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The University of Arizona is a public institution with about 35,000 students. Each fall its Mathematics Department offers fifteen sections of second semester calculus (CalcII), with about thirty-five students per section. Recently we noticed that students entering with credit on the AB Advanced Placement Calculus Examination do not seem to be well served by our CalcII. One possible reason is that the AB calculus syllabus does not mesh well with the way we split topics between our CalcI and CalcII. The standard integration material at the start of the semester does definitely not challenge these incoming students, so instead of fully mastering the familiar material they relax. By the time new material is introduced they are well behind their classmates and many never catch up. Another possible reason is that in CalcII we emphasize written explanations along with numerical and graphical reasoning. Most incoming students are not very proficient with this. As a result, many of these students find their first mathematics course in college frustrating and unrewarding, even though they are often the most intelligent students in the class. (These statements are partially based on...

Disciplines:

• Mathematics and Statistics  / Mathematics  / Calculus