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Re: Energy



Whether energy does or does not flow is in a sense a purely semantic
question which can only be answered by having a universally agreed
definition of flow, and then by seeing if the process observed adheres to
that definition. That being said, is the idea settled? Obviously it has
not been settled, as shown by the various posts on this list.

There are many reasons for this, but few of them have any relation to the
rightness or wrongness of the idea. Perhaps the definitions vary too much
from one person to another, or perhaps the definitions are too loose. I
think that a little consideration of how people learn, and how we make sense
of the world can be revealing.

If what I say is too simple and obvious, I wish to apologize in advance.
Students, faculty, babies, and all of us learn by taking what we know and
then either incorporate new things into the existing structure of by
changing the structure that we have to accommodate the new ideas. The means
that we must refine definitions, change definitions, and come up with new
definitions and terms. Each one of us must individually construct the
understanding based on what we already know and understand.

Within each of us there is a set of rules and connections between ideas that
is unique. Fortunately we have managed to come to some common means of
communicating and understanding so that we can discuss ideas in a fairly
rational manner. Also within each person there are deeply imbedded ideas
which form the basis of most understanding. I think that the idea of "flow"
is probably one of these basic ideas.

Physics instruction works to help students form a consistent set of rules
and ideas so that they can then understand the world around them. This
means that they can behave in what we would call a rational manner. They
can do problems, explain situations, correctly predict the outcome of
experiments and so on. All of these actions can be performed with slightly
and sometimes widely divergent ideas about the world. Mathematical
understanding is the most exact method of prediction, and consequently is
considered the most important. However underlying the math is a set of
ideas which can actually be quite widely divergent, and which can be
expressed in widely divergent fashions. The only real test of the
correctness of these ideas is how well they support the individual in
behaving in a rational physicist like manner. When dealing with abstract
concepts there is often no really right or wrong way of describing them as
long as the description supports a good predictive math description.

Notice that any argument which claims that a particular understanding is
faulty, although it leads to the same end result, is a theological argument
and not a physics argument. I would say that both sides can be consistent,
and that neither is right or wrong, just different. Remember, we are all
experts and that we can dispute freely, but let us realize that some
disputes have no resolution. I think that the flow question is one of them.

That being said, I think that how and what you teach students is a very
different question. Students do not come into class with the same ideas,
and abilities as the members of this list. Most of the ideas and questions
that are being discussed here would be completely incomprehensible to the
average student, and would be difficult to many of the above average
students. When considering teaching we have to be aware of the level of the
students and then provide them with the opportunity to construct a better
understanding of the world around them. This does not mean indoctrinate
them with a particular set of ideas.

As Arlyn DeBruyckere [arlynd@HUTCH.K12.MN.US] so aptly pointed out, many
students do not even understand the conservation of volume or possibly even
the concept of volume. As a result they must construct models based upon
the existing ideas that they already have, and those ideas are at an
extremely low level of understanding. One of the ideas they will use is the
idea of flow. Indeed even the better students will often have the idea of
flow behind their understanding. They may have learned to avoid the word
flow, but they will often be thinking that the energy is flowing from A to B
so that when A has lost X energy B has gained X energy. Notice the
shorthand lost and gained implies flow. We could say instead that A has
lowered energy by amount X and B has raised energy by amount X.

As a result, I would say that the flow terminology can be useful when
dealing with students, and should not be necessarily discouraged. The real
test of understanding is whether they can transfer this terminology into a
more exact description. There are many simple evaluations which can be used
to test students. One such evaluation is the use of a bar chart where they
have to label how much of each type of energy is lost, and how much is
gained. They should be able to show that the amount lost of some types of
energy lost is the same as the amount gained of other types of energy. This
can also be extended to an energy (or momentum) time graph. On such a graph
they should be able to draw curves that show that with time the total amount
stays constant.

Some examples of the types of tasks that students need to learn to do are at
http://umperg.physics.umass.edu/projects/MindsOnPhysics/MOPSamples/ . In
particular the activity
http://umperg.physics.umass.edu/gemsFolder/umperg2/Act077.pdf shows an
example of the type of momentum change graphs (A4) that defeat many
students. You can also go to the various published materials by McDermott
to find good examples of teaching ideas and evaluations. The material at
the UMPERG website may seem to be very simple, but you might be surprised
when you throw a few of these tasks at students. The real test of good
teaching is how well students can do some of the simple tasks on the MOP
samples.

I would in the end summarize my thoughts by saying that flow is a useful
idea, but not always useful. A good physicist uses whatever mental images
that are productive, and will often switch from one image to another to
predict the outcome of various experiments. Even images that are currently
out of fashion can often have some predictive value in particular
situations, so they are not necessarily wrong. A particular mental model
that is not predictive is actually not "wrong" just "unuseful".

John M. Clement
Houston, TX