We all know that schooling functions as a social sieve, with a strong class
bias, including a bias toward dominant-class cultural values and habits of
mind, quite apart from anything more directly economic. That subcultural
bias needs something to get ahold of, in order to make some students look
more qualified for better opportunities and better lives than others ... it
doesn't much matter whether such sieve courses are Latin and Greek, AP
Literature, or AP Calculus. What changes is the rationalization of why this
particular course is important ... giving any other reason (and every
possible reason has been given at one time or another) than the
social-functional reason: to make a nice, neat convincing sieve.
Any course with a heavy writing component and not much direction on what's
actually expected will make a very effective class sieve in most schools,
but such courses are not as easily sold today as being necessary for the
other, disguising reasons. Computer programming is an interesting candidate
for a sieve course; it never caught on, perhaps partly because the
class-culture bias is a bit weak in this case, and too many people resisted
it as new-fangled. "Calculus" has a nice classical ring to it; it's even a
Latin word! And of course, like Latin, doing well in it is evidence of
logical reasoning skills (remember when Plane Geometry served this same
function?), self-discipline (ala Escalante), and the innate and God-given
individual talent and ability to excell at science and technology in the
service of the Machine! [insert Irony here]
On the intellectual side, of course, one _could_ teach calculus as an
intellectually critical topic, looking at the worldview it arose out of and
the ones that have adopted it and which it now indexes or implies. One
could look at it esthetically and as an analytical tool, one could show how
it can be used as part of liberatory projects and ask whether it is being
used there against the grain or whether we can believe claims that as pure
mathematics it is somehow politically neutral (don't believe it!).
One could learn to use calculus along the way, learn to situate it in the
history of mathematics ... and in the history of warfare (which had a lot
to do with its early development), and in intellectual history generally.
One could link it to fascinating mysteries about the nature of the
continuum and the real numbers, whether they reflect nature or just some
cultural views of it, whether they reliably model natural phenomena or are
dangerously misleading, how discrete and continuous mathematical models may
be complementary and both necessary to understanding the emergence of
levels of organization in complex systems, including social systems, and
how cells and brains and actions and cultures are somehow integrated (or
integrable perspectives). You could start with the calculus and teach a
large chunk of European history and intellectual culture, raise many of the
profound questions of the last two centuries in philosophy and science, and
work to reintegrate science and mathematics into the humanities. You could
even investigate whether it had been invented by the Sumerians, or whether
only the superior moral and intellectual qualities (discipline, again) of
Europeans are capable of such insights into the inherent and essential
nature of the universe! [insert more irony]
Or you could just do what is usually done and teach students a series of
complex procedures and how to attach them to a set of standardized problem
types so that they can score well on sieve examinations.
Only one of these fits my definition of education. JAY.
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JAY L. LEMKE
PROFESSOR OF EDUCATION
CITY UNIVERSITY OF NEW YORK
JLLBC who-is-at CUNYVM.CUNY.EDU
<http://academic.brooklyn.cuny.edu/education/jlemke/index.htm>
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