Manipulatives, Diagrams, and Mathematics: A Framework for Future Research on Virtual Manipulatives

Abstract

Our objective in this chapter is to present a framework that can be used as a guide for designers of virtual manipulatives and for researchers who study their effects on student learning in mathematics. Because a significant amount of research has been devoted to the effects of concrete manipulatives on student learning, the crux of the framework is based on the existing literature in this area. Specifically, the framework consists of three interrelated components that align with the research on students' learning with external representations: the surface features of the representations themselves, the pedagogical contexts that support students' meaning making, and the students' perceptions and interpretations of the representations. Where applicable, we integrate the research on virtual manipulatives to support the validity of the framework itself and its applicability for researchers of virtual mathematics tools.