Lyndon Martin & Jo TowersThis research is concerned with the nature of the growth of mathematical understanding, and more specifically with how a group of learners can develop a collective understanding for a mathematical concept. We seek to characterise collective mathematical understanding as a creative and emergent improvisational process, through drawing on theoretical perspectives from the fields of jazz (Becker, 2000; Berliner, 1994; 1997), theatre (Sawyer 1997; 2000) and conversation (Sawyer, 2001). In considering video data, taken from an initial pilot study, we extend improvisational theory to begin to consider collective mathematical understanding as a process with a similar nature and characteristics.