Re: contribution of mathematics...

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

At 8:34 PM -0600 4/26/98, Bob Morse wrote:

> My point is that we need not describe relationships in algebraic terms,
> i.e. as formulae, in order to describe them in quantitative terms, and
> that there is a middle ground, a quasi-quantitative way of describing
> relationships that allows a certain rigor, but may be approachable to
> more students, than the abstruse (to some) short hand of algebra.
>
> Bob Morse

Bob's comment motivates me to compare this to what has been often said
here about physics. I have occasionally asked, playing the Devil's
advocate, "Why do we think physics courses are good for everyone?" This
rouses physics teachers to respond "To deny students the joys and values
of physics is unconscionable and unthinkable."

But, by advocating no more than quasi-quantitative instruction in physics,
aren't we denying students the joys and value of learning mathematics as a
powerful conceptual language? Aren't we passing up an opportunity to show
them examples of the power of mathematics as a thinking tool? Why do we so
easily accept that "Some students won't grasp mathematics above the
rudimentary level, so why force them to do it?" and at the same time we
imagine that these same students can grasp physics without mathematics?  A
curious double standard, it seems to me. Cynically, it seems as if the
physics teachers are saying "Physics, even diluted physics, is more
important than math, or anything else in the curriculum." 

Of course we can't solve the problem within physics courses. We must reach
out across the curriculum. It seems to me that physics teachers ought to
be more supportive of the math faculty by encouraging them to teach more
students more math, to ensure that students achieve not only the math
skills, but also grasp mathematics "conceptually". Then these students
could come into physics courses able to understand physics using their
grasp of math concepts and skills to build more effective physics concepts
and skills. We can demonstrate the sincerity of our support of the
importance of math by actually using appropriate math in our physics
courses, and using it in a meaningful way, not merely as number-crunching
and plug-and-solve.

And we should encourage our colleagues in biology, chemistry and earth
sciences to do likewise. Many faculty in those disciplines are our allies
in this approach.

I still think that the worthwile concepts in physics, the ones you can
*do* something with, are those expressed mathematically, and that a strong
conceptual understanding of math is the best foundation for conceptual
understanding of physics. The trouble is, very often students go through
both math and physics courses without gaining a conceptual understanding
of either of them. The courses are structured to allow students to
"succeed" with a superficial and ineffectual "grasp" of the subject.

	-- Donald

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Professor of Physics                                FAX: 717-893-2048
Lock Haven University, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu                 http://www.lhup.edu/~dsimanek
......................................................................