College Mathematics Students' Perceptions of "Believing" Teacher Actions

Believing and doubting - two methodological processes - deserve equal attention [7, 9]. 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 understanding and she attempts to find virtues and strengths and merits in students' mathematical understanding. Paradoxically, a teacher must believe her own mathematical understanding in order to doubt and a teacher must doubt her own mathematical understanding in order to believe. For this qualitative case study, the professor, Beth, purposefully played the believing game. She created a "believing" teacher action plan prior to teaching a proofs course and she wrote a teacher "believing" stance statement about midway through the course. After the course ended, Shelly interviewed students in order to answer the research question: How did students describe their classroom community, the teacher's actions and interactions with them, and their own learning? Students described some aspects of Beth's teacher action plan; however, their descriptions aligned more closely with her teacher "believing" stance statement. This implies that to move towards playing the believing game the teacher stance is critical.