So we teach Physics only to college junior or senior Math majors? ;-(
I think that you misunderstand me. I didn't say the mathematics
had to be *mastered* to use it for teaching*. Kinematics can be
conceptually understood with the barest introduction to calculus,
or even with the tools of graphical comprehension (these too are
fundamentally mathematical). As Dewey points out, we shouldn't
try to teach quantum mechanics and displacement currents without
mathematics. One appreciates the futility (my speller is working
again - I had a nap) of doing so when one attempts discussion of
quantum mechanics with students educated at the "conceptual"
level. At best, all they seem to have learned is the nonsense of
the Copenhagen interpretation without any idea of how that might
be connected to reality. In fact it is usually presented to the
nonmajor as if it is revealed Truth when we all know it is not.
Here's a challenge for those who think that mathematics can be
avoided almost everywhere in explaining concepts if one really
understands the underlying physics:
-> Explain the rainbow to me without using mathematics. <-
Students find understanding this phenomenon quite challenging
even when they do have the necessary mathematical preparation to
do so. I still remember my own excitement when the penny finally
dropped (I think I was a junior physics major at that time) yet
the rainbow continues to be a topic that is "explained" in some
conceptual physics books.
I just checked the latest book to arrive in my mailbox. Cutnell
and Johnson have an "explanation" with absolutely no conceptual
content. It serves well as an example to support my argument. It
is commendably brief, but it would be less harmful if it were
absent. Serway and Faughn devote two pages to the topic, full of
color pictures, useless diagrams, all devoid of physical content.
Why don't these people realize that the effect of a vacuous
explanation on a discriminating student will be negative, and of
no use at all (except to parrot it to another generation) to
lesser students?
Leigh
* I recall mathematics course I took as an undergrad at Cal. It
was quite sophisticated math, touching at the end on the work
of a mathematician called Peano. In the last lecture the teacher
defined "two" as one plus one. I'm sure that was done for effect.
It had none, I'm afraid, because I didn't come away with the
point, unless the point was to get an "A" in the course.