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Using Connected Curriculum Project Modules - Background

John Hannah

The CCP modules were used in the second half of a one semester second year calculus course, the first half being about multivariate calculus, and the second being about differential equations. There were 107 students in the class, all of above average ability (getting at least B+ in their first year mathematics course). About 60% of the class were engineering students, with most of the remainder being science majors.

The class met for 4 one-hour lectures and 1 one-hour tutorial each week. For the first half of the course, the students were divided into six groups which met for traditional tutorials: discussing previously assigned problems from the text book (Anton), working through additional problems set during the tutorial itself, and getting help from one another or the tutor if they got stuck. Homework problems were not graded, the main incentive to do them being that the exam would be based on them. (This was insufficient incentive for some students, who came to the tutorials unprepared and tended to take little part in the discussions.)

The same six groups were retained in the second half of the course, and the tutorials became lab sessions in which the CCP materials were used. In this more active environment, it was much harder for students to avoid participating. Tutors too needed to adapt to the new environment. For an account of the dilemmas facing tutors in a lab environment, see Winter et al.

Homework problems were still being set, this time from Boyce and DiPrima. To compensate the students for the loss of the traditional tutorials, three extra consultancy hours were offered each week to help students with any problems they might have with their homework or with the CCP modules.

The differential equations part of this course deals with second order linear equations, series solutions, the Laplace Transform and Fourier series -- essentially chapters 3, 5, 6, and the first half of chapter 10 from Boyce and DiPrima. I wanted the students to try each module about a week after I had lectured and set homework on the relevant subject matter. This would give them enough time to prepare for each module. To fit in with this schedule, I postponed the series solutions topic until the end of the course and decided to use the following five CCP modules.

The first of these modules reviews what it means to solve an differential equation. The next two offer different views of the solutions to second order linear equations, the first one analytic and the second one physical. These complemented the lectures, where I mainly talked about ways of finding these solutions. The fourth module lets the student explore the Laplace Transform, and how it can be used to solve a differential equation, without getting bogged down in improper integrals and partial fraction calculations. Finally, the last module offers a visual interpretation of the Fourier series, complementing the analytic approach taken in the lectures and homework.

Ideally, these modules would be graded each week as they were being done but, because of other commitments, I decided to collect and grade the modules all together at the end of the course. To keep the students working steadily at the modules, I had weekly reporting stages in which the students had to show their tutor some crucial graphic or summary statement from the previous week's module.


John Hannah, "Using Connected Curriculum Project Modules - Background," Convergence (December 2004)