Beyond a Psychological Approach: the Psychology of Mathematics Education

The major goals of the international research gmup "Psychology of Mathematics Education" (PME) are to promote international contacts and exchanges of scientific information in the psychology of mathematics education, and to pmmote and stimulate interdisciplinary research in this field [Nesher and Kilpatrick, 1990]. In this context the relevance of pieces of research dealing with didactical phenomena is not clear From my experience as a member of PME since its birth in 1976, I can witness to the fact that that we are very often embarrassed by the status to be given to research projects dealing with classrooms and didactical processes Beyond academic considerations of the quality of such research projects, their relevance with respect to psychology as a discipline is always problematic It is this problem that I would like to consider here in so far as I consider it essential fOr om research community, and, more generally, for the development of relationships between research in mathematics education and research in psychology As a starting point I will consider one of the basic hypotheses of research in mathematics education: the constructivist hypothesis "Hypothese d'un sujet qui explore activement son environnement, qui participe activement a Ia creation de l'espace, du temps, de la causalite" [Inbelder and Caprona, 1985, p 8] This hypothesis has been, and is still, largely discussed in the group I would like to consider it again to show how it calls for a step beyond a psychological problematique in order to understand the nature of the complexity of mathematics learning in a didactical context The starting point for the developmental process according to the constructivist hypothesis is the experience of a contradiction which is likely to provoke a cognitive disequilibrium: it is the overcoming of such a contradiction which results in new constructions [Piaget, 1975] This process concerns the learner as an individual As a result she will have her own understanding of some piece of knowledge But this could turn into a problem since this understanding must be open to exchange and collaboration with others This difficulty can be overcome only once the student's understanding "has been discussed and checked by others," as Sinclair [1988] quoting Piaget [1965] reminds us Actually, this social dimension is always present in the mathematics classroom in so far as all the way along the teaching process the learner interacts with other students and with the teacher. My position is that the relevance of our psychological approach depends on our capacity to integrate this social dimension into ourproblbnatique More precisely, the psychological relevance of the social dimension lies in two characteristics of mathematics learning in a didactical context: