Re: a slightly different thread

["Roger A. Pruitt" <phrp@fhsuvm.fhsu.edu>]

Richard W. Tarara wrote:
> > From: Rauber, Joel              Phys <RAUBERJ@mg.sdstate.edu>
> >
> > Breadth Vs. Depth.
> This IS a primary question.  If the newer techniques COULD cover the
> breadth, then I think there would be a lot less resistance to at least
> trying them.
>
> As I see it the argument goes like this:
>
> What good is it to cover A-Z if the students don't really understand much
> if any of the material?
>
> or
>
> Can we really say we've graduated a physics major (chem major, engineer,
> etc) if they have never had any exposure to K-Z no matter how well they
> understand A-J?
>
> No easy answers here.  I would love it if students came to college with a
> good conceptual understanding of a few basic topics.  This is what I hope
> the outcome of the PER work provides--that the REAL introductory courses,
> those taken at the primary, middle-school, and high-school levels will
> develop into EFFECTIVE conceptualization courses.  Then the colleges and
> universities can provide the depth and the other skills needed by the
> technical students.  We're a long way from that.
>
> Rick
One of the problems with this discussion is that too many of us are
wanting to make it black or white or an either or option. I don't think
the discussion is restricted to one or the other case, but by doing so
the authors of these notes create a straw horse that is easily
destroyed.

What do we mean by "good conceptual understanding?" From some of the
discussions that I have read over the past two years, it seems that we
are still all developing our conceptual understandings. Are we to expect
students, even in an innovative course, to reach this level? If not,
what level then?

I had a student who was taking my senior level quantum theory course
over 20 years ago.
We were dealing with some of the formalism of linear algebra, and he
remarked that this part of the course would sure be easier for him had
he had a course in linear algebra before hand. I agreed since one can
hardly argue with that position. The following year another student was
in my office discussing some of the finer points of the same part of the
textbook dealing with the linear algebra. He remarked that if he had had
quantum theory first it would sure have made his linear algebra course
easier. I also had to agree with him. A few years later I was dealing
with a topic in the second semester of my calculus based beginning
physics class which involved some mathematics that I knew some of the
students may not yet have seen. I related the above story to the class,
and reminded them that somewhere they were going to see new material for
the first time. What they were seeing for the first time in physics
would make it easier for them when they saw it again in mathematics. A
very perceptive student sitting on the front row said, "Yeah, you have
to come full circle before it means anything."

This keeps coming back to me as I read the replies which argue depth vs.
breath. You have to come full circle before it really means anything.
Does a student really understand acceleration without understanding
force? Does a student really understand force without understanding
acceleration? By spending a great deal of time on kinematics, one might
be tempted to believe that students really understand the concepts. Do
they, or are we designing tests that are giving us the results we want
to see? Maybe we are teaching to the tests, and that is were our
successes are coming from.

A few weeks ago, I suggested introducing the concept of g as the
gravitational field along with the concept of the electric and magnetic
fields. They are all action at a distance forces versus the contact
forces that act on objects. I don't expect students to fully understand
electric or magnetic fields at this point, but the hope is that later,
in the second semester, their understanding will come full circle and
that the field concept will be more fully understood than if I
continually called g the acceleration due to gravity and didn't even try
to introduce the field concept.

Roger Pruitt