6: Building Bridges: Cases as Catalysts for the Integration of Mathematical and Pedagogical Knowledge¹

Cases can be used in a variety of ways with practicing teachers and teacher candidates to explore classroom practice and build knowledge needed for teaching. The richness of a case that portrays an authentic episode of teaching can afford teachers the opportunity to examine issues of mathematics content, pedagogical practices that support student learning, and the interactions between the two. In this chapter, I discuss a way of using cases in conjunction with the solving of a mathematical task that allows teachers to build these different facets of mathematical knowledge for teaching and strengthen the connections between them. Using records from a content-focused methods course for practicing teachers and teacher candidates, I examine how solving and discussing a mathematical task, then reading and analyzing a case of classroom practice featuring the same task, influenced teacher learning. This combination of exploring a mathematical task with the analysis of a related case afforded teachers the opportunity to integrate their mathematical, pedagogical, and pedagogical content knowledge in interesting ways.