Improvisational coactions and the growth of collective mathematical understanding

Abstract

In this paper we consider the phenomenon of the growth of collective mathematical understanding and explore its dependence on the particular way that a group of learners work together collaboratively. We label this group process as improvisational coaction. In an earlier paper (Martin, Towers and Pirie, 2006) we drew on the theoretical work of Becker (2000 Becker, H. 2000. The etiquette of improvisation. Mind, Culture, and Activity, 7(3): 171–6. [Taylor & Francis Online] , [Google Scholar]), Sawyer (2001 Sawyer, R. K. 2001. Creating conversations: Improvisation in everyday discourse, Cresskill, NJ: Hampton Press. [Google Scholar], 2003 Sawyer, R. K. 2003. Group creativity: Music, theatre, collaboration, Mahwah, NJ: Lawrence Erlbaum Associates. [Crossref] , [Google Scholar], 2004 Sawyer, R. K. 2004. Creative teaching: Collaborative discussion as disciplined improvisation. Educational Researcher, 23(2): 12–20. [Google Scholar]), and Berliner (1994 Berliner, P. 1994. Thinking in jazz: The infinite art of improvisation, Chicago: University of Chicago Press. [Crossref] , [Google Scholar]) in improvisational jazz and theatre, to characterise the growth of collective mathematical understanding as a creative and emergent improvisational process. Here, we extend that conceptual analysis to a yet-finer grain to explore one element of that framework, improvisational coaction, and its relationship to the growth of mathematical understanding at the level of the group. In particular we identify improvisational coaction as a particular form of interaction, and through using data extracts we derive four characteristics of the phenomenon and consider how these occasion the growth of collective mathematical understanding.