A Transition Course from Advanced Placement to College Calculus

Abstract

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II classes with two very different groups of students, i.e., freshmen and upperclassmen. It is difficult to construct a Calculus II course that caters to the disparate needs of these two groups of students. The second problem is that Duke's Department of Mathematics has been unable to come to a consensus over the debate between Reform Calculus and Traditional Calculus. Members of the department finally settled on a compromise. Two Calculus II courses are currently offered: (1) a Laboratory Calculus course that contains many elements of Reform Calculus and (2) a more traditional course. This presents a confusing choice to incoming students. The graduate student committee carefully crafted a Calculus II course that would hopefully solve both these problems. We will present these problems and the proposed solution in more detail. We will also discuss our experience with running experimental sections of this course and its future in the Duke mathematics curriculum. This article may be of interest to faculty or graduate students who want to take a hard look at the courses at their own institutions, especially if faced with a growing number of students who enroll with AP Calculus credit.

Keywords:

• Reform Calculus
• graduate teaching assistants
• Calculus II
• curriculum development
• AP Calculus

ACKNOWLEDGMENTS

We wish to thank the other members of the graduate student calculus committee, Rann Bar-On, Paul Bendich, Benjamin Cooke, Michael Gratton, Michael Nicholas, Nicholas Robbins, and Abraham Smith, for making the commitment to thoroughly review the Calculus program at Duke University and for the ideas they contributed to Freshman Calculus II. We also wish to thank Jack Bookman, Lewis Blake, and Mike Reed for their support throughout the process of lobbying for this new course.

Notes

¹The slight increase in Calculus I enrollment in 2007 corresponds to the adoption of stricter standards for admission to Calculus II.

²Actually, the situation was more complicated. There were three different Calculus II courses. However, two of them were nearly identical traditional Calculus II courses; one course had slightly more contact hours and a quick review of Calculus I. In 2007, the traditional Calculus II course with review was phased out. To simplify matters, in the discussion and in the presentation of data, we make no distinction between the two traditional Calculus II courses.