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 firstname.lastname@example.org 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