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Topic for discussion
Posted:
Jan 7, 1997 12:13 PM
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I think our whole math curriculum is in doldrums. Math offering across the
country math offerings have remained nearly constant for more than 30
years. During this time, I have seen math enrollment steadily decrease.
Students just aren't interested the way they used to be.
When I asked (the late) Lee Rubel about this, he said: "Our trouble is that
we are teaching mathematics history and not mathematics."
Bill Thurston once gave his view on what's wrong:
"We go through the motions of saying for the record what the students
'ought' to learn while students grapple with the more fundamental issues of
learning our language and guessing at our mental models. Books compensate
by giving samples of how to solve every type of homework problem.
Professors compensate by giving homework and tests that are much easier
than the material 'covered' in the course, and then grading the homework
and tests on a scale that requires little understanding. We assume the
problem is with students rather than communication: that the students
either don't have what it takes, or else just don't care. Outsiders are
amazed at this phenomenon, but within the mathematical community, we
dismiss it with shrugs."
Later I read Saunders MacLane's idea that
"intuition-trial-error-speculation-conjecture-proof
is a sequence for understanding of mathematics."
Then I realized what Rubel was talking about because little of MacLane's
sequence is present in any math grad or undergrad course that I am aware of.
I would like to see lots of discussion on the topic of trying to make the
math we teach more like the math we do.
If we can pull this off, the points made by Rubel, Thurston and MacLane
will be addressed. And once again math courses will be exciting and the
students will come.
-Jerry Uhl
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Jerry Uhl juhl@ncsa.uiuc.edu
Professor of Mathematics 1409 West Green Street
University of Illinois Urbana,Illinois 61801
Calculus&Mathematica Development Team
http://www-cm.math.uiuc.edu
http://www-cm.math.uiuc.edu/dep
"Probably the best thing that Calculus&Mathematica offered me were the
tools and the confidence to attack problems that I would never ever think
to do by hand. "
---C&M alum and current Cal Tech grad student Justin Gallivan
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