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Re: Setting up problems



During the quiz I told them that the mass isn't needed and that they should
proceed by considering what exactly is going on and write down the
appropriate equations.

My small contribution to this thread is somewhat silly, but I hope to
illustrate a point (albeit unknown). The mass certainly *is* needed.
Otherwise, there is nothing for the gravitational field to act on.
The roller coaster never begins to move.

Of course, that's not what you meant, but the point is that the most
subtle nuances in our descriptions of "how to begin" or approach the
problem may keep or take a student far afield what where he or she
"should" be.

To try to rescue this pointless point, I submit my 20-year old son. I
raised him alone, and during his ages of 8-12 I was finishing my PhD.
He, because of many other problems and issues in his life, dropped
out of school in the 8th grade, having never taken physics, and
having never paid an ounce of attention in math. But while I was
finishing the degree, he was immersed in a physics culture, and
regularly interacted with department professors and other grad
students, a most unusual peer group to say the least (to go along
with his other friends).

Now, at 20, he could not begin to imagine how to apply the equation x
= vt, and would have some difficulty doing division by hand to
calculate the velocity. But he regularly runs circles around the
concepts, and knows how to apply them. He has quite a physics
intuition, is superb at practical application of principles, and
rather enjoys explaining to a lay audience how a plutonium-based
A-bomb works. In a sense he's memorized it, but not really: he
actually knows the stuff he picked up, and can ask some inspired
questions. Last week we were thinking of how to bend a very tricky
bumper back into place on his partly wrecked car (he lost a driving
contest with a concrete mailbox); he invented a clever torque scheme
on the spot, chided me for being skeptical, explained it in terms of
moment arms and axes of rotation, and organized the parts to created
the necessary leverage tools, all while I was scratching my head
wondering if it really had half a chance of working (it worked just
like he said it would). If he had the math, I'm convinced he could
hold his own on some college level, never having taken a class in the
subject.

Well, that's my story; there's little new to discover here I guess -
I can see with my own eyes firsthand the power of a conceptual
approach that is consistently applied over the span of a few years,
even one that eschews all math. It's just that we can't have students
learn this stuff while a) not graduating high school, b) never going
to college, and c) generally taking 1 step forward and 2 backward in
their lives.


Stefan Jeglinski