Agents of Change in Promoting Reflective Abstraction: A Quasi-Experimental, Study on Limits in College Calculus

Abstract

We measured student performance on the concept of limit by promoting reflection through four agents of change: instructor, peer, curriculum and individual. It is based on Piaget’s four constructs of reflective abstraction: interiorization, coordination, encapsulation, and generalization, and includes the notion of reversal, as refined into a construct by Dubinsky. Our quasi-experimental study examined the performance of two sections of first-semester calculus students at a midwestern community college. Scores by students in the experimental section were significantly higher than scores by students in the control traditional section on a posttest of limits. A deeper examination of a three-tiered subgroup showed the reflective abstraction section had moderate effect size on mathematical knowledge and strategic knowledge and a large effect size on explanation.