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.
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