Re: Setting up problems

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 15:21 -0500 10/9/03, Frohne, Vickie wrote:

> Halliday & Resnik (the
> older versions, anyway) had these great "Questions" at the ends of the
> chapter. Usually they're skipped in favor of the "Problems," but the
> Questions are there to help with conceptual understanding.  Many other texts
> contain similar questions.

Having taught from H&R for several years, and having at least
referred to many of the others frequently, I have a problem with the
way they deal with the conceptual questions that they almost all
include, and that is that they are separated from the problems, which
makes them all too easy to ignore. If they were mixed in with the
problems, and were made a bit better (too many are either too easy or
too hard, especially those that need the reader to be familiar with
the subject of the question in order to answer). They could also
profitably include conceptual section within the problems, ones that
ask how things would be different if some initial condition or
boundary condition was changed, or even if some physical law were
different, or how some factor that was obviously ignored in the
problem (like friction, for instance) might change the nature of the
answer, or what the next level of complication might be. There are
any number of things that could be added to make any numerical or
algebraic problem partly conceptual.

I also have a problem with the sample problems in most texts. They
are almost always a P&C application of some recently developed or
presented formula. This gives the students no help in getting read
for the EOC problems which are typically more difficult than the
samples. I would prefer that the sample problems be more challenging,
and that the solutions not be given. Rather, the author should
include guidance and hints for working through the problem. This way,
the students would not be able to get away without reading the book,
and when they get the EOC assignment, they can't just try to find a
sample problem that looks similar to the assigned problem and adapt
that. That, in my experience is a standard student problem-solving
strategy. And not a very successful one.

It is also useful for students to see that many problems have an
"easy way" and a "hard way" to be solved. They shouldn't be
discouraged from following the "hard way" (often called the method of
brute force and ignorance). I have had many occasions when, only
after solving a problem by a long and arduous route did I see the
simple solution, which while simple, was not so straightforward. But
by doing that, and by finding the more direct solution at the end, my
understanding was deepened in the process, and I tended to remember
what I learned better.

Hugh
--

Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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