On Thu, 12 Dec 2013 04:09:10 -0700, Robert Hansen <firstname.lastname@example.org> wrote:
> This is not a ?plug and chug? problem, it is an algebra problem.
It is both. And there is nothing wrong with either--as such.
The trouble with this problem is that it's dressed up as an application. But it's an "application" to something with which students have absolutely no aquaintance and can't begin to understand. How are students at the level of beginning algebra supposed to make sense of something called "moment of inertia"?
These students can have no understanding of where the formula comes from or of what it means. So what the problem does when given at Dan's level is to reinforce the notion that mathematics consists of a collection of mysterious rules that are to be memorized so that they can be applied mindlessly when an appropriate stimulus has been presented. (Of course, this approach begs the question of how to decide the appropriateness of a stimulus. But advocates of using mathematics this way don't even notice that there is a question they must beg, as Bob has shown us.)
Not being one, I don't know if engineers approach mathematics this way or not. But I've had engineering students in my classes, and I have my suspicions. Bob's suggestion that the problem in question is a good one tends to confirm those suspicions.
To be sure, Dan fails to give us any of these insights---especially the important one about what the problem really "accomplishes"---when he discusses the problem. He is right about it's being a bad problem, but he's unable to articulate the reason why it's bad.
- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver