Tracing the Evolution of Pedagogical Content Knowledge as the Development of Interanimated Discourses

Abstract

For this article, the development of 1 teacher's pedagogical content knowledge (Shulman, 1986) was tracked longitudinally across 2 years as she taught a new instructional unit in middle school mathematics. Growth in pedagogical content knowledge is characterized as the interanimation of 2 Discourses (Gee, 1999). One Discourse refers to characteristic ways that students talk and act about the mathematics of the unit; and the other Discourse, to characteristic ways that the teacher talks and acts as she guides the development of students' mathematical thinking. At the inception of the unit, the variety of small d discourses students and teacher generated were only loosely coupled. Initially, the teacher responded to variations in student talk and activity by employing general revoicing 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 mathematical understanding, these general heuristics often failed to transform student thinking in ways that she considered mathematically productive. As a consequence, she generated new conversational gambits that were more often tuned to particular elements of students' mathematical talk and activity. Some of these forms of talk created more fruitful classroom discourse about mathematics, which the teacher increasingly recognized as signals of particular ways of thinking about the mathematics (of slope). The teacher was not content with mere recognition. She elaborated and continued to innovate. Conjectures about the growth of pedagogical content knowledge were tested in video-stimulated structured interviews with the teacher and by modeling the syntax of teacher support of student thinking—predicting specific patterns of couplings between student and teacher Discourses. This article concludes with a discussion of the implications of this view for the ontogenesis of adaptive expertise.