A framework for designing problem solving task for secondary school mathematics classroom

Abstract

Although problem solving has been playing a critical role in the teaching and learning of mathematics in K-12 in many countries in the world, anecdotal evidence from mathematics classrooms shows that teachers are still facing challenges in designing mathematical tasks on problem solving for classroom instruction. Despite the effort of several existing research studies on enacting problem solving in the mathematics classroom, the guiding principles for designing problem solving tasks remain largely unexplored, thus teachers are left without being empowered to design their own problem solving tasks. The objective of this paper is to provide a comprehensive framework on designing problem solving tasks through a list of interrelated guiding principles. The proposed framework, which we name MIRACLE, foreground seven key considerations which mathematics educators should take into consideration when designing a task for a problem solving lesson: Mathematical content, method of Instruction, Required knowledge, Assessment, Complexity of problem, Learner’s profile, and Enactment of lesson. This paper also provides two exemplars on how the framework could be used to design mathematical tasks for problem solving through problem solving

Keywords

• mathematical problem solving
• mathematics instruction
• mathematics education
• teaching through problem solving