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.

中文翻译：

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大学数学学生对“相信”教师行为的看法

相信和怀疑–两个方法论过程–值得同等关注[7，9]。当老师在数学教室里玩令人怀疑的游戏时，她自己的数学思维占主导地位，并且她试图发现学生数学思维中的缺陷，错误和误解。当老师在数学教室里玩“相信游戏”时，她放弃了自己的数学理解，并试图在学生的数学理解中找到优点和优点和优点。矛盾的是，老师必须相信自己的数学理解才能怀疑，而老师必须怀疑自己的数学理解才能相信。对于这个定性的案例研究，贝丝教授有目的地玩了一场相信游戏。在教授证明课程之前，她制定了一个“相信”的老师行动计划，并在课程进行中撰写了一个老师“相信”的立场声明。课程结束后，雪莉（Shelly）采访了学生，以回答研究问题：学生如何描述他们的课堂社区，老师的行为和与他们的互动以及他们自己的学习？学生描述了Beth老师行动计划的某些方面；但是，他们的描述与她的老师“相信”的立场陈述更加吻合。这意味着，为了打起相信游戏，老师的立场至关重要。学生如何描述他们的课堂社区，老师的行为和与他们的互动以及他们自己的学习？学生描述了Beth老师行动计划的某些方面；但是，他们的描述与她的老师“相信”的立场陈述更加吻合。这意味着，为了打起相信游戏，老师的立场至关重要。学生如何描述他们的课堂社区，老师的行为和与他们的互动以及他们自己的学习？学生描述了Beth老师行动计划的某些方面；但是，他们的描述与她的老师“相信”的立场陈述更加吻合。这意味着，为了打起相信游戏，老师的立场至关重要。