Date: Dec 29, 2008 3:33 PM
Author: Kirby Urner
Subject: Seasons greetings from Math Forum neighbors
Here's something from math-teach, a sister list:
Even if your school is too poor to access these geo-cams
(used for GPS work), your teacher still has access to
Google Streets probably.
Here's how we teach it in Portland (as of a couple years
ago -- big strides since then). This is from a Public
School for geeks (we're Open Source Capital, take that
So as I've been discussing with some friends (and Friends)
on other lists, a lesson plan for our children involves
discovering the dodecacam, a real piece of equipment
warehoused around SE 10th in our coordinate system,
with a website worth visiting.
The geometry angle is of course the camera itself, with
11 lenses occupying facets of a pentagonal dodecahedron,
in terms of how they're oriented, with the 12th facet
reserved for the pedestal, which attaches the camera
to the camera person, who also lugs the recording media
(a hard drive).
We use SQL to pull up tables of duals, starting with
the Oregon state standard V + F = E + 2 (search for
details), columns in our Polyhedra table. By searching
on (V,F) == (F,V) pairs, E constant, you find which
polyhedra interpenetrate in a dualistic manner -- check
any geometry book for this idea (tetrahedron self dual).
The dual of the pentagonal dodecahedron is of course the
icosahedron, of volume 18.51 relative to the tetrahedron
of same edge lengths (icosa: E = 30, V = 12, F = 20;
dodeca: E = 30, V = 20, F = 12 -- just switch F and V).
Of course actually field testing the equipment is of
interest, as one of our mantras is you can't do math if
you don't have access to a night sky free of light
pollution, i.e. no certification by an "indoors only"
route anymore, unless you're disabled.
So our math lessons have shifted to calories and joules,
their expenditure, in the context of physical work.
This may sound like a detour, but a mathematical
algorithm, such as sorting alphabetically (or by any
dimension -- no limit on how many dimensions SQL might
sort by) takes energy, and less efficient equipment or
programming tends to squander energy (and/or time).
Important lessons for anyone yes? You body is a
mathematical instrument (Keith Devlin good on this).
Getting our hands on actual dodecacams is maybe more
feasible here in Portland. I've met the CTO and know
this company is eager to partner with urban studies type
people, has a long track record in that respect already.
So to keep this properly academic, I will be going
through the professoriate. In fact, the University of
Rochester is responsible for getting me into this loop
in the first place (actually a Reed connection, but
academia is like that -- lots of criss-crossing affiliations).
Speaking of which, congratulations to the VPython team
for the new release announcement (Bruce Sherwood et al),
I'm looking forward to testing it soon.
For those of you just tuning in, VPython is our tool of
choice for actually showing these duals I've been talking
about, i.e. once you're ready to see the progression, of
tetrahedron, cube etc., we have a graphical engine at the
ready, our big departure from TI culture and "technology
in the classroom" ala NCTM, which is rarely anything but
flat, "two dee". We don't go for that. No can do.
Gotta have "shapes" (polyhedra) as 3rd graders called 'em
in the high Himalayas (I used to call this "Bhutanese
Math" when writing for Father Mackey in the 1980s). Of
course you've probably guessed my fantasies, of where I'd
like to take these dodecacams (Paro anyone?) That's hard
country to beat, when it comes to "immersive".
So, to put it another way: I've been working with my
Meeting committees to put together opportunities for our
teens that would involve a field trip to one of our
respected Portland based companies, in the context of a
gnu math unit on duals and Euler's Law for polyhedra (in
it's easiest form -- proofs by cartoon very doable). The
Columbia Gorge is a likely outdoor school for practicing
the camera skills, even with dummy cameras some of the
time (expensive gear can't be wasted). The goal of the
outdoor segment is to fulfill our commitment to keeping
math from being physically wasting, a kind of disease in
that case. If you don't have a physical education
component, you won't get it about calories and joules.
We have lots of gym equipment. Gnu math teachers tend to
be pretty fit.
PS: my daughter is having trouble with Spore suddenly
not working, a very fun biology game, a computer fantasy
of course (long in the making) but good for putting down
hooks for later science, recommended (despite this sudden
glitch...). School is out at this time. Doesn't mean
there's no learning curve.