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

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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.