Developing Knowledge of Student Thinking: Understanding Big Ideas behind Students’ Difficulties with Connecting Representations in Algebra

Abstract

This study concerns preservice teachers’ knowledge of student thinking at the secondary level. In particular, it examines in what ways a three-week unit integrating content and student thinking was beneficial in developing preservice teachers’ knowledge of student thinking associated with big ideas in algebra—such as variation, Cartesian Connection, and graph as a locus of points. In the early stage of discussion of student work, preservice teachers tended to focus mostly on students’ errors/mistakes, correct ways the problems should have been solved, or the types of problems that students had. However, with the progress made in discussion, they were able to attribute students’ difficulties to a lack of understanding of qualities such as definitions, properties, and concepts, and further to a lack of the understanding of big ideas underneath the qualities, with the help from instructors. The majority were also able to design contextualized tasks that could stimulate students’ interests; yet they struggled to explain how they would use the tasks to promote students’ development of big ideas by connecting multiple representations.