Re: Feynman (was pedagogy)

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 22:47 -0500 5/8/04, John Clement wrote:
> Well, what evidence is there that modeling mistakes produces better
> problem solving skills?  Feynman certainly had little evidence for
> his methods, and he called his lectures failures.
I am currently reading Rudolf Peierls memoir, "Bird of Passage"
(Princeton: Princeton University Press, 1985) and this morning I ran
across the following paragraph (pp. 28-29) about his student days in
Munich:

"I also attended lectures in mathematics. I remember particularly
those by Caratheodory, a charming Greek, whose lectures were not very
well organized. On one occasion he came into the lecture room and
said, 'Yesterday I thought of a proof for the theorem I want to prove
today, but on the way to the university I realized that it was
wrong.' So for the whole hour he tried devising another proof, but
got nowhere. As the bell rang, he said, 'Oh, I see now that my proof
of yesterday is all right!' I found that I gained much more from this
kind of lecture, in which you see the mental processes of the
lecturer, than from perfectly organized ones, which tend to hide the
difficulties and pitfalls."

Perhaps the lesson here is that different people learn in different
ways, and we should not be spending all our pedagogical efforts in
looking for the "magic bullet." When I first "discovered" the idea of
helping students by showing them some of the messy processes that
actually occur in problem-solving, I realized that not every student
will gain from this method, and obviously it cannot be the only thing
one does in class, but an occasional dose of it would be useful to
remind students that problem-solving is not a clean, orderly process
that involves just moving from logical step to logical step. I also
need to point out that I used it most in my second-year classes,
where the students were more serious, and were there because they
wanted to be rather than because they had to be.

In any event, we need to realize that there are many learning styles
and many teaching styles, and not everyone does either the same way.
Some learn well from lectures, others need to get down and dirty in
the details. Some will pick up the important points right away, and
others, who in the long run may be just as competent, will only work
them into their world picture slowly. Similarly with teaching. I have
found that personality plays an important role in what any teacher
does well. Some are superb lecturers but are "fumble-fingers" in the
lab, others get really excited about working with "things," but are
not good at explaining them. On p. 19 of Peierls' book, he talks
about Max Planck:

"Planck's lectures were, I think, the worst I have ever attended. He
would read verbatim from one of his books, and if you had a copy of
the book you could follow it line by line."

One wonders, if that was the standard of teaching in German
universities in the 20s, how it came about that Germany was the world
center of physics at the time. Clearly it wasn't. Peierls goes on to
talk glowingly about Sommerfeld's brilliant lectures.

I'm not saying that research into how to be a more effective teacher
is not valuable. It is. But it sometimes appears to me that everyone
is looking for the one teaching method that will work for all
students, and I don't think such a search is realistic. One thing
that I learned in my teaching career was that techniques that seemed
to work for other teachers, and that I thought had great potential,
just didn't work for me, with my personality. Teaching is in a large
measure theatre. and the personality of the teacher plays an
important role in what goes on in the classroom. If the teacher is
trying to do things that are inconsistent with his or her
personality, they will likely fail, because they will come across to
students as forced and unnatural.

On the other hand, different students learn in different ways, and
not all teaching methods will be effective with all students. It is
probably important for students to have teachers with different
styles, so they can get used to the differences that they will be
forced to accommodate to in their learning careers. But teachers
should be aware of the fact that no one method will be effective with
all their students, and even if one find a method that works well
with more students than others, there will be some quite capable
students who will not respond to that method and may not do as well
as they could with a different approach.

I look forward to the reactions of the varied personalities resident
on this list.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

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