[Edu-sig] Algebra 2

kirby urner kirby.urner at gmail.com
Mon Oct 6 16:56:48 CEST 2008

2008/10/4 michel paul <mpaul213 at gmail.com>

> For math classes I think it's more pertinent to focus on functional
> interactions and not on IO issues, and that was what I was trying to get at.

I'm enjoying this thread.

My spin in Pythonic Math has been to suggest "dot notation" become accepted
as math notation, and with it the concept of namespaces, which I tell my
students is one of the most important mathematical concepts they'll ever
learn.  We look at how several languages deal with the problem (of name
collisions, of disambiguation), including Java's "reverse URL" strategy e.g.
net.4dsolutions.mathobjects.vector or whatever.[1]

I tend to look at .py modules as "fish tanks" i.e. ecosystems, with both
internal and external (import) dependencies, with the user of said fish tank
being somewhat the biologist, in testing to find out what's in there, what
the behaviors are.

Starting with the math module is of course apropos, discussing the
functions, not shying away from trig even pre high school, no reason to
withhold about cosine just because they're "young" (this is actually a prime
time to gain exposure to these useful and time-tested ideas).

Because of my "fish tank" idea, and using the math module as a model, I
don't encourage "self prompting" i.e. using raw_input for much of anything.
We need to "feed the fish" directly, i.e. pass arguments directly to
functions, with f ( ) looking like a creature with a mouth, ready to eat
something.  fish( ).

Regarding GOTO, sometime last month I think it was, I told the story of
assembler (JMP) and spaghetti code, Djikstra to the rescue, further
developments.  It's through story telling that we get more of the nuance.
I'm a big believer in using this "time dimension" even if not doing anything
computer (hard to imagine) i.e. the lives of mathematicians, their
historical context, why they did what they did -- critical content, not
side-bar dispensible, not optional reading.[2]

Metaphor:  education systems are like those old Heinlein moving sidewalks
(science fiction), where you can't jump on the fast-moving one at the center
from zero, have to slide from walk to walk, each one a little faster, and
likewise when a approaching a destination, start to slow down.

By including more content from geek world, getting more of a footprint for
the circus I work in, I'm giving a sense of one of those fast moving
sidewalks at the core of our infrastructure (coded reflexes, superhumanly
fast business processes).  Math pre-college should be a door into all sorts
of careers (starring roles) that include numerate activities.  It's not
about Ivory Tower PhD mathematicians having exclusive access to future
recruits, shoving the rest of us aside because our skills are "impure" (not
pure math).

What passes for "pure math" would be something to study in college, after
getting a broad sampling ahead of time, good overview, the job of a
pre-specializing curriculum.  In the meantime, if your school doesn't give a
clear window into computer science in over four years of numeracy training,
then hey, its probably a *very* slow moving sidewalk (more 1900s pedantic
and plodding than fast paced like TV).[3]


[1]  Like when I do the IEEE lecture on Nov 4 at the Armory (theater), I'll
be talking about coxeter.4d versus einstein.4d versus bucky.4d -- three
namespaces, named for thinkers, in which the concept of "four dimensional"
makes sense -- but in quite different language games. (a)

[2]  I like telling the story of those Italian Renaissance era polynomial
solvers, a proprietary model in which mathematicians were like race horses,
gained owner-patrons who would stable them, let them work out, then they'd
have like "cock fights" in the village square, to see how could solve
whatever third of fourth degree polynomial fastest.  Without this kind of
focus, polynomials wouldn't have the momentum they still have to this day,
as a key math topic pre-college (and another kind of "math object" from a
Pythonic math point of view).(b)

[3]  Marshall McLuhan wasn't just blowing smoke.  People who grow up on a
lot of TV are geared differently and in the early 21st century a lot of what
"school" is about is asserting the value system of a pre-TV era (pre
computer, pre calculator...).  To "side with the kids" would be entirely
subversive of traditional classroom thinking, would involve a lot more
learning how to make televisions (multi-track) not just passively viewing
it.  In my model numeracy classes, making "math shorts" (like on Sesame
Street) and uploading 'em to YouTube, for peers to admire (peers thousands
of miles away perhaps -- no problemo) is a big part of the action.

(a) FYI here's the bio of Kirby that went out to subscribers:

An IEEE Oregon Section event

"R. Buckminster Fuller: The History (and Mystery) of the Universe"

with exclusive presentation by local Buckminster scholar and consultant to
the playwright, Kirby Urner Tuesday, November 4, 2008 on the Mezzanine at
Portland Center Stage Gerding Theater at the Armory

128 NW Eleventh Avenue, Portland, OR 97209

Hors d'oeuvres Reception: 5:30 p.m.

Presentation and Discussion: 6:00 p.m.

Theater Performance: 7:30 p.m.

$49 per person. Tickets are limited.

Please register by October 14, 2008. For more information and to register go
to <link here>.

We regret that we cannot offer refunds for cancellations received after
October 14.


R. Buckminster Fuller: The History (and Mystery) of the Universe

Written and directed by D.W. Jacobs from the life, work and writings of R.
Buckminster Fuller


"Everything you've learned in school as 'obvious' becomes less and less
obvious as you begin to study the universe." - Buckminster Fuller

Does humanity have the chance to endure successfully on planet Earth, and if
so, how? This is the question framed by Buckminster Fuller, the engineer,
designer, poet, and philosopher who, among other things, was Mensa's second
president and invented the geodesic dome. Join us for an unforgettable
journey inside one of the most remarkable minds of the 20th century in a
one-man show that blends videos, lectures, poetry and a healthy dash of
humanist humor. A hero of the sustainability movement, Bucky framed many of
the great ideas of his time and ours. This is your chance to get to know the
man behind the world-saving mission.


How has the literature developed since the publication of 'Grunch of Giants'
in 1983 and what are likely outcomes and future directions projects Fuller
started over a lifetime of heavy lifting?


Kirby Urner started exploring Fuller's work in earnest following his earning
a BA in philosophy from Princeton University, while serving as a high school
math teacher in Jersey City. He's served as a contributing editor for
McGraw-Hill, Rockefeller Center, political activist for Project VOTE! in
Washington DC, and computer programmer for myriad governmental and nonprofit
organizations in Greater Portland. Working in cahoots with Kiyoshi Kuromiya,
Fuller's lieutenant on a couple of key books, he snagged the domain name
bfi.org and served as the Buckminster Fuller Institute's first web wrangler.
His 'Synergetics on the Web' is one of the main stops for Bucky scholars to
this day (*www.grunch.net/synergetics*<outbind://83/www.grunch.net/synergetics>).
Kirby is an IEEE member.

(b) yes, tell them early that we have no "closed form algebraic solution" to
fifth degree polynomials, but that doesn't keep Python from being useful in
implementing some of the progessive approximations for root-finding, such as
you get under the hood with Mathematica et al.  I've got a prototypical
Polynomial class out there somewhere that self solves pretty well, maybe
others here do too.
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