Exploring a Structure for Mathematics Lessons That Foster Problem Solving and Reasoning

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks intended to prompt problem solving and reasoning to students, not only to activate their thinking but also to develop an orientation to persistence. The results indicate that such learning is facilitated by a particular lesson structure. This article reports research on the implementation of this lesson structure and also on the finding that students' responses to the lessons can be used to inform subsequent learning experiences.