Back to blogging!
I finished up all my summer obligations on Monday. I'd been teaching integral calculus, the second quarter of the U of Washington's three-quarter calculus sequence. It was a bit depressing: while some people did well, lots of people did, as it were, not so well, and they did not so well in ways that really bugger belief. I think that a fair number of people just didn't have the kind of math background necessary to do a course in calculus: most especially, they were terrible at algebra. This fits in with a general pattern I've noticed, through my time as a TA. People get into the UW with good grades and high test scores and try to jump right into calculus and still don't really know how to do simple algebra. We're not talking finitely-generated abelian groups here; we're talking simple simple, high school algebra. Nobody has ever taught these kids how to do math. (Their grammar's really weak, too.) The impression I'm left with is that high schools now are, by and large, even bigger jokes than they were when I was a teenager. This is quite sad.
More worryingly, lots of people seemed to have a lot of difficulty with slicing arguments. Every problem in integral calculus essentially works in the same way: take your problem, slice it up into little chunks or rectangles or cross-sections, solve the problem for each chunk or whatever, add up all these infinitesimal solutions to give a global solution. We used this sort of argument in every single application of integration we considered. It's a general template that should make integration problems really really easy to set up, and yet a lot of people never seemed to 'get' it. They'd write down the formulae that popped out in the end, but they'd have endless difficulty using them because they didn't seem to think about where these formulae came from. I probably didn't do a very good job explaining this because it just seems so natural to me, but even so...
They weren't picking up on the underlying logic.
Let's be honest: most people will never use any kind of (remotely) sophisticated mathematics in their lives. They won't have to find roots of polynomials. They won't need to integrate trigonometric functions. They won't need to optimise. Basic arithmetic will suit them just fine. But the habits of thought they could pick up from basic and well-designed primary- and secondary-school math courses would be invaluable. It's not the content that's most important for the average hominid, but the technique. The most important thing someone can pick up from even a cursory study of mathematics is the ability to differentiate between sound and faulty logic, or reasonable and bullshit arguments. It's so easy to learn these habits of rigorous thought by doing mathematics; everything in mathematics is so clean, and it's so easy to separate the wheat from the Chalabi. Mathematics is a wonderful, ideal playground for the exercise of the rational faculties, and once the habits of logical thought are ingrained, it becomes almost trivial to import them into real-world problem-solving and decision-making.
Mathematics trains people to be rational entities.
Or it should. America seems to be failing miserably at this.
Americans just don't know how to think. It's really the only conclusion one can reach, especially if one has been paying any attention to politics. This whole Swift Boat Veterans for Utter Bullshit thing, for example. Or Ann 'the Man' Coulter, who still apparently has some kind of career. Or this ghastly Michelle Malkin creature, peddling on the basis of shoddy dishonest research a book defending the internment of Japanese-Americans during World War II, who tried to imply on cable television that John Kerry's wounds in Vietnam were self-inflicted. (At least the host smacked her down for that one.) Or listen to any single thing President Bush has ever said in his life. It's all bullshit. The right wing (I'm generalising, of course) in America isn't offering up any kind of rational, defensible argument in its own favour, but simply pouring thick liquid bullshit like foul, foul syrup all over everything in sight. You can't debate people who work like this. You can't ever win. What else can you do but try to marginalise these people and exclude them from the discourse, and what kind of way is that to run a democracy?
This country is so fucked.
If only people learned more math...
Posted by aloysius at August 26, 2004 03:25 PM | TrackBack |