Cognition and Improvisation: Differences in Mathematics Instruction by Expert and Novice Teachers

Abstract

This study investigates the nature of pedagogical expertise by comparing the planning, teaching, and postlesson reflections of three student teachers (two secondary and one elementary) with those of the cooperating teachers with whom they were placed. Participants were observed teaching mathematics for 1 week of instruction and were interviewed prior to and following each lesson. Differences in the thinking and actions of these experts and novices were analyzed by perceiving teaching both as a complex cognitive skill and as improvisational performance Novices showed more time-consuming, less efficient planning, encountered problems when attempts to be responsive to students led them away from scripted lesson plans, and reported more varied, less selective postlesson reflections than experts. These differences were accounted for by the assumptions that novices’ cognitive schemata are less elaborate, interconnected, and accessible than experts’ and that their pedagogical reasoning skills are less well developed. We offer several recommendations for student teaching based on this analysis.