INVESTIGATING THE PROBLEM WITH PROBLEMS: PRESERVICE MATHEMATICS TEACHERS’ UNDERSTANDING OF PROBLEMS AND PROBLEM SOLVING

Abstract

Problem solving is a key component of mathematics education. Waves of educational reform have focused on the problem-solving aspect within the K-12 educational setting. Yet, the teacher plays a critical role in establishing the problem-solving environment of the classroom. Therefore, preservice secondary mathematics teachers (PSMTs) must examine their understanding of problem solving and tasks that engage their future students in problem solving. This research project aimed to explore and interpret the meanings that PSMTs associate with problem-solving tasks. By examining their experiences with these tasks and the connections they make, this study sought to understand how PSMTs determine the problem-solving criteria they will apply in their future classrooms and investigate the cognitive structures underlying their decision-making within the context of mathematics education. This study centered around questions involving PSMTs' understanding of problems, problem solving, and their criteria for a worthwhile task. This study was a case study design with qualitative data collection within a first mathematics methods course. Participants were three PSMTs enrolled in their first mathematics methods course. Data collection methods involved interviews and analysis of problem-solving tasks and assignments. Common themes for understanding problems were solvable and thinking/sense-making. Problem solving is centralized on uncomfortableness and connecting prior knowledge with new information. The themes involving criteria for worthwhile tasks were mathematical connections, collaboration, and student engagement. Based on the findings of this study, there is a need for mathematics educational institutions to create opportunities for PSMTs to evaluate tasks and refine their criteria for worthwhile tasks. Both mathematics methods courses and content courses should have activities to edit tasks to meet the criteria for worthwhile tasks.