Forms of constructivism, cognitive development and number learning

Genetic constructivism regards the development of cognitive structures as the prod-uct of interactions among three systems of equilibration relating to phylogenesis, sociogenesis and psychogenesis (Cellérier & Decret, 1992). From this point of view, the study of numbers is of particular interest since it reveals visible interactions between the child, his current forms of cognitive organization and his particular sociocultural environments. It is also worthy of note because the major constructivist theories (the genetic psychology of Piaget, the ‘constructive’ innateness of Gelman and the sociogenesis of Fuson) have taken an interest in numbers, focusing their attention in varying degrees on one of the systems in question. Our purpose here is to show the relevance of the complementarity of these approaches to research in and the teaching of elementary arithmetic.