Mathematics Capstone Course Resources: Preparing Secondary School 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，大学教职员工往往对新教师面临的各种教学需求缺乏深入的了解。值得注意的是，教学材料需要故意和明确地将本科生的数学内容与教授中学数学所需的知识联系起来。这个项目将利用在许多大学为未来教师提供的Capstone课程，这些课程汇集了整个大学数学经验的想法，以及政策和学校问责方面的最新发展，以创建和完善供大学教师在任职前教师Capstone课程中使用的活动。这个项目将开发Capstone课程模块，这些模块提供获取高级数学思想的途径，以及以有助于在初中和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包括两个部分。一个是开发和完善两个完整的模块，每个模块都设计为在Capstone课程中花费大约一周的教学时间。第二个方面是细化模块开发流程本身。该项目具有重要意义，因为它旨在加强教师的职前准备，同时也将促进关于改善职前教师数学学习经验的教育研究。每个模块的设计将使用与国家数学标准相联系的评估作为讨论的锚，发展数学知识的场所，以及教学中使用的其他特定数学知识的基础。模块将包括数学任务探索，分析初中生在录像临床访谈中的思维，以及检查样本形成性和终结性评估项目。该项目将WestEd与旧金山州立大学和缅因州大学联合起来：(1)开发和试验用于高级职前中学数学教师学习的多媒体教学模块；(2)为大学数学教师创建针对目标受众有效使用模块的指导；以及(3)从教师和职前教师的课程中收集信息，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)战略，使用迭代过程来审查大学教学实践中的一个长期存在的问题，开发理论和工具，系统地探讨这些模块实施的可行性和准确性。该项目的智力价值在于PI小组的专业知识、将要开发的材料以及将审查可行性(数学教师的可及性和可用性)、PROMISE(基于模块的职前教师学习)和可扩展性(确定有效实施的挑战)的研究议程。更广泛的影响体现在让其他机构的教职员工在项目期间试验测试材料的意图，以及全国教职员工使用这些模块取代或丰富当前顶峰课程设计的可能性。对更广泛的影响也有贡献的是，从项目研究中获得的知识将为今后以研究为基础的发展努力提供基础，以增加可用于培养数学教师的工具。

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.