Re: Constructivist teaching, was quantization

[Hugh Logan <hlogan@ix.netcom.com>]

Jerome Epstein wrote:

> Can't fault Cromer on the program description, at least from the sample
> of topics Hugh quotes (in fact it sounds like my book designed to do
> essentially the same job), but everything is in how the topics are
> presented and what the students are asked to do. If it is all presented
> by lecture, my experience, and a wealth of research, says that for most
> students this is a very inefficient, or impossible, way to lead to
> genuine understanding. To provide that, the evidence is abundantly clear
> that we must allow the students ample ttime to explore, to engage in
> some trial and error, to go up blind alleys and retrace their steps. I
> am aware that this last is a paraphrase of Arons. LEcture teachers
> always convince themselves that THEIR students really do understand,
> only problem is that the teacher in the next course always finds little
> or no residue of understanding. It takes far more time and far more
> internal processing than most teaching allows for.

Despite my unwillingness to accept the extreme logical positivist and
anti-constuctivist philosophical standpoint of Alan Cromer's _Connected
Knowledge_, I think his SEED program sounds like an excellent idea from
a practical point of view. When I first started teaching at a technology
college in 1979, we had three levels of physics -- the highest at the
level of _College Physics_ by Sears, Zemansky (and later Young), the
next lower using _Technical Physics_ whose author I have forgotten, and
the lowest using _Physics for Career Education_ (whose author I have
also forgotten, but he must have been a Naval officer, because all
angles in an earlier edition were given as bearing -- measured CW from
the North). All the teaching was done by lecture, problem solving, and
laboratory exercises to illustrate the theory in traditional fashion. I
have long been aware of the claims that traditional lectures were
largely ineffective, but none of my colleagues were very interested in
educational theories or research. Our lowest level course was
essentially a pre-physics course lower than the high school level. 
We were advised not to do too much lab work, since this would duplicate
the labs in the courses they might take later. We were supposed to teach
the students things like simple measurements, units and their
conversion, simple pre-Newtonian physics like levers and pulleys. It
occurred to me that these were just the students that needed to learn
from experience in the laboratory. One of our experiments was what some 
of the teachers called "measuring the table." In my version I had the
students measure the length and width of the table in inches and then in
centimeters. They then calculated the area in square inches and in
square centimeters, and experimentally determined the conversion factor
between the units of area. I did this because one of the most common
errors among all levels of physics students was to use the linear
conversion factor for areas and volumes. This exercise seemed in keeping
with the sample experimental trigonometry lesson that I tried at the
(Piaget) Workshop on Physics and the Development of Reasoning, which was
an attempt to make trigonometry concrete. Alan Cromer's mainly
pre-Newtonian SEED program, which was then not yet in existence, would
have been ideal for these students. He has another version of "measuring
the table" in which students measure the length and width of a table,
each group using a different standard of length. They discover that the
ratio of the length to the width of the same table is always the same.

 

Jerome Epstein wrote:
> LUDWIK KOWALSKI wrote:
> >
>
> > My little experience in teaching without lecturing shows that this mode
> > of operation puts more demands on me. In a lecture mode I could prepare
> > presentations and follow my plans, more or less. In the student-centered
> > mode, on the other hand, I am a gambler. The success of an activity depends
> > on students, not on me. And I have no luxury of being ignorant of their
> > lack of understanding. It is so depressing to discover the naked truth
> > about ignorance of some university students. And I must learn to control
> > myself ...
> >
> > The lecture mode evolved naturally to protect teachers and keep the level
> > of learning as high as possible. Students who could not make it were
> > expected to drop out. But today we are expected to offer a degree to
> > nearly all students, at least to those who make an effort to learn.
> >
> > In my case teaching without lecturing was about as effective (in terms of
> > what students learn) as traditional teaching, maybe slightly more. Good
> > students liked it, poor students didn't (because they could not hide).
>
> Ludwik has it about right. One really does need to make a conscious
> decision that one wants to know the awful truth. The situation, however,
> is not hopeless. It IS hopeless if courses are still required to (in
> Arons' words): "cover all of physics from galileo to the uncertainty
> principle in one semester, to say nothing of astronomy and metoerology
> on the side."
>
> This is of course an exaggeration to make a point. But a great many
> "standard" courses aim to do a comprehensive survey of nearly all of
> classical physics, including mechanics, electrodynamics, thermodynamics
> and waves, in one year at 3 hours per week. I will maintain until I die
> that such courses will always produce nothing of any lasting value in at
> least 50% of the students. And only a vague smattering of disconnected,
> little understood equations and words in another 40%.
> Jerry Epstein

I have had little experience in teaching without lecture, except in a
more advanced laboratory course. But I agree with Ludwik and Jerry that
one is disappointed to find out how little is understood by the students
after attending lectures. This was particularly evident on the couple
occasions when I tried multiple choice quizzes requiring conceptual
understanding. Like someone said, the students don't want derivations.
In my experience they wanted worked sample problems, hoping that the
problems on the test would be similar. Even better would be sample
tests, hoping that the test questions would be like the sample
questions, perhaps with the givens and unknowns interchanged. The only
way I could get them to do free body diagrams was to make them a
separate part of the problem on tests. In my own experience I disliked
watching professors working problems at the board, but I often did it
myself. More than once I have known professors to say or write, "Working
problems is not only the best way to learn physics, it is the only way
to learn physics." I think David Hestenes says something better:
"Traditional physics courses lay heavy emphasis on problem solving. This
has the undesirable consequence of directing student attention _to
problems and their solutions as units of scientific knowledge._ Modeling
theory tells us _these are the wrong units; the correct units are
models." (from "Modeling Methodology for Physics Teachers" which can be
obtained from links to his homepage).

Incidentally, I recall an unforgettable impromptu discussion by 
Dr. Arons during a refreshment break at the 1976 Piaget Workshop in New
York in 1976, mentioning all the things that had been included in
physics courses when the more basic things were not properly understood. 
He also mentioned how children can and do learn about astronomy by
inquiry. I heard him lecture on elementary science education later that
year. There is a nice summary of his views on science education in
"Whither do we Hurry Hence?" in AAPT Pathways from November, 1981. Does
anyone still use _PSSC Physics_ which he praises so highly? (I have been
away from secondary education since 1979, and in recent years I have
heard of only one or two schools using _PSSC Physics_ with its emphasis
on inquiry . I still have the out-of-print college version with the
Advanced Topics).

Hugh Logan