I've listened to the discussion on calculus teaching and I can't
help but throw in my tidbit as well...
I took freshman calculus with several talented students who had
taken AP calculus in high school. I had had only one semester of
pre-calculus, in which we learned what a derivative and an integral really
WERE. Entering college I could differentiate and integrate polynomials and
that is all. My AP counterparts could integrate and differentiate
polynomials, TRIG functions, exponentials, etc. I sat in awe and felt
myself at a disadvantage.
But when asked to find the area under a curve, they were absolutely
dumbfounded. It took me little time to memorize the trig fuction integrals,
etc., but them the entire semester to think of calculus in the same way I
did. I realized I had been at no disadvantage at all for not having taken
an AP course.
The best thing we can do is give students a firm FOUNDATION in high
school and let colleges build on that in such a way as to make calculus (or
whatever subject) useful later in their college experience. (I didn't USE
calculus until Physical Chemistry and E&M Physics.)
Covering more in high school doesn't mean teaching more. That
attempt creates (or at least contributes to) the difficulties college
instructors now face.
-- Chris Clayton
Senior+, Teaching of Chemistry University of Illinois - Urbana/Champaign
MSN Chemistry Forum Tutor: ChrisC_Asst@msn.com
For those of you following my graduation saga...IT'S NOT EVER YET!!!