We report on a two-year 'concept study' in which a cohort of middle school teachers collectively deconstructed and reconstructed the concept of multiplication. Defining concept study as a collaborative structure through which mathematics educators identify, interpret, interrogate, invent, and elaborate images, metaphors, analogies, examples, exemplars, exercises, gestures, and applications that are invoked in efforts to support the development of students' mathematical understandings, we suggest that teachers' disciplinary knowledge might be more productively construed in terms of a participatory attitude toward mathematics than as an explicit body of knowledge.