ABSTRACT
Three interrelated areas comprise the theoretical perspective of this chapter: abstraction (Piaget, Inhelder, & Szeminska, 1960), proof scheme (Harel, 2001; Harel & Sowder, 1998;), and local conceptual development (Lesh & Harel, in press; Lesh & Kaput, 1988). This theoretical perspective has guided our investigation into three main questions:
What proof schemes does a small community of learners (three middle school classmates) share?
What cognitive disequilibria occur in this small community of learners who are working collaboratively to solve open-ended problems, and how do such disequilibria bring about reconceptualization of existing proof schemes?
What are the characteristics of local conceptual developments in which transitions and reconceptualizations of proof schemes occur during relatively short problem-solving episodes?
