Re: Definition of Capacitance

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

> But not every experiment that CAN be done SHOULD be done.  Once you have
> some good generalizations, you don't test every specific instance.  I
> don't
> need to unplug my computer to know that I would lose this email.
> Similarly,
> I expect from my knowledge of learning that being self-consistent leads to
> improved performance.  I was willing to accept that I could extrapolate to
> this specific instance without need of a new experiment.   (Plus it would
> be
> nearly impossible to segregate the students for 10 yr and shield them from
> the hordes using a different convention to see if there was any long-term
> advantage.  You might actually find they do worse becuase they are forced
> to
> learn a new convention to fit in with the crowd.)
Consistency is probably a better strategy, but there may be measurable
advantages to one formulation over the other.  Such advantages also depend
on other factors such as whether you are dealing with concrete,
transitional, formal operational, or theoretical (category added by Anton
Lawson) thinkers.

As far as I know there have been no experiments to test the advantage of
teaching conductance vs resistance first.  Both of these are defined
concepts.  Also there have been no experiments as to whether it is better to
teach electron flow vs conventional current first.  From what I can see when
you have students who are less than formal operational both conductance and
electron flow are probably superior because the model is much more easily
visualized.  The advantage of electron flow is that it helps the student
establish the one way model.  Conductance has the easily visualized idea
that the flow is changed by the "force" or voltage with conductance as the
proportionality constant.  It is my observation that students can readily
visualize that the current went up as the conductance increased, but have
much more difficulty with an inverse relationship.  The difficulty with
resistance is that it is not easily visualized by students.  I suspect that
first having students learn conductance, and then later introducing
resistance will produce much better understanding.  It would probably also
help students who are still having difficulty with understanding
proportionality.

Such tests have been typically done first with a population of students that
has not been exposed to the standard terminology such as elementary
teachers.  Many of the techniques have been honed on such students and then
used on more advanced students.  One can do a short term experiment where
the non standard terminology is used, and where the students are later
exposed to the more usual terminology.

It is entirely possible that JD is correct in saying that the current
definitions are the most beneficial, but without some experimental evidence
all discussions are purely based on opinion.  Priscilla Laws said that her
intuition about what works is much better than it used to be, but that she
is still confounded because many times things she thought would work simply
do not.  So my suspicions are just as good as anyone else's until the
experiments have been done.  If Laws, Thornton, Beichner, VanHeuvelin ...
came up with an opinion on this topic I would consider that to be more
informed than mine or that of any non-researcher, but I would still like to
see evidence.

John M. Clement
Houston, TX