Abstract This paper describes theoretical design principles emerging from the development of tasks for standard undergraduate mathematics courses that address applications to teaching secondary mathematics. While researchers recognize that mathematical knowledge for teaching is a form of applied mathematics, applications to teaching remain largely absent from curriculum resources for courses for mathematics majors. We developed various materials that contain applications to teaching that have been integrated into four standard undergraduate mathematics courses. Three primary principles influenced the design of the tasks that prepare future teachers to learn and apply mathematics in a manner central to their future work. Additionally, this paper provides guidance for instructors desiring to develop or implement similar applications. The process of developing these tasks underscores the importance of key features regarding the roles of human beings in the tasks, the intentional focus on advanced content connected to school mathematics, and the integration of active engagement strategies.

中文翻译：

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设计用于在本科数学课程中应用中学数学教学的任务

摘要 本文描述了从标准本科数学课程的任务开发中出现的理论设计原则，这些课程涉及中学数学教学的应用。虽然研究人员认识到用于教学的数学知识是应用数学的一种形式，但在数学专业课程的课程资源中，教学应用在很大程度上仍然缺乏。我们开发了各种材料，其中包含已集成到四门标准本科数学课程中的教学应用。三个主要原则影响了任务的设计，这些任务使未来的教师以一种对他们未来工作至关重要的方式学习和应用数学。此外，本文还为希望开发或实施类似应用程序的教师提供指导。