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Re: 10 Myths (Maybe) About Learning Math , Jay Mathews, The
Posted:
Jun 10, 2005 3:06 PM
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> On Mon, 06 Jun 2005, Kirby Urner wrote:
>
> > It's just that I don't feel bogged down while I
> wait for someone to win the Math Wars on math-teach.
> I'm not holding my breath for that decisive victory,
> , when MC/HOLD retreats before the advancing wrath of
> the NCTM or vice versa -- whatever the fantasy. Our
> maps of the battlefield show this not to be a front
> line. No big stakes at stake in this neck of the
> woods. I concede it to my betters (and keep filing
> my reports -- I *do* find a lot that's interesting).
>
> I like the war analogy. The front line as your maps
> see it would be the contest between programming-
> oriented math versus math-centered math?
Good question.
I'd say its more a question of how to leverage various cultural currents to maximum long term advantage. We don't want a lot of redundant, mutually conflictive ways of teaching the exact same material. CS and K-12 math have the potiential to collide in disasterous replication, or in share-the-glory symbiosis. I'm trying to shift weight towards the latter outcome -- I think this'd add more joy to schooling, the frustration level already being plenty high.
Mathematica had to rigorize the syntax e.g. by consistently applying square brackets to denote the function arguments, and curvy parentheses to denote groupings of terms.
Text book math had nested these two rather arbitrarily, plus left expressions like s(cos(3)) to context (is s a function or another term in the product -- no hint to any parser less savvy than a human reader, a very sophisticated client compared to some DLL on a hard drive somewhere).
I go into all this mostly to make the point that automation has already brought a new level of standardization to mathematics notation. I'm proposing we take it to the next level and consciously import dot-notation into the math domain, just like SMSG imported set notation and pushed it towards 2nd graders in the 1960s. Except not "just like" (different strategies required -- "new math" sort of backfired, after all, so it's not a campaign we should just clone and run with).
> You can abhor the horrors of such a war, or like in
> Mash and Catch-22, you can laugh.
I'm more for the comedy end of the spectrum. Part of the fun is my maps of the battlefield are so hilariously different from everyone else's that they can only be taken as satire on some level. Like, if I'm free to make up such mock battles, then I'm equally free to declare the winner, thereby getting away with my own private history of the world. No one expects that to amount to anything but amusing science fiction -- and I'm agreeing (I am likewise amused).
> --
> Greg Matheson, Taiwan
Kirby
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