Wednesday - October 25, 2006
Delay Graphing
As we near the last third of the semester my
college algebra students are almost done with graphing functions. They've been
taught a lot: transformations, shapes of functions, finding zeros, etc.; but
all of it with very poor understanding. Because so much of the theory of
graphing functions is tied up in calculus, we have no choice but to wave our
hands past the math and just teach imprecise techniques that work well enough to
get them to draw something on the paper. For example, this past week we taught
the students about rational functions (functions of the form p/q where p and q
are polynomial functions). When graphing such functions, we have to deal with
asymptotes since the functions approach but never reach some values. Yet,
without limits, we have to talk around the idea of "going to" or "approaching" a
value, rather than just properly describing it. I dislike this hand waving, but
it's a school-wide curriculum choice to make sure students see certain material
in certain courses so other courses have clear expectations of what students
know if college algebra is a prerequisite. Changing it would affect dozens of
courses, including many outside the math department, putting up a large barrier
to improvement.
Personally, I think we should cut some of the graphing and save it for calculus. In its place we could talk more about vectors, matrices, and systems of equations. Then the students will really be better prepared for later math classes, rather than having lots of experience with graphing and no idea what they're doing.
Personally, I think we should cut some of the graphing and save it for calculus. In its place we could talk more about vectors, matrices, and systems of equations. Then the students will really be better prepared for later math classes, rather than having lots of experience with graphing and no idea what they're doing.