Which Approaches Do Students Prefer? Analyzing the Mathematical Problem Solving Behavior of Mathematically Gifted Students

This study analyzed the mathematical problem solving behavior of mathematically gifted students. It focused on a specific fourth step of Polya’s (1945) problem solving process, namely, looking back to find alternative approaches to solve the same problem. Specifically, this study explored problem solving using many different approaches. It examined the relationships between students ’ past mathematical experiences and the number of approaches and the kind of mathematics topics they used to solve three non-standard mathematics problems. It also analyzed the aesthetic of students ’ approaches from the perspective of expert mathematicians and the aesthetic of these experts ’ preferred approaches from the perspective of the students. Fifty-four students from a specialized high school were selected to participate in this study that began with the analysis of their past mathematical experiences by means of a preliminary survey. Nine of the 54 students took a test requiring them to solve three non-standard mathematics problems using many different approaches. A panel of three research mathematicians was consulted to evaluate the mathematical aesthetic of those approaches. Then, these nine students were interviewed. Also, all 54 students took