Understanding the improvisational character of collective mathematical understanding requires us to focus our analysis at the level of the group. As Sawyer (1997a) notes, “the central level of analysis for performance study is not the individual performer, but rather the event, the collective activity, and the group” (p. 4). Our two examples demonstrate that collective mathematical activity is an important and powerful part of learning and understanding mathematics, and one that merits a greater emphasis and recognition than presently exists in many classrooms, where the individual learner is still the dominant focus of curriculum, teaching, and assessment.