Re: Text omission = lost pedagogical opportunity

["JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>]

Hi Bob-
	Then I'm not sure that your presentation is worth the effort, without
much more follow-up.
	My present philosophy is to require students to memorize and
regurgitate any proofs presented in class.  Successful regurgitation usually
requires three or four attempts (the first time).  After a while, though,
the message gets through for most students.
	I am incorporating this philosophy in the calculus text that I
am presently writing.
			Regards,
				Jack
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Hi Jack,
                I have never used this as a test question, but I would
guess that probably noone would be able to do it - unless, perhaps, they
were specifically told that it might be a test question.  But even then
I'm not sure if many, or any, of (my) today's students would be able to
do more than memorize (without a real understanding) the proof.  I think
my students of the 60's and 70's would have done better (but this, too,
is a guess).

I am troubled by this, because the difficulty is clearly NOT mathematical
(in the calculational sense).  I think perhaps that people's difficulties
with such arguments from symmetry have common roots with people's
difficulties in clearly recognizing and articulating distinctions and
similarities in general - everything is one hazy mush!

-Bob

> Hi Bob-
> What fraction of your students can reconstruct  your argument
> without notes by the end of the course?
> Regards,
> Jack
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