Dear mathedu people(*,) At this point, 256 people have now signed on to mathedu, a forum for discussions about teaching and learning post-calculus mathematics, including graduate courses. The list has reached a critical mass to start active discussions of ideas and issues. We have much to discuss. Passions in these areas have sometimes run quite high, since we all have a great deal personally and professionally invested in mathematics education. But despite appearances of polarization at various occasions, I think the mathematical community is actually quite united, especially in the in the fundamental goal of promoting education for genuine mathematical skill and understanding. Our differences are often more apparent than real.
When I was a graduate student learning topology, I worried about whether the "right" kind of topology was general topology, algebraic topology, geometric topology, differential topology, PL topology, point-set topology, etc,---just as if it were a partisan dispute.
As my understanding matured, I came to appreciate how these multiple approaches work together: difference does not imply conflict, that's exactly backwards. Multiple styles and approaches add to each other, together giving much more power and insight than any single approach alone. ---- The big question I've been wondering about is what practical goals do we want for mathematical education, and how can those goals be adequately expressed? I think we have traditionally relied too much on a single mode of expression the "content" lists: curriculum and syllabus. which have often become bloated in a futile attempt to compensate for their inability to capture what we really want the students to gain.
I would love to hear your goals for teaching, learning and the development of our students.
(*) What are we going to call ourselves? Mathedoers?