[Edu-sig] input from physics teaching
kirby.urner at gmail.com
Wed Jan 7 23:34:59 CET 2009
I had a productive meeting with Dr. Bob Fuller, University of
Nebraska, emeritus, yesterday, a long time associate on that First
Person Physics proposal to NSF (close, no cigar). He's working on the
Karplus legacy, in turn stemming from Piaget.
Science teaching went through a more successful transformation to
"constructivist" (in the sense of student centered, construct your own
model of reality) than USA math teaching managed (talking later
1900s), as the latter was mostly a panic response too Sputnik
(so-called SMSG) and it's been a backlash ever since ("back to basics"
to the point of near extinction of the subject, in terms of attracting
I'm not sure how it went in the UK, other Anglophone cultures. Others
on edu-sig will have more place-based stories of curriculum writing
(the evolution thereof) in your respective necks of the woods.
Anyway, the physics community has been interested in video games as
teaching devices right from the get go, with museum-grade simulators
(like the ones pilots train in) representing a kind of high end state
of the art (people actually get sick in those, given the realism).
Speaking of getting sick, you'll find in my Vilnius slides, other
places, a strong emphasis on "grossology" when working with kids.
That's a part of kid culture I've always found missing from Squeak,
which seems too squeaky clean, not sufficiently demented. For
example, if using a system language and defining a function, you'll
like encounter strong type awareness, meaning every type declared
*and* in a specific order e.g. f(int x, str y) and g(str y, int x) are
quite strict about what they "eat" (function as mouth) and if you send
them the wrong args, they will "barf" (has to be OK to say that, or
you lose a lot of would-be attenders).
The "type awareness" we want to induce is very traditional and follows
that time-honored sequence: N, W, Z, Q, R, C. You might not think if
quite those terms (namespaces differ) but we're talking natural,
whole, integer, rational, real and complex respectively.
These are types, and there's an historical narrative explaining the
drive to expand to new horizons, starting with simple geometric ratios
such as the body diagonal of a cube (math.sqrt(3)) or of the 1 x 2
rectangle (math.sqrt(5)). Given the historical dimension, it's quite
appropriate to give these primitive geometric relationships a somewhat
neolithic spin i.e. some talk of "cave people". This helps anchor
some data points for later, when we get into trigonometry and
navigation techniques (over desert, over sea).
(gnu math teacher Glenn Stockton, expert in neolithic tool making,
including for astronomical purposes)
You get these right simple surds (e.g. phi, math.sqrt(2)) out of the
gate, with compass and ruler, scribing in sand (on a spherical
surface, so only locally Euclidean -- "close enough for folk music" as
we say in geography class, zooming in on Greece in Google Earth
maybe). Pi, unlike phi, is transcendental, not just irrational. I
agree with posters here than Ramanujan is a great source of generators
(in the Pythonic sense), plus I like playing that epic song.
The complex numbers get added by those in the Italian peninsula,
seeking to solve Polynomial Puzzles (Pisa a center for this kind of
game playing, lots of betting, not unlike cockfighting). Fractals ala
the Mandelbrot pattern, scribed in the complex plane, come latter
("phi is the first fractal" -- a mnemonic we use).
However, given this is alpha-numeric literacy i.e. string-oriented as
well as numerical, we don't stop with a recap of basic algebra. We
need those regular expressions (good for URL parsing) and Unicode
studies. Fine if the language arts teachers want to pick up the story
at this point, take it away from the algebra teachers. We're talking
DOM (Document Object Model), XML... what became of "the outline" in
Roman times (structured thinking, rhetoric).
I'd like to thank Ian Benson of Sociality / Tizard for confirming my
impression that R0ml is correct in his approach, with strong emphasis
on Liberal Arts (in healthy doses at OSCONs -- the guy is simply
brilliant). 'Godel Escher Bach' is another trailblazing work, in
making sure we keep the string games going, don't propagate the
misinformation that "number crunching" is all that we're about. Knuth
called 'em *semi*-numerical algorithms for a reason.
But the question remains, if you *are* committed to keeping regular
expressions within math: where to put them? I think the answer is
pretty obvious: students need to work as a team to maintain some kind
of Django web site, could be exclusively in-house (not public), with
time line data, events in math history, adding and morphing over time.
Actually parse URLs, triggering real SQL behind the scenes. This is
all completely topical, very job market oriented. Yet we're in a
constructivist realm, giving imaginations free play and lots of
open-ended exploration time.
I continue with the "gnu math" and "computer algebra" labeling, adding
the Bucky stuff as a "secret sauce" -- spices it up to have something
a little questioning of authority, especially in a math learning
context, where some adults are accustomed to unchallenged authority.
No longer, rest assured.
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