Arizona Winter School 1998
Kessel's Course Abstract

Smoothing the discontinuity between high school and college

Introductory undergraduate mathematics courses are often frustrating experiences for students and faculty. Students complain about that faculty do not teach well and that they are indifferent to students' academic difficulties. Faculty often view students as poorly prepared. I claim that part of the problem is the difference in student and faculty expectations of what should occur in the classroom. These expectations reflect very different views of the nature of mathematics and what it means to do mathematics. I review some of the evidence for this claim and give an example of how the problem of differing expectations has been solved.