> > 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 <[EMAIL PROTECTED]> > 2008/10/4 michel paul <[EMAIL PROTECTED]> > > >> >> 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. > > > _______________________________________________ > Edu-sig mailing list > Edu-sig@python.org > http://mail.python.org/mailman/listinfo/edu-sig > >
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