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contribution of mathematics in understanding physics

I want to move a discussion that has been going on over on PHYSLRNR to
Phys-L so that we can discuss our OPINIONS and feelings about some of the
aspects of the discussion without referenced ties to the PER research. I do
this because I think the discussion is important but not necessarily a
strictly PER (Physics Educational Research) issue.

To summarize (and I invite those who have been contributing to jump in with
more detail):

What is the proper role of mathematics in understanding physics?

What is the role of purely Conceptual courses to physics education?

Do we 'turn off' students to physics by insisting on mathematical treatments
even at introductory levels?

Are there certain clientele who really can't handle and don't need the
mathematical treatments that many courses are wont to present?



Since I am pulling the following totally out of context, I won't attribute
it, but this is a statement that was made in response to my own discomfort
about curricula that omit problem solving altogether and which supposedly
produce students able to do something in science--say teach elementary
school.

In my view the only reason for doing problems is to give students another
view
of what the concepts mean.



I really want to comment on this statement (but promised I'd stop bothering
the researchers on the other list).

Unfortunately I didn't copy the reference, but the following is from an AIP
or APS survey of physics trained people working outside of academia (maybe
someone else has the reference). It asked about the most important skills
needed for their work.

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.

The question is then whether we might be doing students less than a great
service in moving the emphasis in instruction TOO STRONGLY toward conceptual
understanding IF at the same time, we move away from problem solving AND
mathematical treatments? Might this even be true for the Non-Science,
Non-engineering student. Can we really articulate why good scores on the
FCI (Force Concept Inventory) test is a high priority goal in non-majors
courses versus problem solving strategies (from a physics point of view) or
Physics and Society treatments of certain topics? The vast majority of the
PER work, new course design, new instructional techniques, etc. _seems_
focused on the conceptual deficiencies that have been clearly defined (and I
don't question that such deficiencies are real). The danger, as I see it,
is that we might 'throw out the baby with the bath water' in our attempts to
'fix' this conceptual problem.

The one group for which I can certainly justify the need for strong
conceptual understanding would be future teachers, but it is this group,
specifically elementary-ed majors, where we find the most resistance to the
more mathematical treatments. It is certainly true at my school (and I
suspect many others) that the level of mathematical sophistication needed to
be certified in elementary-ed, and therefore to teach science in elementary
schools, often falls below basic algebra. That is, a non-zero number of
successful elementary ed students COULD NOT pass a typical algebra level,
problem solving physics course. I question whether that is the level of
expertise we want teaching our children--at any level?

Comments? Flames?

Rick Tarara