Mathematics Capstone Course Resources: Preparing Secondary School Mathematics Teachers

培养最高质量的数学教师和学习者是国家的当务之急。作为大学生，未来的中学教师从具有高等数学学位的教授那里学习许多课程。然而，大学教师往往不具备对新教师所面临的教学需求的深入了解。有一个显着的教学材料，故意和明确连接本科数学内容所需的中学数学教学知识的需要。该项目将利用存在的顶点课程，为未来的教师发现在许多大学，汇集了来自整个大学数学经验的想法，以及政策和学校问责制的最新发展，以创建和完善活动，供大学教师在数学职前教师顶点课程。该项目将开发顶点课程模块，提供访问先进的数学思想沿着的机会，以有助于在初中和高中环境中教学的方式来解包数学。该项目的概念验证工作分为两个部分。一个是两个完整模块的开发和完善，每个模块的设计需要大约一周的教学时间在顶点课程。第二个方面是改进模块开发过程本身。该项目意义重大，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关联的评估作为讨论的锚点，数学知识发展的网站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，分析初中和高中学生的思维说明在视频记录的临床访谈，并检查样本形成性和总结性评估项目。该项目使西教育学院与旧金山弗朗西斯科州立大学和缅因州大学一道：（1）为高级职前中学数学教师学习开发和试验多媒体教学模块;（2）为大学数学系制定指导方针，以便在目标受众中有效使用这些模块;及（3）从导师及职前教师收集有关课程的资料，作为日后发展课程的参考。 设计为基础的实施研究（DBIR）的策略将采用，使用迭代过程来检查一个持续存在的问题，大学教学实践，开发理论和工具，系统的调查的可行性和保真度的模块的实施。 该项目的智力价值在于PI团队的专业知识，将开发的材料，以及将研究可行性（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。更广泛的影响是存在的意图有教师在其他机构试点测试材料在项目期间，并在教师的潜力，全国范围内，使用模块来取代部分，或丰富，目前的顶点课程设计。从项目研究中获得的知识将为今后以研究为基础的发展工作提供基础，以增加培养数学教师的工具，这也有助于产生更广泛的影响。

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.