I have not designed and implemented a careful study of the effects of the CCP materials on students – my college is small enough that there is no feasible way to maintain a control group – so I can only offer the conclusions that I have drawn from my own observations and experiences as a teacher. While readers may legitimately question the value of such anecdotes, perhaps a few might be intrigued enough to give the materials a try, or, even better, design a study to assess the validity of the observations. (Some such studies are under way, I believe, including ongoing assessment work at Duke University.) What follows are student reactions that I perceive to be due to the use of the CCP modules, either directly or indirectly.
- Students retain the material covered in the modules longer and better than many topics covered in a more traditional format. Rarely will students miss questions on a quiz or an exam that are closely related to the material covered in one of the CCP modules they have completed. I believe the fact that they discovered what they have learned aids retention.
- Students tend to be willing to work longer and harder on a mathematical problem when they are working in pairs. They also seem to be more willing to experiment and explore with Maple than with their graphing calculators. I am not sure if the latter is because Maple is faster than the calculators are, if it is because a collaborator can more easily see the results of an experiment, or if there is some other reason entirely. In any case, when students are thinking longer and harder about the obstacles they encounter, they more often overcome those obstacles, and they generally learn something in their struggles.
- Students who regularly use the CCP materials, and more generally a computer algebra system, become more comfortable using technology. Certainly, their ability with the particular technology improves, helping them in later mathematics courses, and often in other disciplines. For instance, students have mentioned to me that they have used Maple to plot data from a science lab, and to compute integrals for physics homework problems. Perhaps more importantly, confidence with technology seems to be cumulative, even across applications. Students familiar with one technology, like Maple, seem more comfortable picking up another, whether it is another software package such as SPSS or the computer interface to a gas chromatograph mass-spectrometer in the chemistry lab.
- Students come to view Maple as another tool in their mathematical toolbox. The questions in the modules consistently encourage students to think about whether or not their answers make sense, and, if not, to investigate what may have gone wrong. Students respond to this re-examination of their work much more readily than might be anticipated. In addition to using Maple, they will consult their text, use their graphing calculators (odd though that sometimes seem to me!), and work with pencil and paper to facilitate their understanding.
- In a broad educational sense, I believe we will see (through student surveys being administered each semester---we will eventually have data for or against this assertion) that students who are regularly exposed to the CCP modules, or are consistently engaged in similar active and application-rich learning environments in mathematics, will exhibit an increasingly strong awareness of mathematics as a science. Even students in their first semester with the CCP materials seem to begin to perceive that there is a continuous scientific process in mathematics, just as in biology or chemistry. I expect that these similarities between mathematics and the sciences will become more apparent to students as they continue in discovery-based mathematics and science courses.
Finally, I want to mention an effect of the materials not on students, but on my colleagues. My institution allows individual faculty members a great deal of autonomy in the content and conduct of courses, but the combination of my enthusiasm, and that of my students, has convinced my mathematics colleagues to incorporate the CCP materials in their courses.
Stephanie Fitchett, "Teaching with Duke's CCP Materials - Effects of Using CCP Materials," Convergence (November 2004)
Journal of Online Mathematics and its Applications