In this article, we consider the phenomenon of improvisation by small groups of middle years students while engaged in rich mathematical tasks in a classroom setting. Working from the premise that improvisation comprises a spectrum of behaviour, we propose that there is a range of improvisational behaviours that may be observed as the students…

Mathematics itself is a living and creative act (Boaler, 2008), and mathematicians themselves often collaborate in their work (Burton, 2004). What, then, is holding school mathematics back? Are educators so conditioned to expect the act of mathematizing in school to proceed in a certain abstract, formalized way that they are neglecting other means…