Perhaps we could raise our standards, not lower them by having a more
balanced mix of procedures, problem solving (including in-depth practical
applications), and quantitative literacy in our classes. Ironically, many
of the skills we teach were historically rooted in a need to apply
mathematics to the real world. The impetus for teaching students to
simplify radicals, for example, resulting in several terms of radicals that
are magically "like terms", was to make calculations easier back in the time
of using logarithms and tables to calculate roots. Now that students can
calculate roots quickly with technology, we still keep the topic and don't
let them use technology for the calculations. I suspect if we analyzed our
algebra curriculum with Bloom's taxonomy, teaching predominantly procedural
skills intermixed with a few template word problems (that are contrived to
justify a skill) would place a good deal of our curriculum at the lower
levels.
Skills are needed, but I don't see very many students learning or
understanding them well even when the predominate emphasis is on skills.
My experience is that students learn and retain skills better when attached
to something concrete. I don't believe we would lower standards if we
changed our curriculum to incorporate more real-life problem solving, even
if it might be useful on a job. I'm just not convinced that our focus,
although it has worked for us and the engineers in the job market now, is
the best possible way to teach mathematical thinking and analysis.
If we want to go back to a traditional mathematics that is rigorous, we
could teach less manipulation of algebraic expressions and teach a lot more
mathematical logic.
Martha
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************