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Re: A Proof of the Definition of Proof
Posted:
Jun 26, 2009 12:03 PM
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> Paul, asked me to clarify my definition of a proof
> and I realized that submitting a logical proof of the
> definition might be the best way to describe it.
>
Or like consider this color poster (first published in
Singapore I'm pretty sure) and used to guide reasoning about
volumes of shapes in geometry. You could say there's
something rigorous going on and the info is all validated,
nothing disputed or non-mathematical. So are we dealing
with a proof? Not a formal one surely. Last row gets into
A&B modules which I write about so much in this archive,
one of those "canary in a mineshaft" things we used to
steer a next generation of math teacher into our fold
(might be maxed out in this region, given Uncle Sam is so
ungenerous and unstimulating some days (yawn)).
http://www.rwgrayprojects.com/synergetics/plates/figs/plate03z.html
Anyway, we moved from this poster to computer animations
long ago, have the students learn to make these animations
themselves (not something for which calculators are well
suited, don't have many of those floating around). When
we talk to lawmakers about charter schools, we show them
the DVDs and say "see, this is about real choice, entirely
alternative ways of learning math that we in the Silicon
Forest think are a vast improvement over what those
charlatan snake oil people are offering." And because
what we're showing is simple enough for a well-educated
adult to follow (imagine some senator), even if not a
formal proof, they're likely to nod and agree with us,
say "yep, you'll need to use charters all right, as it'll
be a cold day in hell before 1900s type teachers ever get
around to doing their jobs".
Some of our schools aren't in the US of course. I recall
taking the above poster (back when we used posters) to
Cairo in the 1980s. The curriculum writing I did for
Bhutan, passed to Father Mackey, had this as well.
Lesotho... One reason we wanted to get this stuff
overseas was to keep corrupt USAID people in the State
Department from trying to dump old editions of textbooks
or get these kids hooked on nasty old calculators and
the dead tree texts that go with 'em.
Now that they're hip to the above (U Thant knew about
it), they can just go to the United Nations and say "look
at the crap the Americans are pushing, LOL" i.e. we have
set some standards outside the US that will help keep the
inferior Lower48 stuff from dragging the others down.
Same with the XO. Even though most people don't have
them, they know MIT is behind computers, not calculators.
OLPC is probably the only program that's giving USAers
much respect in the world, otherwise seen as knuckle
dragging Borg wannabes, belligerent and stupid (and if
you check out their "math curriculum" you come to see
why).
Kirby
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