Recent years have seen a shift in classroom practices and teaching styles, with many teachers using group work. But just because a teacher has students work in groups does not necessarily imply that collective, improvisational co-action and understanding will emerge. Group work is too often viewed only as a technique to enhance individual learning, and is often embedded in broader classroom, school, curricula, and legislative contexts in which individual learning remains the focus. As Davis and Simmt (2003) note, “popular enactments of both traditional and contemporary teaching might ignore the complex possibilities of collective engagements as they focus on the qualities of single subjects” (p. 152). Focusing on the group allows us to better understand the collective processes that are always at play. In this chapter, we have shown how such processes can be understood as improvisational. Our intent has been to provide some clear suggestions for how teachers might think about, stimulate, and value collective mathematical understanding. Through doing this, we suggest that the practice of teaching is shifted into a space where expertise is characterized as the vital capacity to recognize and respond to the emerging understandings of students, and not just the facilitation of student competence as measured through standardized testing.