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It'd definitely be interesting to see how HS math teaching could be improved using code. It could definitely improve interest for some by approaching the meaty,
by tel 17y ago
It'd definitely be interesting to see how HS math teaching could be improved using code. It could definitely improve interest for some by approaching the meaty, interesting bits through a common language.
Unfortunately, though I've not gone through one of the so labelled Math XXXX for CS Majors style classes, I feel a little worried about this approach. It might garner interest initially, but if you're not eventually writing things down using math notation and reasoning at that level then you'll be doing math with a crutch forever.
Mathematical notations are not consistent or testable across any significant body. Most authors abuse notation every chance they get ("syntax sugar", maybe) though the good ones are conscientious about this. The difference is that Math is fundamentally a human language. It exists not to be computed directly but to inspire our non-linear brains to jump to the proper conclusions while laying down a map that (hopefully) outlines some perfectly "consistent" method for getting there.
(Consistent is in quotes because Gödel and so forth. Read the comments at the end of the second chapter of the Jaynes book online for free.)
Computer code is increasingly necessary in anything resembling a practical application of math. I'd suggest that it's as important for an (ugh) applied mathematician as the language of math itself, but I would never think that it could be practiced to the exclusion of the other.
Sure: pique some interest by showing how really cool things can be done with computers that abuse fundamental mathematical things. Do it with graphics or show infinite sum approximations, whatever you like. In the end, your students better be able to at least recognize the mathspeak for what they're doing though. Otherwise you're crippling them even as you inspire.