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Re: Is the sky still falling?
Posted:
Apr 1, 2009 2:50 PM
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> > 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
> > > pseudo-education 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 (anti-derivatives) 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 pre-existing 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/math-thinking-l/2009-February/001300.html
And in blogs:
http://controlroom.blogspot.com/2009/02/wanderers-2009217.html
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