On Mon, Nov 16, 2009 at 9:30 PM, GS Chandy <firstname.lastname@example.org> wrote:
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> Subsequently, I was asked to give a small talk to some interested students at the school. There I showed them the Yoshimoto Cube in some detail, along with an explanation that what they had been taught and were learning was the "alphabet" of math, very similar to the "alphabet" of the local language Kannada of English and so forth. In language, it is essential to do the alphabet in order to get to interesting stories, poems, the fascinating stuff in encyclopedias, and so on and so forth. Just so, they could get to the really interesting stuff in math (like the Yoshimoto Cube, the Mobius curve, etc) OHLY if they applied themselves to learning the alphabet thoroughly. >
Thing is, math is neither static nor monolithic and although touted as "a universal language" there's some confusion about what that means, as what it does not mean is any given mathematician is necessarily conversant with the mathematics practiced in the next cubicle over.
The college departments are currently geared to preach calculus, even though discrete math skills may be more marketable in some economies. The pressure on high schools is to maintain the status quo of using the ETS to define the national curriculum, such as we have one.
In different alphabets, one learns to spell different things sooner, maybe taking longer to reach what would have previously been dismissed as "for children" topics.
When should we introduce the concept of "dimension" and how should we?
Do we want to get into fractals in the sense of "fractional dimension" pre-college?
Some would argue "sure, what better way to introduce the complex plane?" (aka Argand plane, though another guy had it sooner). But then you'd be surprised how N, Z, Q, R, C are not introduced in any formal algebraic sense, in terms of their group and field properties.
Different curricula might dare to diverge around these questions.
True, there's political pressure to just stick with ETS as that's easiest for the colleges and universities, not especially eager to revamp or catch up with the private sector. We've paid a high price for our Calculus Army (the one Rumsfeld had to go with?).
My own view (shared by many others of some considerable IQ) is the "alphabet" currently taught is way too slow at getting them to exciting topics of obvious relevance, before it manages to simply depress them with the seeming pointlessness of it all. There's no reason for this state of affairs to persist other than out of laziness and inertia (lethargy).
In the meantime, what USAers turn up their noses at, remains marketable overseas. Why not export our work on Python generators to Singapore, where the focus is IT? There's an apac.pycon coming up in 2010. Should I be there with my company?