Pedagogical Content Knowledge and STEM Teacher Preparation

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Mathematical Sciences (21) This project is researching and developing a full year course for STEM undergraduates preparing for secondary mathematics teaching. The course integrates carefully structured problem solving activities, video case studies of children learning mathematics, academic readings, and discussions. Undergraduates are asked to reconsider the mathematical content of grades 4 -12 and then be ready to conceptualize the mathematical development of a student in these grades. This type of study results in early forms of pedagogical content knowledge, where content knowledge is blended with an understanding of how students' cognition develops. While analyzing their own work and that of grade 4-12 students, undergraduates pay specific attention to the representations, strategies, language, and big ideas that mark critical transitions in mathematical development. The project's research is analyzing the abilities of undergraduates to understand these components, their ability to understand and interpret children's mathematical thinking, and iteratively develop learning sequences upon which courses of this type can be based. Intellectual Merit: The project builds upon prior research on the teacher professional continuum, and is broadening understanding of the development of teachers during their critical pre-service years as university students. The undergraduates study the important mathematical ideas, cognitive obstacles, strategies, models, and language that surface in middle school and secondary mathematics. A number of recently developed video materials allow users to examine these issues in great detail and enable them to view and study children engaged in authentic classrooms. The project will provide an understanding of to what extent, where, and how such material can best be used in the undergraduate curriculum.Broader Impact: The shortage of secondary mathematics and science teachers is a continuing national concern and as a result, programs designed to move undergraduates more quickly into teaching are receiving increased attention. It is important for STEM undergraduates to connect their study of mathematics with the study of teaching and learning, and for collegiate educators to develop research and disseminate approaches that enhance their preparation. In addition, many state standards are requiring more rigorous material (including algebra) in grades 4-8 than in the past and it is important for teachers to incorporate higher level reasoning in their instruction. This project addresses these issues through research, development, and dissemination of instructional approaches that link STEM undergraduates' learning of content to critical themes in grade 4-12.