Ah yes.. but,

Post #24,169 by Ashton 1/13/02 6:42:31 PM 1/13/02 6:45:44 PM Reply	Ah yes.. but, in my experience, the best math teachers are ones who Do.. tie in some bit of exotica to everyday things. And so much of everyday things are tied into some.. math concept; clearly it is the language of the physical universe. (I get antsy when someone tries to extrapolate math principles into organic componds - and really skeptical when anyone tries to 'explain' human carbon-units with nice neat math theories. But they Will try..) Look at the 2:8:18 progressions of electron shells around nuclei - or the periodic chart itself. That was where 'math' began to live for me. Sounds as if you had one o' those 3x5 card readers for your math.. teechurs, and not Jaime Escalante [link\|http://www.paccd.cc.ca.us/75th/alumni/escalante/escalante.html\|Calculus - only the word is scary..] Anyway you slice it - math education in US sucks; it may suck a lot elesewhere - but it's the Murican version I have experience with. Recommended book: Innumeracy by John Allen Paulos. what (too) many Muricans are. If you've never said to self, about Some piece of math, "that's beautiful!" then.. sorry about what you've missed :( Ashton no mathematician, but need it every day.. PS To me your title is ~ "music is purely a means to an end" - y'know? Edited by Missing User 70 Jan. 13, 2002, 06:45:44 PM EST Expand All History
Post #24,211 by Ric Locke 1/13/02 11:13:59 PM Reply	Games and art forms There are several levels of math. By observation from outside (it certainly doesn't apply to me!) at the very top level, math is a sort of game; it need not have application to the real world, but if it works it gives the mathematician the same sort of feeling that finishing a really great sculpture or painting or piece of music does. A peculiar and highly constrained type of art. The one person I've ever met who unquestionably occupied that level -- a college prof years ago whose name I don't remember, and I'm sorry for that -- called everything below that level "arithmetic". Solving tensors is arithmetic? To him, yes, it was. He would probably have regarded "what color is math" as an interesting question. So once again we see touchy-feely in action. The kids are being asked questions that cannot be meaningfully answered at their level of understanding, because they shouldn't be denied the privileges and/or perquisites of the higher level; one should assume that they have that understanding and go from there. The result is, of course, that, blocked from understanding at any level due to the assumption that it isn't needed on the part of their teachers, they never truly understand anything; 2 + 2 needs electrical power, square roots will forever remain a mystery, and the difference between "calculus" and "magic spells" will never be seen. Regards, Ric
Post #24,233 by Ashton 1/14/02 5:55:07 AM Reply	I can almost agree with that characterization. That is, there is surely Some comparison with 'art', and at higher levels well.. they Are 'higher levels' because you can't get there without learning.. (then unlearning! really) a great deal, in preparation. Perhaps the same sort of emotional response occurs at the level of The New - after all, 'satisfaction' is purely an emotional experience in that part of the brain - the amygdala, at least as is currently 'thought'. But too much is unique to math: in particular re the very large ideas of Truth and of Proof. Only in math: can these ideals be accomplished, precisely because - the areas over which this truth and proof apply - are perfectly circumscribed. (We notice that these concepts become muddied with theological and other overlays in Any other 'area', I submit.. thus becoming blab words in most such discussions.) Maybe it's the most scientific 'art' or the most artful 'science' (?) - take yer pick. That it is a discipline is evident. My 3.14159 Zlotys Ashton IANAM, but I play one when around the innumerate - the arithmetic challenged

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