Prospective and in-service teachers’ perspectives about launching a problem

Abstract

Launching a problem is critical in a problem-based lesson. We investigated teachers’ perspectives on the use of a problem that was analogous to the one provided during a launch. Our goal was to identify teachers’ underlying assumptions regarding what should constitute a launch as elements of the practical rationality of mathematics teaching. We analyzed data from four focus groups that consisted of prospective (PST) and in-service (IST) teachers who viewed animated vignettes of classroom instruction. We applied Toulmin’s scheme to model the arguments that were evident in the transcriptions of the discussions. We identified nine claims and 13 justifications for those claims, the majority of which were offered by the ISTs. ISTs’ assumptions focused on reviewing, providing hints, and not confusing students, whereas PSTs’ assumptions focused on motivation and student engagement. Overall, the assumptions were contradictory and supported different strategies. The assumptions also illustrated different stances regarding how to consider students’ prior knowledge during a launch. We identified a tension between ensuring that students could begin a problem by relying on the launch and allowing them to struggle with the problem by limiting the information provided in the launch. This study has implications for teacher education because it identifies how teachers’ underlying assumptions may affect their decisions to enable students to engage in productive struggle and exercise conceptual agency.