🚀 go-pugleaf

A member of this group responded privately to me on the *forces* thread.
My attempts to e-mail him directly failed: "Service unknown" and the
message was bounced back to me. So I've removed references to his name
here, and included part of the post which might have some general interest
to the group. Perhaps he will see this and tell me why my e-mail gets
bounced back when using his address as given in his message.

I omit much of his message, and include only the portions in which we
have some differences of opinion. On the whole, he and I agree on a lot.

On Wed, 17 May 1995, XXXXX wrote:

>  In my own education I am sad to say that I went through baccalaureate and
>  graduate degrees in physics (at different  institutions) without ONCE having
>  seen a lecture demonstration.

That's a crime of education! But another crime is the 'empty'
demonstration done just for entertainment, without being integrated into
a plan for getting across a concept. Most of the larger institutions have
a dedicated stockroom of demo equipment, and a person hired to maintain
that stockroom, develop ideas and set up and tear down the demos for the
profs.

>      It has been my personal experience that most college-level physics
> teachers know only a piece of chalk and tend to "hide" behind math.

But on the other side of the coin, we find some high school teachers
bandying about the slogan "conceptual" and avoiding math like the plague.
There's got to be a middle ground. Physics without math is empty
sloganeering. Math without physics is usually just number-shuffling.

> As a result, many students tend to become overwhelmed by the math, never
> SEE the basic ideas behind the math, and never develop that intuition for
> physics that is so important to teaching (my own miserable opinion).

And these days most of them never seem to grasp the basic ideas *in*
mathematics, and never develop *math* intuition either.

> To take a stand that these topics can be taught only by using calculus and
> "junior-level mechanics" implies that high school teachers can never teach
> ideas like this, since these tools are not available to us.  The genius of
> great teachers such as Paul Hewitt (and Feynman) is that they were able
> to teach these ideas without math.

Huh? In my copy of _The Feynman Lectures_ I see a lot of math, including
calculus.

You noticed I used the term 'feel' a few times also, but took care,
as Reiter did, to enclose it in quotes. I know some profs who mime quotes
with both hands when they speak such words, so students know that they
are not being used in a precise manner.

>         I personally feel that using intuitive words like" feel" and using
> anthropomorphism in teaching are useful tools.

It's all in *how* you do it. I sometimes do it to add a bit of humor, but
try to convey by in my tone and attitude that I am speaking casually,
or making fun of something.

Sometimes this can be useful, I agree. Here's an example. In discussing
the diffraction of light produced by a single slit, and trying to convey
that the usual classical interpretation is a model, and a somewhat
incomplete one, I do this:  "The book derives the maxima and minima
positions by splitting the aperture into little strips dx, and adding the
contributions they make at a point on the screen by integrating across the
slit width. But, if the point on the screen is offside at angle theta, and
the incoming light was collimated in direction theta=0, why does *any*
light emerge from the slit at any angle other than zero? How does the
light passing through the center of the slit (well away from the slit
edges) 'know' where the edges of the slit are (or that there even *are*
any edges), so it can change direction by amount theta?" Some students
suggest the Huygens principle, and then I ask whether they really 'believe'
that principle, which asserts that from each point along a wavefront (in
free space, even) light re-radiates in many directions. My purpose in this
little exchange is to show how artificial the model is - yet it works!

> If I were "King of the World", I
> would certainly have all physics majors take a conceptual course in physics
> before entering any calculus-based class.

This is in fact what we did when I was a physics major in the 50s at a
large university. The physics majors took the non-calculus course,
along with pre-meds, pre-dents, pre-pharmacy, etc. Some profs joked that
this would give us more competition, for the pre-meds had a reputation of
fierce competition for A grades, and A grades were not so easy to get
then. (I later tutored a girl who was taking the course the third time,
hoping to pass it. I got her through.) There *was* a calculus-based
course, but only engineers took it. Later when I, as a sophomore, had a
job as a 'graduate' assistant, we assistants conspired to give both groups
the same non-calculus final exam, to see which did better. The engineers
did much worse. Not exactly a fair comparison, however. We weren't
surprised at the result, for the engineers had a reputation of being
unmotivated and lazy. They didn't have to compete for grades then.

> The basic ideas of physics can be taught without a substantial amount
> of math.

A small number of ideas can, and that's enough. Introductory courses
should not try to include too much.

> Surely, once students
> develop an intuition for these concepts, the math can be used to formalize
> the ideas and deepen the level of understanding..

