Mathematics Capstone Course Resources: Preparing Secondary School Mathematics Teachers

数学顶点课程资源：培养中学数学教师

• 批准号: 1504551
• 负责人: Shandy Hauk
• 金额: $ 25万
• 依托单位: WestEd
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-07-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1504551&HistoricalAwards=false
• 关键词: Mathematics; Capstone; Course; Resources; Preparing

The preparation of the highest quality teachers and learners of mathematics is a national imperative. As undergraduates, future secondary school teachers take many courses from professors with advanced degrees in mathematics. However, university faculty members often do not possess deep knowledge of the kinds of teaching demands faced by new school teachers. There is a notable need for instructional materials that deliberately and explicitly connect undergraduate mathematics content to the knowledge needed for teaching secondary mathematics. This project will leverage the existence of Capstone Courses for future teachers found in many universities, which bring together ideas from across the college mathematics experience, as well as recent developments in policy and school accountability, to create and refine activities for use by university faculty in mathematics pre-service teachers Capstone Courses. This project will develop Capstone Course modules which provide access to advanced mathematical ideas along with opportunities to unpack mathematics in ways helpful for teaching it in middle and high school settings. The proof-of-concept work of the project has two parts. One is the development and refinement of two full modules, each designed to take about a week of instructional time in a Capstone Course. The second aspect is refining the module development process itself. This project is significant in that it intends to strengthen the pre-service preparation of teachers while it will also contribute to educational research on the improvement of pre-service teacher learning experiences in mathematics. The design for each module will use assessments linked to state mathematics standards as anchors for discussion, sites for development of mathematical knowledge, and foundations for other mathematics-specific knowledge used in teaching. Modules will include mathematical task exploration, analysis of middle and high school student thinking illustrated in video-recorded clinical interviews, and examination of sample formative and summative assessment items. The project brings together WestEd with San Francisco State University and the University of Maine to: (1) develop and pilot multi-media instructional modules for advanced pre-service secondary mathematics teacher learning; (2) create guidance for college mathematics faculty for effective use of the modules with target audiences; and (3) gather information from instructors and the pre-service teachers in their courses to inform future module development work. Design-based implementation research (DBIR) strategies will be employed, using an iterative process to examine a persistent problem of college instructional practice, to develop theory and tools for systematic inquiry into feasibility and fidelity of implementation of the modules. Intellectual Merit of the project resides in the expertise of the PI team, the materials that will be developed, and a research agenda that will examine feasibility (accessibility and usability by mathematics faculty), promise (pre-service teacher learning based on the modules), and scalability (identification of challenges to effective implementation). The Broader Impacts are present in the intention to have faculty members at other institutions pilot test materials during the project and in the potential for faculty, nationwide, to use the modules to replace parts of, or enrich, current capstone course designs. Also contributing to the Broader Impacts is that knowledge gained from project research will provide a foundation for future research-based development efforts to increase tools available for preparing mathematics teachers.

培养最高素质的数学教师和学习者是国家的当务之急。作为本科生，未来的中学教师会从拥有数学高级学位的教授那里学习许多课程。然而，大学教师往往对新教师面临的教学需求缺乏深入的了解。非常需要教学材料能够有意而明确地将本科数学内容与中学数学教学所需的知识联系起来。该项目将利用许多大学为未来教师开设的顶点课程，汇集大学数学经验的想法以及政策和学校问责制的最新发展，以创建和完善供大学教师在数学职前教师顶点课程中使用的活动。该项目将开发 Capstone 课程模块，提供先进的数学思想以及以有助于在初高中环境中教授数学的方式解开数学的机会。该项目的概念验证工作分为两部分。一是开发和完善两个完整模块，每个模块在顶点课程中需要大约一周的教学时间。第二个方面是完善模块开发流程本身。该项目意义重大，旨在加强教师的职前准备，同时也有助于改善职前教师数学学习体验的教育研究。每个模块的设计将使用与国家数学标准相关的评估作为讨论的基础、数学知识发展的场所以及教学中使用的其他数学特定知识的基础。模块将包括数学任务探索、对录像临床访谈中所展示的初中生和高中生思维的分析，以及对样本形成性和总结性评估项目的检查。该项目将 WestEd 与旧金山州立大学和缅因大学联合起来：(1) 开发和试点用于高级职前中学数学教师学习的多媒体教学模块； (2) 为大学数学教师提供针对目标受众有效使用模块的指导； (3) 从课程中的讲师和职前教师那里收集信息，为未来的模块开发工作提供信息。 将采用基于设计的实施研究（DBIR）策略，通过迭代过程来检查大学教学实践中持续存在的问题，开发理论和工具来系统地探究模块实施的可行性和保真度。 该项目的智力价值在于 PI 团队的专业知识、将要开发的材料以及将检查可行性（数学教师的可访问性和可用性）、承诺（基于模块的职前教师学习）和可扩展性（识别有效实施的挑战）的研究议程。更广泛的影响在于让其他机构的教职人员在项目期间试点测试材料，以及全国范围内的教职人员有可能使用这些模块来替换部分或丰富当前的顶点课程设计。产生更广泛影响的另一个原因是，从项目研究中获​​得的知识将为未来基于研究的开发工作奠定基础，以增加可用于培养数学教师的工具。