Creative reasoning and shifts of knowledge in the mathematics classroom

In the course of the last few years, we have investigated shifts of knowledge among different settings in inquiry-based mathematics classrooms: the individual, the small group and the whole class community. The different theoretical perspectives we used for analysing group work and for analysing whole class discussions, and the empirical data, led us to hypothesize links between shifts of knowledge and students' creative reasoning. Therefore, the goal of the current study is to investigate creative reasoning within the shifts of knowledge in an inquiry-based classroom. Specifically, we ask: What is the role of creative mathematical reasoning in the shifts of knowledge between the knowledge agents and their followers in the classroom? To this end, we analysed a whole class discussion and the subsequent work of a small group. Our findings show that creative reasoning has a role in researchers' characterization of shifts of knowledge in the classroom. In particular, we found that the students who expressed creative reasoning all had followers and thus became knowledge agents, while students' contributions that were not characterized as creative were not always followed up. Finally, in cases where both, the knowledge agent and the follower expressed creative ideas, we named these ideas milestones.