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Re: Definition of Capacitance

Can the experiment be done? Does it need to be done? On the one hand,
if students after 1 semester do better, you really want to know how they
would do "down the road", but you could never do a controlled experiment
over the intervening years. On the other hand, isn't the self-consistency
sufficient to guarantee that it would be an improvement?

Can it be done? That is up the ingenuity of the experimenter.
Should it be done? Absolutely yes. You can not find what works by just
using logical reasoning. It is an experimental problem. Researchers like
McDermott, Laws, Beichner ... all find out what works and improve scores on
tests. For example Laws et al found that teaching momentum before energy
works better.

Anyone who reads the literature can find examples of all kinds of questions
that can be researched. One of the interesting results is that paying
attention to the lower level first, pays off in much greater performance
later. Shayer and Adey improve performance on very lower level
underpinnings by targeting the Piagetian tasks. As a result they get large
gains several years later, but no immediate gain. One could argue that in
the introduction to these quantities, a consistent definition which provides
a good mental model is much more vital initially. Then later this can be
broadened. There is also evidence that helping students gain a good
microscopic model is also a strong component in better understanding.

As to whether you can measure a difference in performance for such simple
things as the definition of inductance, I would suspect that this is
impossible in the typical lecture/lab/recitation class. This is because the
real gain is so low that a small change will be washed out in the
statistics. However it may be possible to measure such things in an IE
class. In other words self consistency does not guarantee an increase in
gain if the teaching method is not very effective.

Actually there is a good argument for have definitions for both the original
and the inverse quantity. Then both definitions could be used in a variety
of contexts. The research shows that students need to have a variety of
strategies if they are to "understand" a topic. In the end I would support
any set of definitions that help the student make sense of the material,
consistent or not. I do think that conductance is a much more accessible
concept than resistance so I would definitely vote for that. Again, it
should be possible to teach an intro course one way or the other to see
which works better conductance or resistance.

As to poor old Ben Franklin, obviously nobody is going to change his
convention. I thought it was a good piece of humor, but points out a
serious problem. Perhaps the very labels + and - are a source of confusion.

John M. Clement
Houston, TX