Prospective teachers (PTs), enrolled in a mathematics methods course, were asked to analyze children's mathematical thinking by viewing videotaped clinical interviews over the course of an entire semester. They were also asked to conduct two of their own interviews with children as the semester progressed. While the type of analysis varied, all of the PTs commented on the errors that the children made during the interviews, often providing explanations for them. We describe these explanations and how they evolved over time. We note in particular that the PTs were better able to provide a more in-depth analysis of the videotapes than they were of their own interviews. [For the complete proceedings, see ED584443.]