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Topic: Knocking on MIT's Door
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kirby urner

Posts: 2,762
Registered: 11/29/05
Knocking on MIT's Door
Posted: Dec 9, 2010 2:27 PM
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My second issue of GeekOut! (electronic preprint) features what
I've called the Kabul Dome Rant. Like Vol 1. No 1, it has lots of
typos, which gave me an excuse to publish a follow-up Addenda
and Errata.

The Kabul Dome was a pawn (or maybe higher) on the Cold
War chess board, and is a feature of this book, which I'm
considering assigning.

http://www.flickr.com/photos/17157315@N00/5245035118/

Another feature is an essay co-authored by Polya of "How To
Solve It" fame, wherein he spends a lot of time on Euler's
V + F = E + 2. There's this web cam at an MIT lounge we're
using, to make graph theory come alive. An "edge" might
mean a one-way "we can see you" spy cam.

http://www.flickr.com/photos/17157315@N00/5244608297/

You'll have a better understanding of security systems if
you know how to read directed graphs (similar to wire bundles
in today's aircraft, such as a GS V for $44.5 million -- I might be
off on the price tag, a topic @ FNB the other day, with some
wealthy gathered; LW thought they were under priced).

As I was recounting on MathFuture (a Math 2.0 OER), this
V + F = E + 2 meme has been a part of my generic intro
to geometry lesson plan for like 3rd grade and up for
some decades. I featured it in Bhutan, along with posters
from Peda.com, Lesotho, and in numerous schools
around the North American continent (although mostly
in Portland). I bring quite a few geometry toyz to the class,
as well as slide shows, links to Youtubes.

Schools vary in their ability to accommodate. North Americans
tend to lag, when it comes to Internet access (they have the
technology, but the bureaucracy gets in the way -- a lot
more like India, so blame the UK?).

Anyway, the Kabul Dome was the USAs way of advertising a
brighter tomorrow, and it was actually working its magic with
the Afghanis, who saw it as a kind of glorified yurt (which it is).
The Russians noticed the positive vibe and wisely offered to
buy the thing, so they could take it home and reverse engineer.
The plans are no longer under patent in any case, and you
can find old DEW line radomes on Ebay, as one of my Alaska
contacts once alerted me. Domes feature in many playgrounds
across the land.

But what about V + F = E + 2. Which textbooks have that? And
what do they do about nesting polyhedrons, one inside the
other, like Russian dolls? This is a way to show off important
relationships, found in nature, in architecture. Many of these
were known to Euclid. The Elements is not just about flat stuff.
So given Polya was into it, and Euler, a founder of topology,
we have a great litmus test for judging the worthiness of
elementary, middle and high school geometry textbooks.
No V + F = E + 2? No concentric hierarchy of polyhedrons?
If you wanna go to MIT, you best develop some critical thinking
skills and learn that some textbooks should be derided.

The "gnu math" coming from geek corners involves heaping
scorn on various math texts that clearly avoid walking their own
talk. They may say they're "constructivist" and yet no real
construction goes on. No hands on skills. No camping.
No fire starting. They may say they're inspired by Polya, but
there's no V + F = E + 2. So as future MIT students, we just
laugh and poke fun. How could we possibly take these textbooks
at all seriously?

This freedom to rip into books and tear them apart, critically,
is encouraged throughout the humanities, is the basis of
speech and debate. The Cleveland Cannibals in our district
are coached to be ruthless (within the rules of academic
propriety of course) in a sportsmanlike manner. The attacks
need not be ad hominem.

No sphere packing? Ridiculous. In Vol 1, No 2 follow-up,
I find the web page about biomes that shows both the Desert
Dome in Omaha and the Garden of Eden domes in Cornwall,
and yet does nothing to link to the Dymaxion Projection, House
or Car, the house being on exhibit in the very same town as
this college or university (Dearborn MI). Talk about lame
lesson plans.

Our goal is to have students (MIT students among others)
going out over the web and critiquing the math teacher resources
they find. Apply various filters and criteria. Establish a ranking.
Cosmetics should matter a lot less than content. Don't be shy
about questioning authority either. Grade those teachers. Let
the world know you have taste and style, not to mention common
sense.

I think as a student activity, "grading teachers" is going to be
popular. Of course what we're really doing is grading curricula.
We're looking for memes like V + F = E + 2, and if we're not
seeing much of anything going around that, we're forming a
judgment. Not all math texts are equally deserving. Many are
ridiculously devoid of relevant content. Lets put those on display.
Virtual museums etc.

Here's the Polya paper:
http://mathplace.net/pdf/polya.pdf

Kirby

FNB = Food Not Bombs
OER = Open Education Resource (e.g. Wikieducator)
MI = Michigan
V = Vertexes
E = Edges
F = Faces
MIT = Massachusetts Institute of Technology (a STEM center)

Message was edited by: kirby urner



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