In this article we explore the mechanisms through which one group of preservice teachers engage in "Collective Property Noticing"--a phenomenon in which group members integrate individual contributions such that the group, as a unit, notices mathematical properties of their collective image. Drawing on improvisational theory to help to illuminate these collaborative processes, we claim that Collective Property Noticing is a capacity that is vital for mathematical sense-making in collaborative groups and we propose several conditions under which it is appropriate for a teacher to intervene in students' learning in a problem-solving setting in order to provoke Collective Property Noticing.