Teacher listening: The role of knowledge of content and students

In this research report we consider the kinds of knowledge needed by a mathematician as she implemented an inquiry-oriented abstract algebra curriculum. Specifically, we will explore instances in which the teacher was unable to make sense of students’ mathematical struggles in the moment. After describing each episode we will examine the instructor's efforts to listen to the students and the way that these efforts were supported or constrained by her mathematical knowledge for teaching. In particular, we will argue that in each case the instructor was ultimately constrained by her knowledge of how students were thinking about the mathematics.

► We show the importance of listening when enacting an inquiry-oriented curriculum.
► We detail cases in which a mathematician was unable to decipher students’ struggles.
► We tie this inability to a lacking in knowledge of students’ mathematical thinking.
► We offer elaborations of the construct of knowledge of content and students.