Snapshots of productive noticing: Orchestrating learning experiences using typical problems

Abstract

In this paper, we re-examine the commonly-held notion that typical problems, such as textbook exercises and examination questions, are not useful for orchestrating mathematically-rich learning experiences. Drawing from a larger design-based research project, we present a case study of Alice, a secondary school teacher, who orchestrated a productive discussion by using examination questions. We describe how she perceived and harnessed the affordances of such typical problems before and during her lesson. Findings suggest teacher noticing as a key mechanism to enable teachers to unlock the mathematical potential of such problems.