A spectrum of possibilities: levels of improvisational behaviour in middle school mathematics.

Abstract

In this article, we consider the phenomenon of improvisation by small groups of middle years students while engaged in rich mathematical tasks in classroom settings. 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 work together. We discuss four levels along the spectrum – interpretation, embellishment, variation, pure improvisation – and draw on vignettes from our research to illustrate each of their characteristics. We argue that improvisation is a valuable way to view students’ mathematical performance as it highlights how students draw on their own experiences and understandings when problem solving, and how students need to be given opportunities to “stay with” mathematical tasks.