On Dec 12, 2013, at 11:52 AM, Louis Talman <email@example.com> 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.
At least we agree on that.
> > 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??
They pulled it from a course at an engineering college. Silly kids, they get into everything. But what does ?moment of inertia? have to do with it? Can you create as involved an expression about something they would know about? Granted, this is an algebra 2 problem. I don?t know why Dan is commenting on an algebra problem at all, at any level, he doesn't teach it in his blog. But he did comment on it. I look at this problem in the context of the level it is meant to be. It would be a horrible arithmetic problem.
> > 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.)
No, it shouldn?t be mysterious. It appears to be mysterious to Dan and his group as well. But the stimulus is there. We went right to it. It?s that mess of letters and numbers off to the left. That is the challenge, to train the student to see the math. Students figure out very soon that mathematics is not just a collection or rules to be memorized. Well, differential equations is, but the rest of it isn?t.:) You know how they figure this out? Cause they fail the damn tests! Assuming of course that the tests are of sufficient quality. Our challenge is to make them think and not about something entirely else, but about this. About all the things around the collection of rules to be memorized and that make the collection of rules work in the first place. The more you do that, then the more they will rely on sense and instinct and less on memorization. But you still have to have substance to do this and technical problems like this are a mainstay in that exercise, for several reasons. Primary of which is that in applied math these are the problems algebra is used for. Secondly, you just can?t find a better source of technical problems than nature itself. Sure, the subject of any problem with this many terms is going to be unknown to the students, but that doesn?t hurt the exercise when your focus is on the math and not the subject.
The real solution is to inch the students into technical problems in subjects the student doesn?t know. This is the type of stuff I was expecting from Stanford edu. Instead they sent us Dan.
> > 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.
It is applied mathematics. That is why I majored in physics and not engineering. Not because the math was better, it was pretty much the same. But at least the physics was better.
> > 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.
What is bad is that students are not born with a complete understanding of the principles of everything, except math, so that we can then show them how to apply math to everything. It is not feasible, effective nor pedagogically sound to design an algebra course around the theory of the physical world an 8th or 9th grader has. That?s one of the challenges of being an algebra teacher.