Date: Dec 12, 2013 4:08 PM
Author: Louis Talman
Subject: Re: Poor Dan (but much poorer Robert)


On Thu, 12 Dec 2013 12:51:21 -0700, Robert Hansen <bob@rsccore.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.

> 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.

> 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?

> It appears to be mysterious to Dan and his group as well.

What is mysterious to Dan and his group is something very different. They
understand only that there is an issue; they haven't identified it.

> 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.


But here, the real mathematics is beyond the level at which the students
are working. It lies in knowing what moments of inertia are, what they
mean, and how the formula that confronts them is developed. That's the
irremediable flaw in presenting the problem as "real engineering
mathematics" when it is really nothing more than a poorly camouflaged
exercise in making simple substitutions.

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?

> 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.


> 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.


Are you suggesting that *this* is a technical problem? That's funny!
Especially because problems whose goal is learning to substitute numbers
for letters are problems that the kids you call "mathy" shouldn't need to
do more than two or three of!

> 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.


That's the trouble. It doesn't hurt the exercise--it hurts the vast
majority of students.

>
> The real solution is to inch the students into technical problems in
> subjects the student doesn?t know.


The real solution is to inch the students into the mathematics that the
students don't know. The time for what you are now calling "technical
problems" is when they are studying the science itself, using appropriate
mathematics that they have already learned or are learning at the same
time.

> 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.


Could that just possibly be because there is no excuse for pretending that
we are doing physics in a mathematics course, when the real physics is
beyond the students' mathematical capacity? And yet, your teachers
evidently made the mistake of trying to carry out that pretense. And in
so doing, they taught you something about mathematics that is incorrect.

> 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.


Just so. (Except that students aren't born with a complete understanding
of the principles of mathematics, either.) And if it is neither feasible,
nor effective, nor pedagogically sound "to design an algebra course around
the theory of the physical world an 8th or 9th grader has," then why
pretend to have done so?

The point is this: Students know when we are lying to them, and they
resent it. And regardless of whether or not engineers work problems like
this, the suggestion that this problem should mean something to students
of elementary algebra because "It's an application" is a lie. It's an
exercise (nothing wrong with that!) dressed up in
Sunday-go-to-meeting-clothes in a dishonest attempt to convince students
otherwise (and there's plenty wrong with that!).

--Lou Talman
Department of Mathematical & Computer Sciences
Metropolitan State University of Denver

<http://rowdy.msudenver.edu/~talman>