Most prospective secondary mathematics teachers in the United States 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’ actionable content knowledge and pedagogy. The theoretical model and designed curriculum launches the study of advanced mathematics content, in this case, real analysis, via authentic 7–12 classroom situations, abstracts the secondary mathematics, and uses that content to motivate the presentation of the advanced mathematics content. Subsequently, the curriculum then reconnects to practice, asking the teachers to translate ideas from real analysis in ways that are appropriate for teaching high school content to students. This study evaluated the success of the curriculum in terms of the students’ proficiency with real analysis, challenging secondary mathematics content, and the use of that content in teaching situations via both written post-tests and interviews and showed the viability of the model and experimental curriculum.

中文翻译：

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ULTRA评估；基于转化理论模型的实验性真实分析课程

美国大多数准中学数学老师都完成了真实分析的课程，但认为这些内容与其未来的教学无关。我们利用理论驱动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可行内容知识和教学法提供信息。理论模型和设计好的课程启动了对高级数学内容的研究，在这种情况下，将通过真实的7-12个课堂情况进行实际分析，对中学数学进行抽象，并使用该内容来激发高级数学内容的表达。随后，课程重新连接到实践中，要求教师以适合向学生教授高中内容的方式，将真实分析中的想法转化为现实。