
Re: Pure Mathematics Courses in High School?
Posted:
Mar 11, 2009 11:20 PM


While I agree that "schoolish math" (also known as "fish ladder math") as meted out in the grammar schools, is rather far from the real deal, I don't think the solution is "pure" anything, as overspecialization has taken a real toll, and anything further towards "getting a PhD in elementary school" (because precocious or something) should not be considered an optimal design.
Precollege, we definitely need to fix the math track, which the engineering professions judge to be broken, given their best technologies (e.g. computer languages) hardly get a footprint. As taxpayers, not just business execs, we have little patience for all this dillydallying, while the rest of the world gears up for business.
So as I've many times mentioned, here in Portland there's more interest in let's call it "dirty math" (if you're thinking of Britney Spears, hold that thought **). What we mean is we want to blend the disciplines far more, especially in terms of geography. You'd be amazed how many kids can't tell north from south, in this age of Google Earth. Consider that a "minimum job interview", to sit in front of some desk and point to the cardinal directions. Can't do that? You don't know "the math". A lot of other stipulations of this kind.
On another front, some of you have been asking about A&B modules. These come from one of the core geometries of the 21st century, by way of another bold entry, Regular Polytopes and the MITE on pg. 71, our minimum spacefiller. You'll want to compose MITEs into a spacefilling disphenoid known as the Rite for example (as distinct from the Bite and the Lite, all Sytes). If this nomenclature is unfamiliar to you, that's because you're not enrolled in Portland's "dirty math" courses, brought to you by... your Silicon Forest.
http://controlroom.blogspot.com/2009/03/matrixofsytes.html
Anyway, I'm definitely all for keeping some calculus and my Pythonic Math handout for Chicago, which I need to send to the organizers next, does include 1st, 2nd and 3rd derivative of this polynomial. Let me cut and paste some of the code:
You'll need plaintext view if looking through web archive and wanting to see indentation (of syntactic significance in this noncurlybrace language):
def testme(): """ >>> from stickworks import testme Visual 20050108 >>> testme()
See: http://www.4dsolutions.net/ocn/graphics/cosines.png """ from math import cos
def f(x): return cos(x)
d = dgen(5, 0.1) axes(5,1,0) graph = xyplotter(d, f)
for i in xrange(100): graph.next()
def testmemore(): """ See: http://www.4dsolutions.net/ocn/graphics/pycalculus.png """
def snakeywakey(x): """ Polynomial with xaxis crossings at 3,2,3,7, with scaler to keep yvalues under control (from a plotting point of view) """ return 0.01 * (x3)*(x2)*(x+3)*(x+7)
def deriv(f, h=1e5): """ Generic df(x)/dx approximator (discrete h) """ def funk(x): return (f(x+h)f(x))/h return funk
d1 = dgen(8, 0.1) d2 = dgen(8, 0.1) d3 = dgen(8, 0.1) axes(8,5,3)
deriv_snakeywakey = deriv(snakeywakey) second_deriv = deriv(deriv_snakeywakey) graph1 = xyplotter(d1, snakeywakey) graph2 = xyplotter(d2, deriv_snakeywakey) graph3 = xyplotter(d3, second_deriv)
Edge.color = (1,0,0) # make snakeywakey red for i in xrange(130): graph1.next()
Edge.color = (0,1,0) # make derivative green for i in xrange(130): graph2.next()
Edge.color = (0,1,1) # make 2nd derivative cyan
for i in xrange(130): graph3.next()
if __name__ == '__main__': testme() Anyway, back to work, gotta get that handout posted and out the door (some port on my laptop).
Kirby
** Silicon Forest execs may be good at marketing. As CMO for CSN, I'm not above making mathematics seem like something more interesting to a broader audience:
http://controlroom.blogspot.com/2008/04/meetingmath.html http://controlroom.blogspot.com/2008/08/backtobasics.html

