Playing the believing game: Enhancing productive discourse and mathematical understanding

- A temporal continuum of believing and doubting (Elbow, 1986) was identified.
- Reserved believing occurred when a teacher looked for merits in students' thinking.
- Reserved doubting occurred when a teacher looked for flaws in students' thinking.

In mathematics classrooms, the practice of doubt pervades. However, Elbow (1986, 2006) contended that teachers must balance their practices of methodological doubt and methodological belief. The study reported here builds upon previous research which revealed the professor played the believing game (Elbow) and students were motivated to do mathematics. We addressed the question: How does a teacher (professor) play the believing game in a mathematics classroom? Videotapes, interviews, and field notes from an entire semester were collected and analyzed qualitatively. Although the professor was not consciously attempting to believe or doubt, we reveal when and under what circumstances they occurred. A temporal continuum of believing and doubting existed for the professor's practice. Reserved believing and reserved doubting prevailed for the professor when she heard answers or comments she deemed incorrect and rich mathematical conversations transpired as she opened herself up to a deeper understanding of mathematics.