Constraint and cooperation in algebraic problem solving

Piaget (1965/1995. Sociological Studies. London: Routledge) proposes that neither the individual nor the set of individuals modify individual mental processes. Instead, what matters are the continuously modified relationships among individuals. But not all types of social interactions are sources of logical reasoning. Social interactions based on constraint only provide the individual with superficial notions, while cooperation, as a system of interpersonal actions governed by the laws of equilibrium and organized into reversible systems, allows for the development of objective and coherent system of operations. With examples of how children try to solve problems involving algebra relations and notation, we will contrast the effect of learning that results from the transmission of rules to the effect of learning that occur in cooperative interview settings. We will argue that Piagetʹs analysis of the role of social life and cooperation constitute a rich theoretical approach for understanding how children come to develop, understand, and use culturally developed mathematical representations.