On Dec 12, 2013, at 4:08 PM, Louis Talman <firstname.lastname@example.org> wrote:
> > On Thu, 12 Dec 2013 12:51:21 -0700, Robert Hansen <email@example.com> wrote: > > ...what does ?moment of inertia? have to do with it? > > That is indeed the question. At the level the kids are working, "moment of inertia" has absolutely nothing to do with it, and it is dishonest to suggest that it is otherwise. The kids are learning to substitute numbers for the symbols found in a formula. In spite of the "moment of inertia" label, this formula is meaningless to them. What is the point of pretending otherwise? Be honest: Give them a meaningless formula, tell them it's meaningless, and ask them to make the substitutions.
Ok, take away the title, and the text. Is the formula now meaningful to them? I am not suggesting that problems like this be the cream and crop of an algebra 2 curriculum. The majority (2/3) is still just math. But if you want aspiring engineers in your class, or anyone that aspires to use algebra for that matter, you are going to have to apply it to something. That is what I call technical problems. Problems with technical details outside of the math.
> Can you create as involved an expression about something they would know about? > > Why would I try? There's nothing wrong with involved expressions in general, or with this one in particular. But the issue here isn't how involved the expression is, or even where it comes from. It's the pretense that the student is doing something meaningful---when that is anything but the case for the student. When we make such misrepresentations, we teach students things we don't want them to learn---as you confessed below.
Ok, I see one of your grievances. I think you are confusing me with those real world problem clowns with red noses. That isn?t my philosophy and I have no pretense that the student is doing a real world problem. That?s not going to happen till they get a real world degree and a real world job.
> > 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. > > Exactly: Look at the problem "in the context of the level it is meant to be." That context includes no understanding of where those complicated formulae come from or how. Why pretend otherwise by giving the formulae meaningless labels and suggesting that the kids are doing something real? Every one of them who thinks at all knows damn good and well that they are not. I'm not objecting to the substitution part of the problem; I'm objecting to the cloud of misrepresentation that surrounds it. > > No, it shouldn?t be mysterious. > > Then what is the point of making it so?
Because they are inspiring to the students that aspire to technical fields like engineering that use this stuff. They get the math just fine and they are anxious to apply it. They don?t want the problem to teach them what multiplication is. They already know what multiplication is, quite well. They don?t need a problem to show them what math can do, they already have the muse, and they are excited. They want to calculate the orbit of mars using just its speed, the mass of the sun and some formula you gave them that they wouldn?t know from the drag equation of a Cessna 150. And the problems are real. The pretending is the students pretending that they are engineers. And they are having fun and applying the math they have learned.
> Do you really want the majority of students to think that what engineers do consists of sitting around and spending their days making simple substitutions in complicated formulae they don't understand?
They aren?t going to do that. They got the juice. And the problems get tougher over time, well, they used to. Do you not remember this time? When every day of math class was new.
> > 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! > > A few do this. The vast majority write mathematics off as devoid of intellectual content.
Those brilliant bastards. And all along I thought they just weren't good at math. No wonder it has been so tough to find engineers (not needing green cards) lately. I'll have to call our recruiter and have her rewrite the entire recruiting process.
This is your (an many others?) hypothesis and you don?t know how much I wish you were right. That would be so freaking easy to fix. Seeing that this idea and a dozen variants have been around now for 3 decades and there was no fix, doesn?t bode well for it.
The algebra courses I grew up with had enough math for the aspiring mathematicians and enough (pretend) engineering for the aspiring engineers (and physicists, programmers, etc.). And for the others they had solid business math courses with business algebra where needed. Who have I left out? Other than the kids that aspire to something that doesn?t need algebra at all. They took math for daily living. And those weren?t tracks, they were paths. Tracks are when everyone takes algebra except not the same ?algebra?.
If you have examples of a better class of problems I am all ears. This particular problem isn?t the best, but not for the reasons you mentioned. Throw it in with 4 other pretend problems and it would rank 5th. But what do you expect, it was picked by clowns out of an engineering class.
Attached are a few pages from my Algebra 2 book with pretend engineering word problems, with some worked examples so that the student wasn?t entirely in the dark. Some are simple, some require the statement of the formula (in words) with nothing to back it up.