I haven't thought about it enough to try to answer John Denker's
questions, but I admit that in teaching I agree with John Clement. I
always write it a = F/m and I tell students that writing it this way
ought to help them grasp it better than writing F = ma.
Quite a few students who encountered F = ma in high school have told me
it never made sense to them until they viewed it as a = F/m. Therefore
I am convinced that students generally view equations as effect = (some
function of cause). If that is the common student way of viewing it, we
might as well try to capitalize on that.
Along the way I try to show students other ways of viewing equations.
For example another way to view an equation is (idea or property) =
(definition). I view work that way: w = integral(F dot dr) is the
definition of work.
I think there are some equations that are more nebulous. Should the
work-energy theorem be written as deltaE = w or should it be w = dE.
Again, from my experience, students seem more receptive to deltaE = w
and they view it that a change in the energy of something was caused by
work having been done on that something, or that the something did work
on something else. But it is clear a few students debate which is cause
and which is effect. Could it be that something naturally changes
energy and work is the result? An example where they think this way is
water naturally flows over a waterfall and spins a turbine. Here the
work done on the turbine is the effect and the change in gravitational
energy of the water was the cause.
Of course there are multiple steps involved in this example and I can
challenge their thinking by saying that gravity did work (cause) on the
water giving it kinetic energy (effect) and then the turbine did work on
the water (cause) reducing its kinetic energy (effect).
Some students never get to this level of seeing physics equations.
However, if I can get students to discuss whether they are viewing
physics equations as definitional or as cause/effect; and if
cause/effect then which side is cause and which side is effect, then I
think we have arrived at a higher level of appreciation of physics.
Therefore this discussion of how equations are viewed is very
worthwhile, especially if we focus on getting students to think about
what equations might mean rather than nitpicking too much on the deeper
philosophical issues of cause/effect.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu