Enhancing Preparation of Secondary Preservice Mathematics Teachers: Mathematical Reasoning and Proving as a Lens for Teaching

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This project will contribute to the National Science Foundation's goal of improving undergraduate STEM education to broaden and strengthen the U.S. STEM workforce. Preparation of mathematically literate and STEM-oriented majors begins prior to students reaching college. It begins with highly qualified and knowledgeable teachers, who inspire and prepare students to pursue STEM disciplines. Thus, it is imperative to prepare excellent mathematics teachers capable of enacting effective teaching practices in their classrooms. This project will address this teacher knowledge base through design, implementation, and study of a new, technologically rich capstone course called Mathematical Reasoning and Proving for Secondary Teachers. The course will enhance prospective secondary mathematics teachers' content and pedagogical knowledge to promote deep conceptual understanding, problem solving, reasoning, and proving skills. This emphasis concurs with the vision put forward by the National Council of Teachers of Mathematics and the Common Core State Standards for Mathematics. The successful implementation of this vision relies on a well-qualified and knowledgeable teacher workforce. The project will generate evidence-based approaches, instructional modules and facilitator guides to improve preparation of secondary mathematics teachers throughout the country, and by extension the project will enhance the mathematics education of thousands of middle school and secondary school students.The innovative aspects of the capstone course Mathematical Reasoning and Proving for Secondary Teachers will include university-based experiences supported by virtual learning environments, a structured practical experience in local schools, and an emphasis on reasoning, justification, and proving as an overarching approach for teaching mathematics. The project will develop a concept model of the capstone course, four instructional modules, and the accompanying facilitator guides. The instructional modules will each address a critical topic related to proving, such as quantification, conditional statements, direct proof and proof by contrapositive. The project will utilize design-based research methodology to study how prospective teachers' content and pedagogical knowledge for teaching mathematical reasoning and proving develop throughout the course. The results will help to better understand the impact of the learning environment and its design components on enhancing prospective teachers' knowledge. Specifically, the project will contribute to the literature on mathematical reasoning and proving and the ways to incorporate them in teacher preparation and, consequently, in the mathematics classroom. The theoretical and the empirical knowledge generated by the project will be broadly disseminated to help to improve preparation of secondary mathematics teachers nationwide. The Robert Noyce Teacher Scholarship program will provide co-funding for this project in recognition of its alignment with the broader teacher preparation goals of the Noyce effort.