🚀 go-pugleaf

Connie Cooper wrote a thoughtful response, with a concrete example of how
she teaches a topic in conceptual physics, and also in more traditional
physics:

On Tue, 14 Mar 1995, Connie Cooper wrote:

>    How do we know when a student truely understands the physics that we are
> trying to teach them about?

That's the truly big question. Too often we have no idea what sort of
understanding students achieve. It's very difficult to determine by an exam.

>I teach both Algebra based (B level AP Physics)
> and Conceptual Physics.  I find that in many ways, the understanding and
> appreciation for what is occuring is stronger in those students from my
> conceptual class and the ideas last longer.

Here's where we'd like to know what sort of evaluation process you use to
compare the understanding in these two different cases.

[Part of Newton's law example cut.]

> mass was doubled etc.  We look at the formula as a ratio to give us a feel
> for how the forces change with changes in the various variables, and
> different combinations of variables.  The students do not see this as working
> with math formulas and numbers giving them answers.  This removes them from
> the idea of getting *the right* answer, to say nothing of the problems in the
> physics comprehension when they do not.  Do they have less of a feeling for
> the physics than those student who do everything with numbers, I think not.

Now here's something which I think is very important. It seems, from your
description that what you are doing, in part at least, is reinforcing
*mathematics* concepts, like ratio and proportion. This is a very good
approach, and shouldn't it *also* be done in the higher level physics
courses? But, shouldn't much of this also be done in *mathematics*
courses? Why should physics teachers have to do the job the math teachers
aren't doing? I submit that many students get through math courses with
some ability to manipulate equations, but no conceptual understanding of
mathematics (in spite of the fact that the new math was *supposed* to do
that). I don't mean that the math professors should be teaching physics
problems or even doing physics examples. I'd rather they leave that to
us. I'd just be overjoyed if they taught *math with conceptual
understanding*. If they did that, those students coming into physics
would pick up physics concepts much more easily.


>    Do not assume that these conceptual students are not worth our time.
>  These are not the people who will go into physics related fields, but may
> have a greater influence on the direction of science than we can see.  People
> who do not see that science is not a mystical study of things that was too
> hard for them to understand, will not support funding and legislation in any
> area.

So are you advocating, for them, a feel-good 'physics appreciation' course
*about* physics. That's ok; it's done in other disciplines. I just wish
more people would be honest in admitting that such a course isn't real
physics. Real physics isn't simple. Simple (simplified) physics doesn't
adequately describe the real world.

Is it better that these people in related physics *like* physics, even if
they have only an oversimplified and distorted understanding of it, or
that they not take it at all, or that they take a real physics course and
realize that it is beyond their abilities and comprehension. Which is
more intellectually honest? I'm not presuming to say which is best.

I recently had the experience of hearing a faculty member at a medical
school give a talk purporting to show how important physics was to the
field that person taught. An example was given, in which the physics of a
situation was seriously misrepresnted. The Physics in the example was
simply wrong, and a number of physics teachers in the audience spotted the
error. Yet that example came from a textbook in that field, and the people
in that field thought they were teaching something important, based on
physics.  That, I submit, is the frightening result of giving people the
feeling of understanding physics, when in fact they don't have it right.
Which is worse: Knowing nothing and admitting it, or thinking you know and
understand things which are not true? Would I want such a medical
practitioner making decisions which might affect my health, or my life and
death? I often say that if your life or death depended on your doctor's
understanding of physics, you might as well say your prayers, it would do
about as much good. (And I'm a born-again atheist!) Fortunately those
medical applications which really require physics are usually in the hands
of medical physicists, who understand this stuff, or are designed
(engineered) to be so fool-proof that even a doctor can use them
properly. Ask your doctor to explain something medical which depends on
physics, listen to the explanation (which should reflect your doctor's
understanding)--and be afraid...!

It's dangerous to give people the "illusion of understanding". And, I
fear, many purportedly 'conceptual' courses do just that. Oh, such physics
is harmless enough, if these folks never *use* it for anything important.

>    A question that you might try asking your students on a test, perhaps as a
> bonus, is what *is* physics?  You might  be surprised at the answer.

The members of this discussion group might give some surprisingly diverse
answers also.

While we are at it, ask them to distinguish between a hypothesis and a
theory. Ask them what is meant by scientific induction, and how is it
fundamentally different from mathematical induction. Ask them whether F=ma
is a law of physics, a definition of force, a definition of mass, or two
of the above. Ask them why F=ma would be useless without Newton's *third*
law. Ask them for to state Newton's third law (and do not accept
"action=reaction" insist on something like "If body A exerts a force on
body B, then B exerts and equal and opposite force on A) Ask them for the
*definition* of centripetal force. (In the context of the elementary
course, F= mv^2/r is *not* the definition.  It is derived from the
definition: "Centripetal force on a body is the radial component of the
net force on the body.") One thing which stands in the way of students
grasping the logical structure of physics is that they are often unclear
what things are: (a) empirical laws, (b) laws derived from a theory, (c)
definitions. We don't often enough emphasize how things connect one with
another.

What is physics? An edifice of theories, laws derived from theories, which
in turn predict facts about nature, which can be tested. It is a logical
structure held together with the cement of mathematics. Its purpose is to
economically *describe* the observable world, and must always be held
accountable to skeptical experimental testing. Though it is a deductive
structure. It is built so that the progression from theory to law to facts
may be accomplished by strict mathematical deduction. However, deduction
does not *build* the structure; it is built by induction *from* facts, a
process which is *not* strict logic, but involves creativity, intuition,
solid concept understanding, risky extrapolations, brainstorming, and once
in a while, dumb luck. But in the end, no matter how beautiful the
conception of this structure, it will stand or fall not on its beauty or
emotional appeal, but on whether it fully and precisely accounts for the
mundane facts of observation.

>     I now step down from the soap box.

Return to your soap box from time to time so we can hear more of your
thoughts. The rest of us get on our soap boxes quite (too?) often.

        -- Donald