What is the current balance of algebraic techniques that should be
taught? I remember many of my high school and college mathematics teachers
refusing to do more than one example of solving simultaneous equations by
graphing because it was too time consuming and precision of the solutions was
in question. We emphasized symbolic manipulation in those cases. What
becomes the balance point considering the technology advancements?
Recently, a chemistry professor gave a fourth degree polynomial equation
to her class to solve, should I tell my students to solve it by symbolic
manipulation? The numerical values in the problem were not integers?
If we agree that there are different expectations for the algebraic knowledge
that a student should possess to be prepared to enter different majors in
college, might it better to write these expectations down rather than
make it uniform for all majors? It might be a good idea to communicate
them to teachers on other levels of education also.
How does this dialogue blend with the CROSSROADS IN MATHEMATICS? For
those of you interested in my personal position on this issue, it may be
best described as under continual review. I am giving a presentation
this fall at an elementary/secondary mathematics conference in which I
maintain that aspects of algebra which during my education were
de-emphasized need to be reconsidered. I am not advocating for
elimination of anything in the mix of algebraic techniques but a change
in the proportion of time spent on algebraic manipulation, tables, graphs
and even proofs.
Len
+====================================================================
===+
| Len Malinowski Finger Lakes Community College |
| malinolt@snyflcc.fingerlakes.edu Canandaigua, New York |
+====================================================================
===+