Making sense of student mathematical thinking: the role of teacher mathematical thinking

In mathematical whole-class discussions, teachers can build on various student ideas and develop these ideas toward mathematical goals. This requires teachers to make sense of their students' mathematical thinking, which evidently involves mathematical thinking on the teacher's part. Teacher sense-making of student mathematical thinking has been studied and conceptualized as an aspect of teacher noticing and has also been conceptualized as a mathematical activity. We combine these perspectives to explore the role of teacher mathematical thinking in making sense of student mathematical thinking. In this study, we investigated that role using video-based teacher discussions in a teacher researcher collaboration in which five Dutch high school mathematics teachers and one researcher developed discourse based lessons in cycles of design, enactment, and evaluation. In video-based discussions, they collaboratively reflected on whole-class discussions from the teachers' own lessons. We analyzed these discussions to explore the mathematical thinking that teachers articulated during sense-making of students' mathematical thinking and how teachers' mathematical thinking affected their sense-making. We found five categories concerning the role of teacher mathematical thinking in their sense-making: flexibility, preoccupation, incomprehension, exemplification, and projection. These categories show how both the content and the process of teacher mathematical thinking can support or impede their sense-making. In addition, we found that the teachers often did not articulate explicit mathematical thinking. Our findings suggest that sense-making of students' mathematical thinking requires teachers to (re-)engage in reflective thinking with regard to the mathematical content as well as the process of their own mathematical thinking.