Re[2]: My view of science and science teaching

[Leigh Palmer <palmer@sfu.ca>]

>  Even Newton's laws can be taught like factoids....'factoid' probably
>  describes the level of most students' understanding of Newton's laws,
>  even those who have completed a descriptive intro physics course.

I feel this goes unrecgognized by many teachers. The problem is somewhat
greater than that, however. A couple of years ago I taught a mechanics
course at second-year level in which I discovered *after my own teaching
of the material* that, while the students knew and could apply Newton's
second law of motion mathematically

              -> ->     They did not believe it!     <- <-

It was a shock to me, a naive fellow who had been teaching for a bit
less than three decades.

I discovered this by setting up a simple demonstration and asking the
students to predict what would happen. They pretty much all failed to do
so correctly, and the demonstration was a revelation to them. It is
somewhat unsettling to realize that I (and my colleagues) must have been
turning out nonbelievers as physics graduates for all that time.

>  Flipping the same token, Kepler's laws can be taught at a deeper level.
>  For example, the second law describes conservation of angular momentum,
>  and this can be demonstrated graphically.

Thus Kepler's second law is an exemplary factoid. The more general
principle underlying it should always be introduced whenever Kepler's
second law is taught; one should *never* stop without making that last
step, even if it can only be done in words. Otherwise the student will
be left with the misconception that Kepler's second law is a special
property of planetary orbits, and one of those many things a physicist
must know, the sheer number of which makes physics so difficult!

As we all know, physics is not difficult. It is certainly less
difficult than playing the violin well, which may explain why there
are fewer good violinists than there are good physicists. It is very
hard to explain this to our students and make them believe it. I feel
that many teachers do not want to dispel the myth that physics is
difficult because that misimpression enhances their status.

>  Moreover, with simplifying
>  assumptions and some basic physics, students can be shown how the 3rd law
>  can be used to derive Newton's law of gravitation.

Well... Circular orbits around immovable force centers, I think you
mean. In my opinion it would be deleterious to the students'
intellectual development to hoodwink them into thinking that the law
of gravitation can be derived, since of course it can't. After giving
them the factoids of Kepler's laws I simply *tell* them that the first
and third laws were derived by Newton using the law of motion, the law
of universal gravitation, and the calculus, all of which were his own
inventions (oversimplifying a bit). Derivation of these results (not
of the laws themselves - those are "received factoids") usually has to
be postponed until the students' mathematical armamentarium has been
considerablt enhanced. I like to introduce Kepler's laws very early in
a science student's education.

Leigh