One of the most important factors in this group's success was how they interacted. Jim summed up the group:
By the time we got done meeting, we all agreed that it was a great experience and we were lucky to be in each others' groups. Because w all pretty much complimented each other, Brad pretty well took the lead, just because we maybe felt like, me and Neal, couldn't do it, and then all of a sudden Brad would show up, and "yeah we could have done this." But we worked very well together. When one of us didn't get something, one of us did, and when one of us didn't want to work, well hey, we'll work on this, and it wasn't, you know we all went back and forth, but one of us wouldn't want to work, the other two were OK, we'll handle this tonight for the project ...
One of the key points here was how after meeting with Brad, the attitude that Jim and Neal shared was not that the work was beyond them, but rather that "we could have done this." Jim and Neal found their interaction with Brad as equal partners (contrasted to how Teri and Ellen interacted with Mary).
Brad saw himself as an equal partner also. In fact during an interview after the class was over, when I told him that I saw him as the most mathematically gifted of the students, he felt that was inaccurate. He saw an important piece of working together in that
when we had an idea we were free to talk about it. We could explore ideas and needed to justify them... In every case we would give a quick explanation of what we had done...
Thus all three members of the group saw it as a partnership of equals. They all mentioned bouncing ideas off of each other as one of the important parts of group work. Contrast this to Mary's comment about her group:
I don't know, maybe it was just like the group members, … they didn't think what they contributed was good enough or something and they just didn't contribute.
When asked why the explanations were necessary, he related that otherwise the other students wouldn't be able to contribute their ideas to the problem, nor could he bounce ideas off of them. Thus Brian, too, saw the group as a partnership of equals trying to solve the problem.
Neal also saw the group interactions as an example of people working together.
I think we each at the beginning of the term at the beginning of the semester saw each other as all equal in terms of mathematical ability and mathematical confidence, maybe not exactly equal, but we were somewhere about the same...