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Re: Is the sky still falling?
Posted:
Apr 1, 2009 2:50 PM


> > On 31 Dec 2008, Dom wrote: > > > > > The article by David M. Bressoud at: > > > > > > > http://www.ams.org/notices/200901/tx090100020p.pdf > > > > > > provides more evidence of the continuing > > > pseudoeducation of American students. > >
I agree that calculus isn't that fun to just play with, and so fails to induce that constructivist mindset, which a few seem to have no matter how objectivist the curriculum, but in the remaining 98%, in math especially, the word "induce" is indeed apt, even better than "motivate".
What's missing of course is any taking up of the question of how to develop dogged tenaciousness, aptly circled by Kaplan & Kaplan (Out of the Labyrinth, OUP 2007) i.e. what forms of play *are* fun and more within range? Yes geometry 'n stuff, as they said, but the authors above skirt the issue of learning to program, vs. simply punching calculator keys and/or scrawling in pencil, then checking the back of the book. Let's take control of that silicon and keep our sciences alive, how about?
I take it for granted that (a) some math labs already put a generously sized screen not far from the face or (b) use a projector slaved to a computer of some kind (not just a calculator). Ergo it follows from (a) and/or (b) that in math class especially, it'd be silly to give Polyhedra a wide girth (as many 10th grade teachers have been doing until now). We need those Platonics, Archimedeans and Johnsons, I won't say how at the moment, just that we need them.
OK, now I'll say how: here are your vectors, your rotation matrics, your symmetry groups (permutations), your trig (omnitriangulate if you don't see 'em), your XYZ space or other scaffolding for graphing / plotting whatever curves, and derivatives (antiderivatives) thereof. I.e. with these Polyhedra, and the guts it takes to make 'em scale, rotate, translate, trace great circles, you get at least 69% of the preexisting objectivist curriculum, including big chunks of calculus. All we've added is something to play with, sink teeth into, fight with (debug). We've added a computer language (gasp), both state of the art (best of breed), and free (as in beer, as in liberal too), so why aren't we using one?
Because this is the Lower48, that's why. We're not known for our intelligence around here. Elsewhere though...
Kirby
** more of my Lower48 rhetoric (unlikely to score me many votes as a politician, except maybe in Oregon (we're elitist, think it's really Lower47 that's nitwit)):
http://mail.geneseo.edu/pipermail/maththinkingl/2009February/001300.html
And in blogs: http://controlroom.blogspot.com/2009/02/wanderers2009217.html



