For the last three years, I have been using the CCP materials at Florida Atlantic University’s Honors College, primarily in second semester calculus. My first attempt at using the materials in this new setting was not particularly successful. Unlike the more advanced students in my linear algebra class at Duke, my first year calculus students had no experience using Maple.
That first semester, we completed three modules from the PostCalc Project collection, a set of longer modules intended for high school students who have finished calculus. The modules were fantastic – the difficulties arose from the way I structured the course and the fact that I needed to provide more support for learning and using Maple. I did not set aside enough class time for the CCP projects. I did not force the students to work in pairs– some did, but some did not, and those that chose to work individually often struggled. And the length of time between projects allowed students to forget a lot about Maple in the interim.
While I was unhappy with my arrangement, the students were not overly bothered. On their course evaluations, where I specifically asked them to comment on the laboratory portion of the course, they said they generally enjoyed completing the modules and felt that they learned a lot of mathematics in doing so. Their biggest frustration was in having to complete the modules outside of class, when I was not around to quickly answer questions, especially questions about Maple.
Properly chastised, and recognizing at least some of my errors in structuring the first course, the next time I taught the course we completed seven modules, meeting in the lab roughly once every two weeks. I used shorter modules from the Integral Calculus and Differential Equations sections of the main CCP site, with just two excursions to the longer PostCalc modules, and in those two cases, we did only portions of the available modules. All of the students worked in pairs, and I felt the course progressed much more smoothly. As others have noted -- see (Bookman and Malone, to appear) and (Hannah, 2001), for instance -- students do struggle with Maple at times, but having them work in pairs alleviates this difficulty somewhat. The pairing also helps facilitate discussion of mathematical concepts and seems to encourage students to experiment – even struggle – with material more before becoming frustrated.
In recent semesters, partly because of limited lab availability, I have been using the CCP modules with Texas Instruments graphing calculators instead of Maple. Moreover, our college emphasis on environmental issues has led me to choose calculus modules that emphasize applications such as Accumulation (on air pollution), World Population Growth, the Logistic Growth Model, and Predator-Prey Models. Using calculators has the advantage of portability (I gave students printed versions of the modules), but does not allow for the same sort of interaction as pairs work through the materials. For instance, in the lab, students almost invariably divide control of Maple: One student runs the keyboard and the other runs the mouse -- Bookman and Malone (to appear) mention this, and it seems to be a common observation of instructors teaching in similar settings -- whereas with a graphing calculator, this sort of sharing is impossible. Students must either work individually with the technology, or one works while the other watches, and neither option is optimal. Pedagogically, I far prefer to teach in a computer lab with Maple, but the modules are flexible enough to work outside of a lab.