Having to communicate with fellow students encourages students to articulate, and perhaps clarify and deepen, their mathematical thinking. However a computer can stifle such communication. In my own institution, Boustead [Section 8.3, page 8-12] reported on four tutorial groups of first year students, two groups working with the CD-ROM version of a calculus text and two working in more traditional, computer-free, tutorials. The former students
opted to work alone with their CD-text. After a few weeks there was little if any interaction between students as each worked at their own pace on different aspects. During one week in which the students were forced to share a CD between pairs, there was increased student discussion, the students took longer to go through the work and there was considerable frustration. Some students wanted to concentrate on the concepts, others wanted to do just the exercises. All the students opted to return to one CD ROM per student.
Experience at Duke University also suggests that more communication takes place when the CCP modules are tackled by students working in pairs Bookman and Malone. Furthermore (David Smith, personal communication), the interaction is often better if the two students are relative strangers, perhaps because in that case their thought processes have to be made more explicit for communication to take place. Because of this, I paired my students off more or less at random, picking neighbours off an alphabetic listing of the particular tutorial group the students belonged to (these groups having been assigned at the start of the course to fit in with timetable constraints).
In the first half of the course, I had offered the students the option of doing their first assignment either individually or in teams of two or three students. About half the students chose the team approach. With this background, and with Boustead's experience, I might have expected some student resistance to enforced team work, but as an observer I felt that it worked well. Most pairs worked as teams both physically and verbally. Thus, it was very common for one student to control the mouse while the other typed -- a significant feat in communication and cooperation. Furthermore some students, who had seemed to be struggling in the lectures and ordinary tutorials, now became confident investigators.
In the end-of-course survey only 15 of the 96 students thought this aspect was worthy of comment, and they were marginally in favour of the idea of working in pairs. Their comments reinforce the issues raised above. One student voiced the ideal of cooperative learning:
#57: group work was good as we learned off each other well
while another felt that it helped to pull them up to a higher level:
#79: I found it useful to work in pairs as some of the work was too difficult for me to do by myself . It was also good motivation to work in pairs.
but a third student felt this arrangement was unfair:
#4: I take long time to understand what the questions mean while my partner is "too brainy" and understands quickly so, he does most of the work during lab so it is not fair for him. But I go back to lab and go over the questions in my own time. So it is not fair for me because I spend a lot of time.
although, as we have already seen, this same student admitted not preparing for the labs.
Some of the difficulties reported by students may be the consequence of having a non-homogeneous class. Thus some reported difficulty in finding times when both partners were available to finish off the work started in the lab sessions. Language differences also caused difficulties for (at least) two of the pairs:
#22: I found that doing the assignment in pairs made the assignment much harder than it would be otherwise. I think I spent a lot of the time just trying to communicate with my partner. This would have been okay if we were discussing the weather but trying to communicate complex mathematical ideas was rather tricky. I would have preferred to submit my own version of the assignment as I think others would agree. This is partly because some partners who don't speak English very well insist on answering the questions in there words and often there words make absolutely no sense.
Some of these difficulties were apparent before I conducted the second survey, and I asked a student from one of the dysfunctional pairs whether it would have been better to let everyone choose their own partner. To my surprise he said No, and went on to explain that all the other pairs he knew were working well together, and it was to be expected that there would be one or two unsuccessful pairings. This, together with the small number of students who felt moved to comment, suggests that cooperative learning is an accepted (and perhaps unremarkable) feature of the educational landscape for most of these students.