A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice

This study contributes to an emerging body of research on how to develop prospective teachers' pedagogical content knowledge (PCK) in teacher education. The main focus is on the knowledge transformation process and on the cognitive strategy used to shift prospective teachers' instructional explanations within the domain of integer subtraction from an instrumental to a relational understanding of mathematics. The strategy rests on the observation that transformation is not a unidirectional process from subject-matter knowledge to pedagogical content knowledge as the literature suggests. The adequacy of prospective teachers' instructional explanations, and the depth of their subject-matter understanding, is analyzed using a modification of Perkins and Simmons' levels of subject-matter understanding framework. The study concludes with observations about the interface between student achievement and prospective teachers' subject-matter and pedagogical content knowledge.