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Hi Bob-usually
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
requires three or four attempts (the first time). After a while,though,
the message gets through for most students.mathematical
I am incorporating this philosophy in the calculus text that I
am presently writing.
Regards,
Jack
*********************************************************************
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
(in the calculational sense). I think perhaps that people'sdifficulties
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