[Edu-sig] Algebra 2

michel paul mpaul213 at gmail.com
Tue Oct 7 05:09:26 CEST 2008

> My spin in Pythonic Math has been to suggest "dot notation" become accepted
> as math notation

I absolutely agree with this.

In about 5 weeks I'll be giving a California Math Council presentation that
I titled *Fractions are Objects, not Unfinished Division Problems*.

I submitted the proposal with the attitude of 'who cares?  Let's just see
what happens.'

Surprise!  They accepted.

OK, so now I have to have something to say.  : )

I think the theme of 'dot notation' as a kind of standard math notation
would be valuable.

Generally, I want to present

1.  The importance of 'computational thinking' as a math standard
2.  Python as a vehicle for this

Thanks very much for any helpful suggestions along these lines.

- Michel

2008/10/6 kirby urner <kirby.urner at gmail.com>

> 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]
> Kirby
> [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
> Play:
> "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.
> Presentation:
> 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?
> Speaker:
> 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*). 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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