Planning and presenting meaningful instruction in the mathematics classroom is a demanding task requiring mental flexibility as well as a solid foundation in relevant content knowledge and pedagogical strategies. In the last three decades, there has been a growing interest in the way teachers utilize this specialized mathematical knowledge for teaching algebra in the practice of teaching, specifically in planning and presenting classroom instruction. Even more recently, a growing area of emphasis has been the application of these domains of knowledge in a specific focal context involving a singular topic or unit of instruction in the mathematics classroom. This study is such an inquiry, with a focus on a unit of instruction on solving quadratic equations in a first course in algebra. Using a mixed-methods design, the study investigates the cognitive connections between the dimensions of teachers’ knowledge for teaching algebra and the planning and implementation of instruction using the KAT Framework from Michigan State University. Findings indicate that classroom teachers access and utilize their knowledge in ways that reflect the depth of KAT they possess. Further, the degree of knowledge in the three dimensions of the KAT Framework is a strong indicator of teachers’ ability to enact effective instruction, extend learning experiences, and make connections across the mathematical domain. Both internal classroom dynamics and external factors beyond the teachers’ control emerged as surprisingly strong influences in these processes. The study has implications for teacher preparation, metrics for teacher effectiveness, social justice, and professional development programs.
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Knowledge of algebra for teaching quadratic equations : the impact of knowledge dimensions on planning and pedagogical strategies.
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