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Re: teaching 'em to learn, to think, and to decide what's important



Well put. Much of this comes under the heading of sharing with students
in an overt way what we do covertly...ie we just do it and don't think
about it.
Thanks for the references on ideas about learning. The Nat
Acad of Sci recently published a book entitled How People Learn. It is
downloadable chapter by chapter from their website...or you can buy it.
It has a long section at the end on implications for teaching.

cheers,

joe

On Wed, 24
Jul 2002, John S. Denker wrote:

This morning's discussion of the "spiral approach"
leads me to ask a question:

How many teachers explicitly discuss things like
the following?
1) study habits in general.
2) how to decide what's important, so you (the
student) can avoid wasting time memorizing
unimportant stuff.
3) how to consolidate the memory of something
you consider worth remembering.
4) how to think about the future; in particular
recognizing that there are some behaviors that may
seem like short-term disadvantages, but in fact
give you tremendous long-term advantages. For
instance, if you don't cheat and don't cram for
tomorrow's test, you'll be disadvantaged relative
to those who do ... but next year you'll know the
material and they won't. You will progress from
understanding to greater understanding, while they
spiral from cheating to grosser cheating, until
they get caught or give up. Eventually the non-
cheaters will be the only ones standing.


There is a tremendous literature on how to remember
things, going back at least to Simonides (2500 years
ago). And as previously mentioned, William James had
some pretty keen insights into teaching, learning, and
memory (110 years ago).
http://www.emory.edu/EDUCATION/mfp/ttpreface.html

Courses in this area are required for a high-school
or grade-school teaching certificate -- but does any
of it get communicated to the students? I don't
recall ever getting the least bit of useful advice
on the topics enumerated above.

This may seem a bit off-topic for a physics course.
But the math teacher will say it's off-topic in that
class, and so on for history and every other topic.
So who's supposed to do it? The homeroom teacher????
I claim that each and every one of them ought to do
it, explicitly and repeatedly.

The spiral approach is necessary but not sufficient.
It rewards those who stumble onto the right approach,
but students who don't start out with the right
approach won't have an easy time figuring out what
their mistake is.

I'm not saying I know how to teach this. I don't
think it's easy. But I think it's important.

To illustrate what I'm talking about, here are some
partially-baked suggestions:

*) It would be good to super-explicitly point out the
various interconnections in science, e.g.
-- magnetostatics is related to electrostatics is
related to inviscid hydrodynamics is related to
soap films on wire frames, etc.
-- pattern recognition is related to machine learning
is related to data compression is related to complexity,
probability, and entropy, which are related to
thermodynamics and (parts of) cryptography.
-- boosts are related to rotations.
http://www.monmouth.com/~jsd/physics/rapidity.htm
-- cross products are bad news because they don't work
in two dimensions or in four dimensions, but there
is something else (the wedge product) that works just
fine and allows you to exploit the similarities between
two, three, and four dimensions.
-- et cetera.

*) It would be good to point out the value such interconnections
have in helping make memories more solid and more useful.

*) It would be good to teach students to play games that
have an element of strategy, where the greedy algorithm
doesn't pay off in the long run. Even a simple game such
as Reversi (Othello) will illustrate the point: if the board
is mostly black halfway through the game it doesn't mean the
black player has the advantage. No sirree. But the point of
the lesson is lost unless students are taught the strategy,
and taught the difference between strategic and non-strategic
behavior. If they just play the game in the greedy, childish
way they learn nothing.

*) Similarly, "plug and chug" homework problems should not be
assigned, because they foster the foolish expectation that
problems can be solved in the obvious way. As an example of
something better, include two or three irrelevant factoids
in the statement of the problem. Someone who takes the
childish, greedy approach of exploiting the given factoids
in the order they are presented will get stuck.

============

Anyway, I don't claim to know exactly how to teach this.
But:
a) It seems self-evident that it is important for the
students to know how to learn, to think, and to decide
what's important.
b) It must be possible to teach such skills.
c) In my limited observations, it appears to be taught
horribly indirectly, or not at all. Reports of success
stories would be welcome.


Joseph J. Bellina, Jr. 574-284-4662
Associate Professor of Physics
Saint Mary's College
Notre Dame, IN 46556