Reflective abstraction as a mechanism for developing pedagogical content knowledge

Abstract

A mathematics teacher’s instruction is informed by their pedagogical knowledge (teaching theories and tactics) and content knowledge (ability to solve and understand math problems). A successful teacher must utilize both of these knowledge bases to support students’ conceptual learning of mathematics. Last year, we analyzed interviews previously conducted by my research mentors to examine how a pre-service secondary mathematics educator’s own conceptualization for rate of change, a foundational mathematics topic, progressed. In addition to a series of interviews to assess the participant’s individual understanding of rate of change, the participant reflected on the same set of recorded lessons of her teaching rate of change in the classroom pre-intervention interviews and post-intervention interviews. The participant noted moments of high quality instruction and room for improvement in each lesson, however these noted moments changed after her series of interviews. Prior to the interviews asking the participant to delve into her own capabilities of interpreting rate of change, her assessment of her teaching was focused on the pedagogical tactics implemented in her classroom and their effectiveness. However, after the interviews, she took into account whether her teaching was actually helping her students make the connections they needed in order to understand the concept. We hope to distinguish and emphasize the differences in her reflection before and after working through interviews that challenged to use reflective abstraction and blend her pedagogical and mathematical content knowledge.