Preparing Secondary Mathematics Teachers with Video Cases of Students' Functional Reasoning

该项目旨在解决数学的一个关键领域，函数，这是K-12数学中的一个统一概念，适用于代数，几何，概率和统计学的研究，但对学生来说仍然是一个挑战。 为此，本项目将开发一系列基于视频的在线学习模块，用于本科数学课程，以便未来的中学数学教师（PSMTs）能够更好地识别，分析和建立学生功能推理模式之间的联系。 许多学生离开高中时，在他们的能力与功能的原因严重限制。 与此同时，教师教育计划面临着一个挑战，即教师要准备好以学生带到课堂上的非正式知识为基础的教学方式。 善于建立学生思想的教师对数学思想是如何联系在一起的，如何以有意义的方式表达思想，以及学生推理的常见模式都有专门的知识。这种类型的数学知识不能仅仅通过实地工作来发展。这个项目的理论基础来自于（1）学生对关键数学思想的非正式和正式推理，（2）学生对函数的思考，（3）使用视频让PSMT学习学生的思维，以及（4）设计和使用基于视频的学习环境，其中包括在线组件。 使用基于设计的研究方法，该项目的前两年将专注于为PSMT设计的本科数学课程中的四个视频模块的开发和测试。 该项目的最后两年将侧重于在合作伙伴UTeach机构传播和实施这些模块，以及研究实施过程中产生的数据。 在整个项目中，大约250名PSMT和20名大学教员将参与这些模块。 完成的模块系列将为教师教育计划提供一种简单的方法，将特定于教学的数学内容整合到现有的数学课程中，同时增加本科阶段精心设计的混合学习机会。 通过评估和研究，该项目将产生（1）一个基于模型的PSMT学习模式，在模块学习环境的背景下学习学生的思维，以及（2）理论和设计原则，支持PSMT学习与学生思维的视频案例。 有关该项目的信息，其材料和成果将通过研究出版物，会议演示和大学讲师研讨会与当地和国家教育受众分享。 该项目得到了NSF改善本科STEM教育（IUSE）计划和罗伯特·诺伊斯教师奖学金计划的支持，目标是通过实施强调精心挑选的学生思维案例的在线视频模块来帮助改善中学数学教师的准备。 该项目将使教师教育工作者能够更好地装备他们的本科PSMT，使功能推理能够为广大学生所用，从而有可能扩大学生在STEM领域的参与。

This project seeks to address a critical area of mathematics, function, which is a unifying concept in K-12 mathematics that applies to the study of algebra, geometry, probability, and statistics, but persists as a challenge for students. To this end, this project will develop a series of video-based online learning modules for use in undergraduate mathematics courses so that prospective secondary mathematics teachers (PSMTs) are better equipped to recognize, analyze, and make connections between the patterns found in students' functional reasoning. Many students leave high school with serious limitations in their ability to reason with functions. At the same time, teacher education programs are faced with the challenge of preparing teachers to teach in ways that build upon the informal knowledge students bring to the classroom. Teachers who are adept at building upon students' ideas have a specialized knowledge of how mathematical ideas are related, how to represent ideas in meaningful ways, and common patterns in students' reasoning. This type of mathematical knowledge cannot be developed through field-based work alone. The theoretical foundation for this project arises from (1) students' informal and formal reasoning related to key mathematical ideas, (2) students' thinking about functions, (3) the use of video to engage PSMTs in learning about student thinking, and (4) the design and use of video-based learning environments which feature online components. Using a design-based research methodology, the first two years of this project will focus on the development and beta-testing of four video modules in an undergraduate mathematics course designed for PSMTs. The final two years of the project will focus on the dissemination and implementation of these modules at partner UTeach institutions, as well as the study of data emanating from the implementation. Throughout the project, about 250 PSMTs and 20 university instructors will engage with the modules. The completed module series will provide teacher education programs a straightforward way to integrate mathematical content specific to teaching within their existing mathematics curriculum while simultaneously increasing well-designed hybrid learning opportunities at the undergraduate level. Through evaluation and research, the project will result in (1) an empirically-based model for PSMT learning about student thinking in the context of the module learning environments, and (2) theory and design principles for supporting PSMT learning with video cases of student thinking. Information about the project, its materials, and its outcomes will be shared with local and national educational audiences via research publications, conference presentations, and university instructor workshops. This project is supported under the NSF Improving Undergraduate STEM Education (IUSE) program and the Robert Noyce Teacher Scholarship program, with the goal of helping to improve secondary mathematics teacher preparation through implementation of online video modules that highlight carefully selected cases of student thinking. This project will enable teacher educators to better equip their undergraduate PSMTs in making functional reasoning accessible to a broad population of students, thereby potentially broadening student participation in STEM fields.