🚀 go-pugleaf

Richard's thoughtful posting gives an opportunity to clear the air of
some misconceptions and other intellectual pollution.

On Wed, 15 Mar 1995, Richard L Taylor wrote:

>     This thread is driving me nuts! (...as well as a number of other high
> school physics teachers, apparently.) Why must everything be "this" or
> "that," not a little of both or something in between. Physics without
> math--I know (as many others here do) what conceptual physics means, but
> whatever physics we teach, we _are_ teaching math. Physics _is_
> math--that is, using symbols, looking at relationships, thinking
> logically. Mathematics is _not_ just writing equations with Greek
> letters! And the use of equations is only one (separable) part of physics.

Right on, mostly, IHMO. I think we can all agree that conceptual
understanding *ought* to be a goal of courses at *all* levels (high
school and college) in *all* fields, (math, physics, and other) and for
*all* students (preparing for science, or non science fields). We do not
wish to turn out mindless clerks and number-crunchers and computer-jockeys.
It's not either-or. All intellectual resources should be encouraged.

However, it seems to me that all but the most trivial physics concepts are
*expressed mathematically*. Let's look at your examples (you are the
first to offer any). Equations are only the language for expressing
concepts, but you can't *use* the concepts, test them, be creative with
them, without mathematics.

>     Physics is about understanding the world using symbolic logic and
> based on experiment. There is a great deal of understanding that can be
> achieved without formal equations. You want a physics concept without
> equations? How about this one: "When you come upon an icy patch in the
> road, don't hit your brakes!" Or, "When you compare measurements to see
> if they are the same or not, keep in mind that measurements have
> uncertainty." Or, "When you tighten a screw with a screwdriver, a fat
> handle works better than a skinny handle." None of these statements is
> the last word in physics, but each illustrates relationships, results
> from logical considerations, and is useful and accessible to people
> without using formal equations.

The ice thing is well known to anyone from experience, even before they
take a physics course. Does the physics course help them to avoid falling
on slippery ice?

The screwdriver thing is well known to anyone who has ever used a
screwdriver, and I doubt that a physics course will help a person use a
screwdriver better. (My wife has had a college physics course, and still
grabs the wrong screwdriver.)

Comparing measurements and the uncertainties in measurements. That's a
very important thing we should be including in our physics courses. But in
its verbal form, it's virtually useless. Not until one asks: "How much
uncertainty is there in each data source? How do we find out? How do we
express its size? How do those sizes allow us to predict the *size* of the
uncertainty of the result?" Only then do we get anything useful, and we
had to use mathematics to get it (some mathematics of finite differences,
or maybe calculus which isn't considered appropriate to a high school
physics course). I am sensitive to this issue, for I consider the
treatment of error analysis and error propagation in most lab manuals to
be wrong, misleading, and useless, and I'm talking about lab manuals at
the *college* level. This is one thing I *know* students aren't 'getting'
in high school.

>     And that's the other thing that's crazy--what _is_ the last word in
> physics? To say that no equations is not physics, then how many equations
> must a course have in order to be physics?

Equations represent concepts. The equation without understanding of the
concept is dangerous. The concept without the equation is usually useless.

> Will one do?

Wouldn't that be nice!

> Or have any of us
> yet seen enough equations to be sure that we have had the "real" physics
> course?

I haven't. I don't think anyone ever does, if they are honest. Physics is
not a closed, complete system, but a continually changing and evolving
structure.

> Thomas Huxley said, "If a little knowledge is dangerous, then who
> among us has so much as to be out of danger?"

Not I. Why just last week I agonized on a question related to a
simple physics demonstration (one never discussed or done in textbooks), and
finally realized (after two days) that the answer should have been obvious.

> We should not be afraid of
> students having only a little knowledge of physics--that's all any of us has!

It helps a lot if one clearly knows what one knows *and understands* and
what one does not. Know the limitations of one's knowledge. The thing I
fear is students who have an *illusion* of knowledge which is either
wrong or incomplete. We, as teachers can encourage students to know the
difference and to clearly define the limitations of their knowledge.

>     By the way, I don't think that conceptual courses are "about
> physics," they _are_ physics. If students are figuring out the world
> logically, symbolically, and empirically, then they are doing physics.
> Making distinctions about good physics and bad physics, about real
> physics and ...whatever the alternative is, is much ado about nothing.

What's in a name? Does a label matter? Is it a matter of "Truth in
advertising?" Just an observation or two. I remarked that there used to be
music courses called 'music appreciation'. An honest label, though as a
student I said "Why do I need a course in music appreciation? I already
appreciate music." Now those courses are labeled 'introduction to music'.
Still an honest label. Physics courses used to be labeled 'introduction to
physics'. Fine. In the 70s, when we in colleges and universities realized
we had to teach remedial high school material (because we are admitting
unprepared students--it was our own fault) some schools had courses
labeled 'remedial', often required, but with no academic credit. They
disappeared. The word 'remedial' was considered politically incorrect, and
'demeaning' to students. Now such courses have 'safe' names, usually names
with profound sound which imply more than the course can deliver, and
carry college credit. One of the commonest complaints I hear from
university colleagues is "Why should we have to teach material they should
have learned in high school. They come to us claiming they've had 'college
prep' courses, but it doesn't show." (Must be that our college admissions
standards at fault. Or maybe we are expecting the wrong things.)

As I was writing this, a physical chemist colleague with long experience
in industry and universities, and as an industry consultant and journal
editor, looked over my shoulder at what I was writing and distracted me
into showing him the other messages in the thread and into a discussion of
'conceptual physics' courses. His response: "Those courses are garbage.
That's just another indication of the continuing decline of standards."
And you folks think *I* am a meanie! Actually, folks, I am on your side,
but just trying to get examples and clarification of the lofty ideas you
are talking about. And if you are preparing students for college, prepare
them for meanies like my chemist colleage, and myself, who expect at
least some conceptual understanding, and the ability to use those
concepts correctly with some mathematics. This isn't about equations vs
no equations. Equations aren't the issue. The issue is *concepts*, and I
still am not convinced that any but the most trivial physics concepts can be
learned *and used* without some *conceptual* understanding of mathematics.

Since, as someone remarked, this is a group for sharing resources, not
discussion and philosophizing, perhaps you folks could share examination
questions you have found effective in determing whether students have
developed conceptual understanding, and questions which thwart equation
memorizers and math jockeys from achiving good grades without
understanding. Now *that* would be useful to many of us, even at the
college level.

        -- Donald