In this paper we explore the growth of understanding of a group of preservice teachers, and their instructor, as they work collectively together on what we describe as a "mathematics for teaching" task. Through drawing on elements of improvisational theory, in particular the notion of the "better idea," we analyse how the preservice teachers' understanding of a particular mathematical concept as a teachable idea emerges as they work together. We build on this analysis to suggest that certain kinds of improvisational actions can be a powerful means through which student teachers might think about and learn mathematics for teaching.