That's been the traditional method of teaching physics. It wasn't invented
recently. I have near me a copy of Millikan and Gale's _First Course in
Physics_, 1906, and it does just that. I often go to the older books for
inspiration, and have a pretty good collection of them. The older books
are models of brevity and clarity, without much math. And they were small,
not the overblown high priced 'encyclopedias' of today. I urge teachers
to take a look at them, and learn from their style.

>         Physicists tend to fear criticism from their colleagues, and so try to
> be very precise in their teaching (I think we're all a little insecure).  This
> attempt to be rigorously precise, though, often seems to result in a failure
> to communicate on an intuitive level.

I haven't observed this fear. Most teachers around here are the *only*
physics teacher in their school, and have no colleagues qualified to judge
them. I haven't observed them trying to be rigorous and precise, either -
quite the opposite. Here, I think, is where I disagree most with you. I
don't think one *can* communicate on an intuitive level, for our intuitive
approaches are so individually different. Perhaps we can find a common
language for communicating, and through it *develop* physics intuition.

Our job, it seems to me, is to develop in students a *way of thinking
about the world*, in particular, the physicists' way of thinking (we *are*
talking about *physics* courses here). We should not pander to the
students' naive modes of thinking, but lead them, step, by painful step,
to more effective modes of thinking (and learning). For physics *is* all
about learning - learning how the universe works. Throughout the history
of physics we have abandoned many ways of thinking about the world because
they were ineffective. Thus we have narrowed physics down to methods which
work - and they *are* necessarily bound up with mathematics. To suggest
otherwise is to misrepresent physics itself.

As has been said, too much rigor can lead to rigor mortis. I do not
advocate rigor for its own sake. What I complain about is *unnecessary*
and potentially misleading carelessness of language, and inattention to
detail. I complain about 'faking it' when a question forces the teacher
beyond his or her knowledge.

Should we make an issue of the fact that the mathematical
representation of torque is not a vector, but is mathematically a
pseudo-vector? I think not. That can be corrected later.

Should be fuss about the difference between the concepts of gravitational
mass and inertial mass? No. It can be dealt with later.

Should we be careful never to speak of 'current flow'? (As silly as
saying 'rate of speed'). Yes. It's easy to do, doesn't take additional
time, and sets a good example of consistency and clarity to students.

Shall we agonize over the *best* definition of weight? Perhaps not. But
when we (as do most textbooks) tell students that weight is defined as
W=mg, then later describe an astronaut in circular orbit around the earth
as 'weightless', and later speak of the 'loss of weight' of a body
immersed in liquid, serious student confusion can result. These are
clearly contradictory uses of the word weight, and alert students
notice that, and are bothered by it. I've had students complain about
colleagues along these lines: "I thought physics was a *precise* science,
yet professor X can't even get his technical terms defined consistently and
precisely."

Does it matter that so many students think F = mv^2/r is the *definition*
of centripetal force, when it's actually a derived result? It surely does!
This is one of the reasons students so often misuse centripetal force in
problems. So what's the use of 'knowledge' if it is misused? What's the
use of it if it is correctly used, but by rote rather than understanding?
Better not to discuss it at all. But then we wouldn't be able to have the
fun of a field trip to the amusement park to do 'amusement park physics',
would we?

>         So, here's a vote for anthropomorphism!  Here's a vote for sacri-
> ficing precision for clarity (at least at the beginning).  Here's a vote for
> having the center of mass FEEL!!

Before sacrificing precision, let's carefully examine the alternatives, and
determine whether there's an overriding need, and value, to justify the
sacrifice. We need an 'educational impact statement' study for things
like this. We need monitors for intellectual pollution. :-)

Physicists do not advocate rigor and precision out of a desire to be
obscure. They do it because rigor and precision aid understanding, promote
correct concept development, and help prevent ambiguities and fuzzy
thinking. We teachers need to make that point by example.

One way I combat student complacency is to put forth examples or
demonstrations which clearly show that analysis based on naive
'understanding' gives the wrong answer, an answer which simply does not
agree with observation! Anyone who has been in the ed-biz a while knows
most of the common student misconceptions, and can easily devise questions
and demos in which those misconceptions are exploited. It is only when a
student realizes that his or her 'understanding' leads to demonstrably
wrong predictions, will that student be motivated to improve that
'understanding'.

Once, years ago, when someone challenged me on this, I made out a multiple
choice exam based on student misconceptions. Everyone flunked. But more
important, after the fact, the students agreed that the questions were fair.
I did not include this exam in their grade.

Thanks for your thought-provoking response. I wish this group did more of
this kind of give-and-take collectively. But very often a provocative
statement, or even an outright boner, just lies there and nobody
responds, not even with a good flame.

        -- Donald