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Re: contribution of mathematics in understanding physics

Problem Solving (real world complex
problems--not end-of-chapter problems) 90%

Interpersonal Skills (working in groups) 80%

Technical Writing 75%

Advanced Computer Skills 55%

Using Special Equipment and Processes 55%

Business Principles 55%

Statistical Concepts 40%

Advanced Mathematics 40%

Knowledge of Physics 35%

Likewise, at the joint APS/AAPT meeting last week I heard a talk from a PhD
physicist working at Ford who also shared a different survey about important
skills, but again PROBLEM SOLVING was at the top of the list and Conceptual
knowledge was nowhere to be found.
This is a bit of an eye opener and raises a new question for me.
I have been most deeply
influenced by Arnold Arons, whose most basic point I think is that
we can kill what we teach, reducing it to "inert ideas", or we can
bring it alive. He certainly brings physics alive for me. (See
especially his long out of print text "Development of Concepts of
Physics".) One aspect of what he has advocated is that students ought
to understand and not simply parrot things back to us. In the name
of this imperative we have "emphasized" concepts more than we had
previously. That's fine as long as we don't go too far with it, and
the fact is that all the basic concepts require SOME mathematical
skill. (N's first law at the introductory level is the only real exception
that comes to mind.) However, if we are honest we have to admit that we are
also being driven down the road to "more concepts" and less problem solving by
our students weakness in math.
Solving a difficult problem by rote without any understanding of the physics,
is now only one of two great pitfalls. The other is of course the hand waving that often
passes for "coneptual" understanding.


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Gary Hemminger
Dwight-Engelwood School
315 E. Palisade Ave.
Englewood, New Jersey
07631
e-mail: hemmig@d-e.pvt.k12.nj.us
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