The Constructivist Researcher as Teacher and Model Builder

Abstract

The constructivist teaching experiment is used in formulating explanations of children's mathematical behavior. Essentially, a teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of time—anywhere from 6 weeks to 2 years. The explanations we formulate consist of models—constellations of theoretical constructs—that represent our understand-ing of children's mathematical realities. However, the models must be distinguished from what might go on in children's heads. They are formulated in the context of intensive interactions with children. Our emphasis on the researcher as teacher stems from our view that children's construction of mathematical knowledge is greatly influenced by the experience they gain through interaction with their teacher. Although some of the researchers might not teach, all must act as model builders to ensure that the models reflect the teacher's understanding of the children. Our methodology for exploring the limits and subtleties of children's construc-tion of mathematical concepts and operations is the primary object of attention in this paper. We argue that, in such an exploration, there is no substitute for experi-encing the intimate interaction involved in teaching children. We then discuss the constructivist view of teaching and stress the importance of modeling children's mathematical realities. Next, the similarities and differences between constructivist and nonconstructivist teaching experiments are highlighted. In the remainder of the paper, we focus on models and model building.