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…

The Zen concept of beginner's mind describes how one's level of awareness can open one's mind to growth and possibilities, an attitude that would be beneficial for many mathematics students. In this naturalistic case study, two small groups of middle years students engage in the same mathematical task, one group demonstrating the characteristics…

Peer collaboration in schools can be a locus for negotiation of power and cultural norms. Set in the context of ethnically and linguistically diverse urban schools, this study discusses the possibilities and limitations of utilizing video-mediated interviews to reveal multiple voices. Our research method is based on video-recorded peer-to-peer…

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…

This naturalistic case study investigates the problem posing patterns that emerge as four small groups of 12 year old students in Western Canada work collectively on a structured mathematics task. A method of data analysis is introduced that blurs the data to create transcript "tapestries" providing visual evidence of collective patterns…

This article describes a set of learning activities that use algebraic problems and written student work to help preservice and in-service teachers understand students' algebraic thinking. (Contains 4 figures.)