Abstract:

We discuss how three middle school urban math teachers, responded to their students when confronted with difficulty in understanding their mathematical thinking during class. We highlight the ideas encountered, how they were addressed during class, and the teachers’ own understanding of the math. We also elaborate on their thoughts and perceptions about the decisions, including their reflections on their own mathematical thinking during subsequent debriefing sessions. Our findings indicate that the teachers tended to highlight the ideas that they seemed to understand, and became frustrated by their inability to understand and interpret other ideas and/or misconceptions. Further, they felt disappointed in themselves for not being better able to respond to their students in more mathematically sound ways. On the bright side, they resolved to be more diligent in considering a wider variety of potential student solution trajectories prior to class in the future, and to embrace the fact that they may not always understand the many unique solutions and strategies that arise. They also became more accepting of the fact that when students develop and share their own ideas they may, in the process, develop different and/or incorrect ways of thinking, some of which will be difficult to understand at the time.

Keywords:

Mathematics education, students’ mathematical thinking, teachers’ mathematical understanding, teacher decisions.