Bridging Psychological and Educational Research on Rational Number Knowledge

Abstract

In this paper we focus on the development of rational number knowledge and present three research programs that illustrate the possibility of bridging research between the fields of cognitive developmental psychology and mathematics education. The first is a research program theoretically grounded in the framework theory approach to conceptual change. This program focuses on the interference of prior natural number knowledge in the development of rational number learning. The other two are the research program by Moss and colleagues that uses Case’s theory of cognitive development to develop and test a curriculum for learning fractions, and the research program by Siegler and colleagues, who attempt to formulate an integrated theory of numerical development. We will discuss the similarities and differences between these approaches as a means of identifying potential meeting points between psychological and educational research on numerical cognition and in an effort to bridge research between the two fields for the benefit of rational number instruction.