Teaching Mathematics through Problem Posing: four practices for handling students’ posed problems

Problem posing is both a learning goal and an effective instructional approach, but what are the details of using this approach to foster students’ learning? In this paper, we use teaching cases to demonstrate a step-by-step instructional model that teachers can use to convert non-problem-posing tasks into problem-posing ones and use the tasks to foster students’ learning. More importantly, we provide a detailed illustration of the four practices that teachers and students can use to handle students’ posed problems. The paper ends with a discussion of future work to validate and improve the model and the challenges that teachers experience teaching through problem posing.