Toward an analytical framework for contextual problem-based mathematics instruction

Abstract

ABSTRACTScholars propose that contextual problems can be used to ground students’ understanding of mathematical ideas, and recent curricular trends have resulted in a plethora of resources that introduce and develop new mathematical ideas through contextual problems (CPs). Given the tension between this approach and the traditional role of CPs as opportunities to apply, rather than develop, mathematical ideas, there is a need for a common language that teachers, curriculum designers, and scholars can use to learn from each other about the types of tasks that are central to contextual problem-based instruction. To fulfill this need, the author proposes an analytical framework, developed through observations of a contextual problem-based algebra unit. After describing the categories in the framework using examples from the written and enacted lessons, the author uses existing theories and empirical observation to describe the significance of each type of activity for the development of understanding.