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

这个项目试图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、概率和统计的学习，但对学生来说仍然是一个挑战。为此，该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(PSMT)能够更好地识别、分析和联系学生在函数推理中发现的模式。许多学生离开高中时，他们的函数推理能力受到严重限制。与此同时，教师教育项目面临着这样的挑战：如何让教师准备好以学生带到课堂上的非正式知识为基础进行教学。善于以学生的思想为基础的教师，对数学思想是如何相关的，如何以有意义的方式表达思想，以及学生推理中的常见模式都有专门的知识。这种类型的数学知识不能仅通过实地工作来发展。这个项目的理论基础来自(1)学生对关键数学概念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)以在线组件为特色的基于视频的学习环境的设计和使用。利用基于设计的研究方法，该项目的头两年将重点开发和测试为PSMT设计的本科数学课程中的四个视频模块。该项目的最后两年将侧重于在UTeach伙伴机构传播和实施这些单元，以及研究从实施中产生的数据。在整个项目中，大约250名私营军校教师和20名大学教师将参与这些单元的培训。完成的模块系列将为教师教育计划提供一种直接的方式，将特定于教学的数学内容整合到现有的数学课程中，同时增加本科生水平的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)在模块学习环境中基于经验的学生思维的PSMT学习模型，以及(2)通过学生思维的视频案例支持PSMT学习的理论和设计原则。将通过研究出版物、会议报告和大学教师研讨会与当地和国家教育受众分享关于该项目、其材料和成果的信息。该项目得到了美国国家科学基金会改善本科生STEM教育(IUSE)计划和罗伯特·诺伊斯教师奖学金计划的支持，目的是通过实施在线视频模块，突出精心挑选的学生思考案例，帮助改进中学数学教师的准备工作。该项目将使教师教育工作者能够更好地装备他们的本科生PSMT，使广大学生能够接触到功能推理，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.