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...

[sui66iy.livejournal.com]

Yeah, and the questions aren't only relevant for young students. Many college professors aren't really teaching per se. They're often better resources than they are teachers, but that leaves success to those students who can figure out how to extract the knowledge.

Here's a (weak and naive) analogy: in elementary school, they teach you how to use the library. Rather than have you read every book, they teach you about card catalogs and where the reference section is and so forth. Supposedly, then you can go and find the knowledge you need when you need it. But teachers are resources like libraries, and so is your own learning style. I wonder if there's a way to teach some sort of meta-learning skill.

I sometimes wonder what college would be like if I went back now. On the one hand, my brain is probably less flexible, but on the other hand, I'm a lot more mature and have a lot more experience teaching myself...

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

[siderea]

But teachers are resources like libraries, and so is your own learning style. I wonder if there's a way to teach some sort of meta-learning skill.

Heh. http://siderea.livejournal.com/440902.html

I sometimes wonder what college would be like if I went back now.

Hehheh. I'm running that experiment now. I've returned, at the ripe age of 35, to college to finally get a degree (this time). Things are much better this time, for a whole bunch of reasons, but not least because I've gotten over my past schooling and become an autodidact. Apparently, this is normal in "adult learners", according to the returning student orientation materials the school gave me -- and backed up by my experience in all-"adult-learners" classes. The grown-ups are voracious and keep the profs on their toes. They'll show up with their own learning (and other) agendas and hold the profs accountable for meeting them. They're no little bit cynical and know how the world works, and have an attitude of "I'm paying for this, so you'd better live up to my standards." They butt into lectures to demand clarifications. They raise contradictory examples to challenge professors' examples. They have no problem saying, point blank, that school has to take a back seat to work/kids/etc. when they feel it does. They're intensely involved in the classroom and with the material, just like professors always are saying they want. As one prof put it, "The up-side is you guys bring an incredible wealth of experience and engagement to the classroom. The down-side is, damn, ain't nobody can tell you guys nothing!"