The Construct of Decentering in Research on Mathematics Learning and Teaching

Mathematics education researchers describe decentering as a form of reflection consisting of the mental processes involved in constructing a model of another’s thinking (from the perspective of the other). Piaget first introduced the decentering construct to characterize children’s development from an egocentric state to awareness of other perspectives. Mathematics education researchers adapted the construct’s use over time to facilitate cognitively oriented research programs. For example, researchers describe attempts to understand and model another’s thinking as decentering, with the resulting model explaining how the other might have been thinking to act as they did. Researchers have also described a teacher’s instructional effectiveness in terms of the teacher’s decentering actions or their propensity to notice and model a student’s thinking and use that model to inform their instructional actions. In this chapter we discuss Piaget’s construct of decentering and its usefulness when characterizing aspects of a child’s cognitive development. We elaborate features of research design for modeling another’s thinking and illustrate the symbiotic relationship between a researcher’s conception of what is entailed in understanding and learning an idea and the researcher’s decentering actions. We conclude by offering a framework and examples that illustrate how a teacher’s decentering actions while planning, delivering, and reflecting on instructional interactions with students, relative to a specific idea, can advance the teacher’s ways of thinking about teaching the idea.