Building Assessment Items and Instructional Tasks to Build Intercommunity Capacity to Develop Teachers' Mathematical Knowledge for Teaching

探索研究K-12计划(DRK-12)旨在通过研究和开发创新资源、模型和工具(RMT)，显著提高K-12学龄前学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发努力的基础上，这些研究和开发工作为拟议的项目提供了理论和经验证明。改善美国数学教育的基础设施需要将数学和数学教育方面的人力资源建设成一个能够响应该领域关键需求的专业社区。这个项目旨在建立一个专业社区，共享对专业内容知识(SCK)的理解-关于教学中使用的数学知识的特殊形式和推理方法(MKT)。这个社区将有助于提高教师在数学方面的SCK的进一步研究和发展的能力，这已被证明与学生的成绩有关。在专业团体共享知识的基础上，该项目还将利用说明性数学小组为K-12学生开发的类似任务和项目开发平台，合作开发MKT/SCK项目和任务的题库。更好的措施，加上更大的题库，将有助于支持教师MKT/SCK的学习和评估。根据实践共同体的理论，该项目将把数学家和数学教育工作者聚集在一起，通过努力开发测量SCK的项目和开发任务库，建立一个对数学SCK有共同理解的专业社区。在他们参与制定先前措施的“项目夏令营”的基础上，该项目将为教职员工和教师或研究生举办12个为期4天的夏令营，主题各不相同，确保数学家和教育工作者的混合。这项工作将导致MKT/SCK的认证。他们还将制定大约60个项目，并有一个今后审查和发布项目的机制。该项目将采用个案研究方法，研究这些伙伴关系的发展情况以及营地内和营地之间的专业团体。

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. The infrastructure to improve mathematics education in the US requires building human resources in mathematics and mathematics education into a professional community that can respond to the critical needs in the field. This project seeks to build a professional community with shared understanding of the specialized content knowledge (SCK) - the special forms and ways of reasoning about mathematical knowledge used in teaching (MKT). This community will help increase the capacity for further research and development on teachers' SCK in mathematics, which has been shown to relate to student achievement. Building on the professional community's shared knowledge, the project will also work to collaboratively develop an item bank of MKT/SCK items and tasks using the platform developed by the Illustrative Mathematics group for similar task and item development for K-12 students. Better measures, with a larger item bank, will help support both the learning and assessment of teachers' MKT/SCK. Based on theories of communities of practice, this project will bring together mathematicians and mathematics educators to build a professional community with a shared understanding of the SCK in mathematics through engaging in efforts to develop items to measure SCK and the development of a task bank. Based on the "item camps" they engaged with to develop prior measures, the project will host twelve 4-day camps with varying themes for pairs of faculty and teachers or graduate students, ensuring a mix of mathematicians and educators. This work will lead to a certification for MKT/SCK. They will also develop approximately 60 items and have a mechanism for the future review and publishing of items. Using case-study methodologies, the project will study the development of these partnerships and the professional communities within and across the camps.