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:

http://www.immersivemedia.com/#home

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

seriously).

http://www.4dsolutions.net/ocn/winterhaven/

Kirby

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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".

http://www.unbf.ca/education/bhutanproject/brief_history.htm

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.

Kirby

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.