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

为中学数学教师提供学生函数推理视频案例

基本信息

批准号：
1726543
负责人：
Laurie Cavey
金额：
$ 159.69万
依托单位：
Boise State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1726543&HistoricalAwards=false
关键词：
Preparing Secondary Mathematics Teachers Video

项目摘要

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.

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、概率和统计的研究，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、分析学生功能推理中的模式，并在这些模式之间建立联系。许多学生离开高中时，他们用函数推理的能力严重受限。与此同时，教师教育项目也面临着这样的挑战：如何让教师以学生带入课堂的非正式知识为基础进行教学。善于建立学生思想基础的教师对数学思想之间的关系、如何用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了解。这种类型的数学知识不能仅仅通过实地工作来发展。该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参与学习学生的思维，以及(4)设计和使用具有在线组件的基于视频的学习环境。采用基于设计的研究方法，本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。项目的最后两年将重点关注这些模块在UTeach合作院校的传播和实施，以及对实施过程中产生的数据进行研究。在整个项目中，大约250名psmt和20名大学讲师将参与这些模块。完成的模块系列将为教师教育计划提供一种直接的方法，将数学内容具体到现有数学课程的教学中，同时在本科阶段增加精心设计的混合学习机会。通过评估和研究，本项目将得出(1)基于经验的PSMT模块学习环境下学生思维学习模型；(2)利用学生思维视频案例支持PSMT学习的理论和设计原则。有关该项目的信息、材料和成果将通过研究出版物、会议报告和大学讲师研讨会与当地和全国的教育受众分享。该项目由美国国家科学基金会改善本科STEM教育（IUSE）计划和Robert Noyce教师奖学金计划支持，旨在通过实施在线视频模块，突出精心挑选的学生思维案例，帮助改善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psmt，使广大学生能够使用功能推理，从而有可能扩大学生在STEM领域的参与。