at age 18, whether or not they've met the standard?

Or are we providing an educational opportunity from ages X to Y, during which kids are entitled to make the most of themselves, whatever that is?

Are we trying to prepare a mete workforce for the exigencies of the 21st century? Are we trying to unleash human potential? Are we trying to educate an electorate?

What is the purpose of the enterprise? And how will we know if/when we're achieving it?