This interpretive cross-case study investigates complexity in the ways teachers frame mistakes and the reasons behind their framing, challenging the assumption in the literature that productive beliefs about errors generate productive error-handling practices, while unproductive beliefs result in unproductive practices. The study draws on interviews and classroom observations with three secondary mathematics teachers who were selected using purposive sampling. Analysis examines how the teachers framed mistakes in their classroom practice and the instructional moves that enacted each frame. We paid particular attention to epistemological frames, which concern the value of mistakes in the construction of mathematical knowledge, and positional frames, which concern the roles that students are authorized or obligated to take to address errors, researching how teachers’ epistemological and positional framing of errors were related. The results suggest that teachers invoked four primary frames related to errors: a epistemological frame of errors-as-resources, a positional frame of students-as-capable, an epistemological frame of errors-as-deficiencies, and an positional frame of students-as-incapable. We discuss barriers to using mistakes as resources for learning and implications for mathematics teacher education.

这项解释性的跨案例研究调查了教师构建错误的方式的复杂性及其背后的原因，挑战了文献中关于错误的有效信​​念会产生有效的错误处理实践，而无效的信念会导致无效的实践的假设。该研究利用了对使用有目的抽样选出的三名中学数学教师的访谈和课堂观察。分析检查教师如何在课堂实践中构建错误以及制定每个框架的教学动作。我们特别关注认识论框架，它涉及数学知识构建中错误的价值，以及位置框架，涉及学生被授权或有义务解决错误的角色，研究教师的认识论和错误定位框架之间的关系。结果表明，教师引用了与错误相关的四个主要框架：错误作为资源的认识框架、学生作为能力的位置框架、错误作为缺陷的认识框架和学生的位置框架无能为力。我们讨论了使用错误作为学习资源的障碍以及对数学教师教育的影响。