
Re: Mathematics in Everyday Events
Posted:
Aug 21, 1994 3:18 PM


I'm glad to hear Andrei Toom's comments on "Applications". I don't agree with all of them, but I do remember from my own schooldays how bored we all were on some occasions when supposedly practical problems were discussed. It often meant merely that one had to spend some time stripping off some superfluous words to get at the real problem, which might then become more interesting (but often didn't!). I'm ABSOLUTELY SURE that Pythagoras' theorem was not "invented to solve the practical problem of adding two squares"! What it DOES solve, and probably was in some sense "invented to solve" is the much more practical (and theoretical!) problem of finding the distance between two points specified by rectangular coordinates. (To make this sound more Greek, let's say between two points lying on lines at right angles at known distances from the intersection of those lines.)
If one's students are already interested in a problem, whether for practical or theoretical reasons or just because it IS interesting, then that's the time to teach the mathematics that can help to solve it. So problems that arose from computer graphics might well motivate some students very strongly to learn some elegant geometry. In fact I know many instances where this has been the case.
I think it very much depends on who's in one's class. I worry, for instance, about the possible sideeffects of basing too much motivation on certain sports, especially the traditionally maledominated ones like baseball and football, since the interests of many girl students in particular may be slighted. Of course the answer is to keep a careful watch to makes sure that every student gets a fair proportion of topics that directly interest himself or herself, but we're not all saints enough to ensure this!
John Conway

