Re: Hand waving in physics teaching?

[John Clement <clement@HAL-PC.ORG>]

Actually building a conceptual foundation is of primary importance to having
the students understand the equations.  Equations are just one component of
understanding, and sometimes the least important.  As an example the problem
of two athletes running toward each other from opposite ends of a field with
different speeds and times is most easily solved using a simple position
time graph.  Students can then determine when and where they meet.  This can
be done by students who have difficulty with algebra, but it is also
extremely easy for higher level students.  Once the graph has been sketched,
the equations are then easy to generate from the graph if an "exact" answer
is required.  However in practical terms the answer easily read off of the
graph is as really no less exact than the answer found on a calculator
because of the uncertainty in defining when and where for large objects
which are not rigid.  The graphical answer will be fully as accurate as an
experiment done with a stopwatch, so it really makes sense.  I have found
that most advanced students have difficulty constructing equations for this
situation, but even math challenged students can solve it graphically or by
using a motion diagram.  As a result you may not see this type of problem in
a calculus based book.

Unfortunately the way in which math is generally taught, students lose all
sense of connections between math and meaning in the real world.  So the
mathematical meaning is often just the ability to remember and manipulate
equations.  That ability usually does not confer the ability to predict what
you will observe in a physical situation.

Now the professor is right about one thing.  Most "hand waving" is exactly
that.  It confers no understanding.  However a dedicated research based
program, of which we now have many, does confer understanding as well as
improved problem solving ability.  A good example is that most lecture
demonstrations are remembered as gee-whiz experiences and the concepts do
not come across.  However the research by Catherine Crouch and Ron Thornton
have revealed that it is possible to craft much more effective
demonstrations.  The most important factor is prediction, but overall
improvement of engagement is also vital.

So yes, you are right, but I would put it much more strongly.  The professor
in question probably has some good conceptual understanding, but really has
no idea of how to get students to also construct understanding.  The
techniques are coming as research based methods are being developed for QM &
EM.  In this case I would say that the professor has some severe pedagogical
misconceptions.

John M. Clement
Houston, TX

John M. Clement
Houston, TX

> Hello,
>
> I just had an interesting conversation with a physics professor. He said
> how he tries to explain physical phenomena to students without
> mathematical models, say
> in electromagnetism at a undergrad level. Then he continued that this
> "hand waving" is not enough, and of course students need also to master
> the topics; by this
> he meant the mathematical mastery.
>
> I think that he identifyed conceptual understanding with
> hand waving. I guess that this may be a common idea amongst professional
> physicists who are mainly concerned with research. On the other hand I
> would state that mathmatical mastery is only a part of physical
> understanding. In my opinion the real understanding involves well
> developed conceptual understanding linked with mathematical apparatus in
> physics.
>
> Perhaps there is a place for "hand waving" in physics teaching. Sometimes
> there may not be any good way of explaining a piece of physics for high
> school students (e.g. invoking quantum mechanics or Maxwell's equations is
> pretty meaningless for them); then I might wave my hands
> :-) and say that these ideas will become available at the university
> physics. But building a solid conceptual understanding with little
> mathamatics is a valuable goal - not just hand waving - in an introductory
> level. Of course,
> a more mathematical treatment has its place in high school physics as
> well.
>
> Do you have any experiences with "hand waving" in physics?
>
> Best regards,
>
> Antti
>
> Antti Savinainen
> Kuopion Lyseo High School
> Puijonkatu 18
> 70110 Kuopio
> FINLAND
> E-mail: antti.savinainen@kuopio.fi
> Web site: <http://kotisivu.mtv3.fi/physics/>