Learning through interacting with students' ways of thinking

This paper reports on the ways in which one middle grade teacher listened to, supported, and learned from her students ’ mathematical reasoning within the context of a modelling task in data analysis. The teacher implemented a sequence of tasks that focused on the development of rating systems through selecting, ranking, and aggregating quantities. Analyses of the teacher’s practices suggested that: (a) the teacher’s mathematical background governed her understanding of both the modelling task and the students’ reasoning; and (b) the teacher adopted new roles in her interactions with the students, including a focus on listening and observing, asking questions for understanding and clarification, pressing for explanations and justifications, and encouraging reflection on learning at a meta-level. This study illustrates the potential for using modelling tasks that provide a rich source for revealing not only the students ’ thinking but also the teachers’ understanding of the students ’ thinking. Such tasks provide a learning tool for teachers as they listen to, interpret, and support students ’ emergin