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: I work for one of those companies...

[siderea]

(Huh, LJ never emailed this comment to me. Hrmph!)

A question for you about your math background: were you in any sort of special classes, or was that instruction given to everybody in your school? One apparently common pattern is that the advanced kids get more "theory", but the other kids just get drill.

At the grade school I (and many of those 7th grade peers) attended, they mouthed all the right words about needing to understand. And they did things which, I suppose looking back, were meant to enhance understanding -- but they were just different forms of drill and rote learning (e.g. memorizing the communicative and distributive laws). In the end, it all boiled down to memorizing answers or methods.

Re: I work for one of those companies...

[cellio]

A question for you about your math background: were you in any sort of special classes, or was that instruction given to everybody in your school?

With two possible exceptions, I got the same math education everyone else did. The first curriculum split was in 8th grade, when some students took algebra and the rest took something called "math 8". (One of my frustrations with my school was, in fact, that I thought they didn't do enough for me. So I found ways to fill the time on my own.)

Possible exception 1: I had this tutor from the blind association for one class period a week. We did assorted stuff. We didn't do anything math-like that I can remember until either fifth or sixth grade, when we did some algebra. We did do logic puzzles and stuff like that a lot earlier; to the extent there is a correlation between logic and arithmetic, I was getting more there. On the other hand, I read (and solved) books of logic puzzles for fun all on my own, so the tutor might not have been relevant there.

Possible exception 2: my father enjoys math. I don't recall him tutoring me, and he explicitly refused to teach me "tricks", but he was all too happy to talk with me about the tricks and patterns I'd discovered on my own, and either help me validate them or show me counter-examples.

My education in arithmetic involved a lot of rote memorization -- timed multiplication drills particularly stand out in my memory. This is why I thought I hadn't been much affected by "new math", but I don't know very much about that approach (beyond Tom Lehrer :-) ) and it appears I was wrong about that. I'm not sure; I could attempt to describe what I remember in more detail if that would help.