College Mathematics Students\u27 Peceptions of Believing Teacher Actions

Believing and doubting – two methodological processes – deserve equal attention according to Elbow (1986; 2006). When a teacher plays the doubting game in a mathematics classroom her own mathematical thinking dominates and she attempts to find flaws and errors and misconceptions in students’ mathematical thinking. When a teacher plays the believing game in a mathematics classroom she surrenders her own mathematical thinking and she attempts to find virtues and strengths and merits in students’ mathematical thinking. Paradoxically and succinctly, a teacher must believe her own mathematical thinking in order to doubt and a teacher must doubt her own mathematical thinking in order to believe. For this qualitative case study, the fifth in a series focused on playing the believing game in mathematics classrooms, students in a college Proofs course were interviewed after the course ended. Throughout the semester, the professor purposefully played the believing game, using a list of a priori teacher actions she created prior to the beginning of the course. Students described some aspects of her a priori teacher actions. Although the original focus of the research was on the a priori teacher actions, it became evident that the students perceived the teacher’s stance. This implies that to move towards playing the believing game the teacher stance is a critical component that impacts teacher actions