| The redevelopment of one mathematics teacher's expert pedagogical content knowledge is tracked across two years as she teaches a new instructional unit. Growth in pedagogical content knowledge is modeled as the interanimation of two Discourses. One Discourse refers to characteristic ways that students talk and act about the mathematics of the unit, and the other, to characteristic ways that the teacher talks and acts as she guides the development of students' mathematical thinking. At the inception of the unit, these two Discourses, although not independent, were only loosely coupled. Initially, the teacher responded to variations in student talk and activity by employing general heuristics, such as repeating what a student had said so that others could hear, or by asking a question to elicit further elaboration of a particular student's pattern of thought. As the teacher attempted to orchestrate classroom conversations oriented toward developing understanding, these general heuristics often failed to transform student thinking in ways that she considered fruitful from a disciplinary perspective. As a consequence, the teacher generated new conversational gambits that were more often tuned to particular elements of student talk and activity. Some of these were successful in creating more fruitful classroom discourse about mathematics (from the teacher's perspective), and hence classroom conversation increasingly reflected more tightly coupled and interanimated Discourses. Evidence that the teacher was building these Discourse couplings include chronological Discourse analyses of classroom videotape, the teacher's daily reflections in a notebook, and video-stimulated structured interviews with the teacher. Results demonstrate both the interanimated nature of the Discourses emerging in local interactions as well as broader patterns illustrating couplings used across the two years, and repeatedly across the second year of instruction. With greater numbers of teachers and students, this model of pedagogical content knowledge has potential for developing accounts of prototypical student thinking Discourses and typical teacher assistance Discourses within specific instruction designed to foster understanding. |
