Re: Setting up problems

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 10:57 -0500 10/9/03, Rick Tarara wrote:
> I can provide the equation--say that for centripetal acceleration or for the
> Gravitational force and ask how the acceleration or the force changes if we
> double the distance (or radius).  To MANY, MANY students, this is like
> asking them to translate Aristotle from the original Greek.

The answers to this type of question are not obvious to beginning
students, most of whom would never think of putting in some numbers
and seeing what happens. What they have to have is practice at doing
this sort of problem. Start with some shapes for which areas or
volumes are readily calculated (squares, cubes, circles, spheres) and
have them figure out the ratios of areas, volumes, etc., for
different sizes, then extend it to irregular shapes, and along the
way show them some practical applications of  these ideas that can
help them to make sense of something they already may know. An
example I like is to use the scaling of volumes and areas to explain
why elephants have a very slow heartbeat while mice have an extremely
rapid one, or why a baby's heartbeat is faster than an adult's
(although the difference isn't as dramatic here).

> Can we, should we, be teaching basic Algebra in our physics course?  Or
> maybe it's not the Algebra, just a lack of critical thinking skills.   ??
I suspect it's neither, at least in the main. What students need in
order to cope with any new idea is time and practice. And they need
to be browbeaten into doing algebra before doing numbers. The method
that works is grades. Simply give no, or substantially reduced,
credit for problems that are done numerically before or without
having done them algebraically. They may not understand why you are
being so hard-nosed about this early on, but they will thank you
later for the habit. Of course, that means that you must always do it
that way in class, too. It won't hurt if, at least in the beginning,
they believe that you have to do it that way in order to get an
answer at all, and that everybody does it that way, even at the
highest levels (which isn't all that for from the truth). But, in
order to inculcate this discipline, time and practice are needed.
Time taken early on in a course to emphasize scaling techniques, and
algebraic manipulations, will pay off later. And rather than making
the scaling exercises just sterile manipulations, tie them to real
world examples as soon as you can. There are lots of examples that
will expose the students to interesting physics before you have to
get at much of the physics formalism. If there is some physics that
they need to know, as long as it isn't more than a couple of simple
facts, it can be given to them, and then later when those ideas are
presented in their full context, they will already have some feel for
the ideas.

Hugh
--

Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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