Most prospective secondary mathematics teachers complete a course in real analysis, yet view the content as unrelated to their future teaching. We leveraged a theoretically motivated instructional model to design modules for a real analysis course that could inform secondary teachers’ pedagogy, focusing on how this model was implemented in a single module about “attending to scope.” The central aim is to document how teachers’ experience in this real analysis course influenced their subsequent teaching. In the majority of lessons we observed from six participating teachers, the following occurred: (i) the teacher explicitly attended to the scope of statements discussed in class; and (ii) in post-class interviews, the teacher highlighted their deliberate attention to scope and attributed this behavior to their experience in the experimental real analysis course. We discuss the design approach, its relation to teachers’ actions in the classroom, and potential implications for teacher education in advanced content courses.

中文翻译：

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设计高等数学课程以影响中学教学：培养数学老师的“关注范围”

大多数准中学数学教师完成了真实分析的课程，但认为内容与他们未来的教学无关。我们利用具有理论动机的教学模型来设计用于实际分析课程的模块，这些模块可以为中学教师的教学法提供信息，重点是如何在有关“关注范围”的单个模块中实施该模型。中心目的是记录教师在此实际分析课程中的经验如何影响其后续教学。在我们从六名参与教师那里观察到的大部分课程中，发生了以下情况：（i）教师明确地关注了课堂讨论的陈述范围；（ii）课后访谈中，老师强调了他们对范围的刻意关注，并将这种行为归因于他们在实验性真实分析课程中的经验。我们讨论了设计方法，它与教室中教师行为的关系以及高级内容课程对教师教育的潜在影响。