Friday, April 06, 2007

Hey, what's it to you?

Math's not for everyone, for sure.

But I get the feeling that more people would be gung-ho about mathematics if they'd not been actively turned off to it somewhere along the road from K to 12.

Last week those cute little kiddies in my Super Saturday program got visibly excited about the L-tiles I had them playing with. They really went to town on those suckers.

I mocked these babies up out of particolored poster board to work on induction with the 280 folks earlier this semester, and I realized then that they'd make a great toy for introducing fractals to the Super Saturday kids. Thus I spent several hours here and there during the past few weeks cutting out a few hundred more tiles, giving myself enough stock to build truly titanic Ls.

And so we did, last Saturday. Five of the seven in the class eagerly worked away, fully cooperating with one another, offering friendly suggestions and pointers, gradually piecing together the L10 monster with 100 tiles in it. (Meanwhile I had to keep the other two from braining each other with a half-empty bottle of Aquafina.) It didn't take long for the sharpest among them to detect the patterns one needed to build larger and larger Ls; if I'd let them, I'll be they would have started work on the L20, though I doubt I had enough Ls to make that one work.

So here's my question: how is it that five bright elementary schoolers were more excited about mathematical discovery than a roomful of math majors? Granted, the stakes are lower in Super Saturday: no assignments, no grades, no deadlines, not to mention the fact that the young 'uns are simply living one of the most carefree periods of their lives. But all that aside, aren't math majors supposed to...oh, how shall I put this? math? When faced with designing larger and larger Ls in our 280 class, the reaction from many was disinterested torpor. A few were definitely engaged, but most looked on languidly.

What do we do to these poor kids before they get to college?

We teach them to take tests.

We teach them that math is hard, and only really smart people can do it.

We teach them that "proof" and "poorly-taught high school geometry" are synonymous.

By the time they get to my calc class, I've got to do all I can to convince them that if math isn't fun, then at least maybe it's useful.

Today I found myself explaining to my Calc I kiddies why it is we care about minima and maxima, and like a good little moneymaker, I pulled out the example of a profit curve. A good example, and a sure justification for differential calculus...but why not care about Fermat's Theorem for its own sake? It's a really beautiful theorem, and the road to its discovery is a storied one involving the arduous work of many of history's brightest minds.

I could have said this, yes, but the cold I'm trying to kick has taken the edge off, and I didn't have the energy to fight today what might in most classrooms be an uphill battle. (Would it be so in my classroom?)

Tomorrow morning my Super Saturday kiddies and I are going to work at building a model of the Menger sponge, a "3-d" fractal that we'll put together out of 400 tiny cubes of paper that we'll fold ourselves. You should have seen how stoked these kids were last week when we made that our plan.

Next week, what? Codes 'n' cryptography? More fractals? Who knows.

Next week in 280? Relations. Beautifully flexible, eminently useful: order relations alone make the careers for hundreds of brilliant mathematicians (and in no small measure have contributed to my own).

Why can't they love it as much as I do?


eliz said...

I can't speak for everyone, but I thought the L activity was fun. However, you broke the whole class into just two groups, so there were like 10 people trying to do the same thing, which makes it hard for those of us who don't like speaking up. I really enjoy trying to solve puzzles, but there were just too many people that I had to take a back seat because there were too many ideas going around to actually do anything. So I just sat and watched and drew my own design on my paper. It wasn't that I didn't want to do it, because I did, it's just that if I try to get an idea out, there are too many people that I probably won't get a chance to finish my idea before getting interrupted so why even try?

DocTurtle said...


Word! You know, you're right, I hadn't even thought about that factor.

A great big mea culpa on that one. If I'd had cut out more of those damned things by that point, it might have worked out better, huh? You think I should have a do-over now that I've got more of them?

Update: Today's Super Saturday was called off due to snow, so the kiddies will have to wait another week before their Menger sponge comes to life.

Chris said...

Well, as a student in this Calc 1 class, I'd just like to let you know that I personally am interested in the content, even if I don't show it. As far as projecting my thoughts and ideas, I guess I'm nervous about their validity? Sometimes I say things wrong, even though I know the right thing. I have a friend who can be a bit pompous at times (he's a good guy though). He uses the energy from that to propel what he's thinking in a sense; people listen to him automatically, as they sense someone who knows what he's talking about.
I am unsure about the uphill battle. It reminds me of a Kate Bush song though. Maybe use a scare tactic or something to jar the class into action.