Orchestrating mathematics lessons: Beyond the use of a single rich task

Abstract

Teachers have several challenges when designing and implementing mathematically-rich tasks, and hence, these tasks are not prevalent in many mathematics classrooms. Instead, teachers often use typical problems, such as standard textbook tasks and examination questions, to develop students’ procedural fluency. This begs the question of whether, and if so, how teachers can think about, and use these typical problems differently to develop conceptual understanding. In this paper, we report findings drawn from a two-year design-based research project and highlight two teaching vignettes to illustrate how typical problems were used to orchestrate instructional activities. Our findings suggest three important principles for teachers to consider when using typical problems.