Developing Knowledge of Student Thinking: Understanding the Big Ideas Behind Students' Difficulties With Connecting Representations

• In Event: Preservice Teachers Focusing on Student Thinking in Math and Science Classrooms

Abstract

This study concerns prospective secondary teachers’ knowledge of student thinking, and in particular the big ideas behind students’ difficulties in connecting representations in algebra. We designed and implemented a three-week unit to help prospective teachers to construct big ideas relating to the connections among representations—such as variation and the Cartesian Connection—as well as to understand the role of big ideas in students’ understanding of algebra. Qualitative analyses of video and written data showed that the 17 participants were collectively able to discuss students’ difficulties connected to the big ideas at a somewhat deep level, and that the majority were able to design tasks that had some potential to promote students’ understanding of big ideas.

Authors

• Kyunghee Moon, University of West Georgia

• Bill Jacob, University of California - Santa Barbara