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Topic: Perils of Modern Math Education
Replies: 19   Last Post: Jun 21, 2007 8:44 PM

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Kirby Urner

Posts: 4,713
Registered: 12/6/04
Re: Perils of Modern Math Education
Posted: Jun 20, 2007 2:53 PM
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I don't recall the integer based sqrt algorithm,
akin to standard long division in structure,
featuring in any of my K-12 text books for
teacher led discussions. Here in this archive,
I squandered a piece of my adulthood learning
it late and rewriting it in Python so I could
make it go faster. I don't regret the exercise.
I'd be happy to do it again here sometime.

Going back to my standard line: I think the
college math buffs will have an easier time
recruiting from my geek corps of gnu math
graduates. They'll not be soured on the
subject, plus appreciate the historical
significance and ongoing importance of such
as the square root algorithm, Euclid's for
the GCD, completing the square, along with
more recent algorithms for finding a convex
hull, linear programming or whatever.

But it'd also be clearer to them, as it's already
apparent to us, that this version of K-12 quite
appropriately has no "boot camp" for wannabe
mathematicians, nor a "weeding out" process vis-a-vis
this particular department, as in "controlled by
its inner sanctum minions."

That'd be too narrowed and focused in a time of
life when overview and "how things work" should
be of more central concern. Go through those
gates later if you like, but don't expect your
public school system to kow-tow to some top
ranking math general in some army of mathematicians.
Let your post K-12 math teachers play by those rules,
after students have had ample opportunity to survey
the fields and make some choices. Some will prefer
computer science, another branch of engineering.

K-12 wasn't so weighted towards pure math teaching
that these other doors weren't even opened.

But what if that's your goal, as a kid, to become a
pro mathematician, an inner circle math giant? Well,
by all means supplement then. The K-12 I'm describing
won't hurt your chances I don't think, will give you
a boost. But don't expect it to warp into a completely
different shape. Take responsibility for your own
self-education, like a real mathematician (it's never
too early to cultivate the right habits of mind).

And by K-12 I mean some archetypal public school that
doesn't really exist except in the governmental
blueprints, like abstract classes in Java.

But anyway, it's numeracy, a cultural mix of stuff,
that we teach. I'm sympathetic to Everyday Math using
a lot of pages to teach geograpy, not sympathetic to the
between the covers promo of calculators. Schools sytems
shouldn't have to pay publishers for the documentation
the calculator companies should be providing online.

But geography, that's useful, because the planet is
spherical and trigonometry pertains. And because the
logic of latitude and longitude has sophisticated
mapping relationships to various whole world projections
that're flat instead of round. So yeah, we're doing a
lot with geography in numeracy training (XML, GIS/GPS...
Google Earth). And now let's include astronomy as an
extension of geography (Celestia... Google Moon).

A mathematician comes along, sees all this "concrete
content" encroaching on what in his mind is supposed to
be closer to a pure Platonic philosophy, and says "wait
a goddamn minute, this isn't *math*!" -- by which he
means something more like Adrian in this archive: a
sequence of definitions, axioms, proofs, more definitions,
more proofs, tweak an axiom, alternative paradigm and so
on. A few pictures, a joke or two.

My reply to the mathematician above, with respect to our
K-12 charter schools for geek kids on the Pacific Rim
(think of gypsies, open camp fire along the road
someplace, lots of LCD screens), is "you're right, this
isn't math!". Then I might flip up my laptop lid and
show the ~M! emblem, glinting in the firelight, a
trademark of the made-for-TV series I'm working on.

Kirby



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