Making Mathematics Challenging Through Problem Posing in the Classroom

Abstract

Problem posing, the process of formulating and expressing problems based on a given situation, is an essential practice in mathematics and other disciplines. Although this is acknowledged in policy documents, problem-posing tasks are neither substantively nor consistently included in school mathematics. In this chapter, we consider problem posing from the perspective of challenging and worthwhile instructional tasks. We examine the current state of problem-posing tasks in school mathematics, and we put forward arguments for how and why teachers should make use of problem posing to engage their students in achieving challenging learning goals. We present a variety of examples of problem-posing tasks to illustrate a framework of problem-posing task characteristics focusing on problem situations and problem-posing prompts. Finally, we put forward recommendations for how to support teachers as they learn to teach mathematics through problem posing.