The three students in this group all had very different attitudes about what mathematics they found interesting and about their own success in mathematics.
Mary, one of the top students in the class, found problem solving interesting in mathematics and saw herself as a talented student. From the beginning of the projects, she was hooked on trying to solve the problem, to the extent that she reported to me having discussions about the problem with her parents. The Ellen and Teri also report that Mary seemed fixed on solving the problem.
Ellen, a weaker student in the class, liked using computers and technology to attack problems. While a capable student, she seemed to have a low opinion of her ability to solve mathematics problems and understand mathematics. Throughout much of the term she would come to my office at the same time as Mary, and often Mary would forge along in answering problems without making sure that Ellen was following what was going on. Even as early as the second week of the class, I was making notes in my journal to this effect.
Teri, one of the weakest students in the class, saw herself as never being particularly good at mathematics. She was quite quick to check herself out of classroom discussion and appeared throughout the class to be struggling to keep interested with the material. In fact, the few times I could get her to work with me, she was capable, but her attitude appeared to get in the way.
In working on the problem, it appeared that Mary did most of the work, while the other two both coasted along. I used the word "appeared," because I am not convinced this is exactly the way it worked. When the three would come in my office to talk, Mary did most of the talking, but she mostly talked with me, not with Ellen and Teri. Thus the ideas that might come out of the other two were often filtered through Mary. Moreover, because of the nature of the students self-confidence, Ellen and Teri would often allow Mary to be the only one in conversation with me during these sessions. At one point, I actually asked Mary to simply listen while I worked with Ellen and Teri on the problem. Even so, she found it difficult not to enter the conversation by telling me her own insights. This clearly wore on Ellen and Teri. In fact, Teri reported to me much later in the term that the students had at one point broken the problem into pieces for each to work on, and that Teri had been disconcerted that Mary seemed to have worked on and solved all three pieces. Teri's comment at this point was that it had kind of made her not want to keep working on the problem.