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It is difficult to get reliable data on this question when dealing with a large number of students. I was worried that the time students spent on the CCP modules would mean less time being spent on the more traditional elements of the course, leading to a poorer performance in the exam on those skills we all hold so near and dear -- e.g., doing a double integral, solving a DE, finding a Fourier series, all by hand. But in fact they did really well in the exam. There were some confounding influences -- e.g., one student explained to me that they had done DEs in three separate courses that semester, so they were very familiar with Des by exam time. But it would appear the traditional skills were still being learnt -- the "no harm done" conclusion mentioned by Heid et al.

On the other hand, the students were learning things in the labs that I would never have tried to teach in a more traditional setting, such as the detailed behaviour of solutions to initial value problems, and how this behaviour responds to parameter changes. So my impression is that the students acquired a deeper understanding by using the modules, combining graphical and physical interpretations with the mechanical methods learned in more traditional courses.

What did the students themselves think about this question? In my second survey, 62 students commented about whether using the CCP materials had helped them to a better understanding of the mathematics. Of these students, 37 made generally positive comments, 14 made generally negative comments, and the rest voiced mixed feelings.

A few students offered their own explanations for why the lab sessions had helped their learning. Some of their explanations could apply to any active learning experience. Thus, in one case, the prospect of a session where they knew they would have to do something encouraged the student to do some preparatory study:

#45: It does help me to understand more because I have to read the lecture notes and reference book to do the Maple assignment.

Another student observed the converse:

#4: I know that we are suppose to do H.W. [homework] problems before Maple sessions so we can understand but, most of the time, I don't have time to do H.W. problems before the session and I end up understanding nothing.

The CCP modules are designed to be completed in about two hours. As I had only one hour of class time available each week, I expected the students to finish off each module in their own time (although they were always welcome to take advantage of spare computers at one of the other five scheduled sessions each week). One student saw this as a useful way of encouraging deeper learning:

#54: . . . having labs which you couldn't quite finish meant you had to come back and learn the stuff again [giving] greater understanding.

On the other hand, some of the students' explanations of the efficacy of the sessions refer to specific features of the technology. Thus, for one student, the Maple laboratory sessions

#95: Allows you to explore enough possibilities to see the patterns.

while for another the sessions were

#85: Time consuming, frustrating, easy to get bogged down in a morass of numbers and errors, but in the end worthwhile, both in building our skills in Maple and getting a good feel for the topic. It let us see things graphically that would've been too time-consuming to investigate by hand. In short - a trial, but worth it!

John Hannah, "Using Connected Curriculum Project Modules - Do CCP modules encourage greater understanding?," *Convergence* (December 2004)

Journal of Online Mathematics and its Applications