1- 1 2011. In xxxx (Eds.). Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, pp. XXX-YYY. Ankara, Turkey: PME. PROOF IN CLASSROOM SOCIAL PRACTICE João Filipe Matos Universidade de Lisboa, Instituto de Educação Margarida Rodrigues Escola Superior de Educação de Lisboa How does the construction of proof relate to the social practice developed in the mathematics classroom? This report addresses the role of diagrams in order to focus the complementarity of participation and reification in the process of constructing a proof and negotiating its meaning. The discussion is based on the analysis of the mathematical practice developed by a group of four 9 th grade students and is inspired by the social theory of learning. INTRODUCTION The present study dealt with the problem of proof in school mathematics (Rodrigues, 2008). Its main goal was to identify the ways in which students validate their mathematical results, relating them to the social practice developed in the classroom. The questions posed were: 1) what is the nature of proof in a school context?, 2) what is the role of proof in students‟ mathematical activity?, and 3) how does the construction of proof relate to the social practice developed in the mathematics classroom? We will present in this paper just some results related with the third question. The study‟s framework is rooted in the theoretical frame of social practice in the line of Wenger (1998). Mathematics learning is seen as a situated and a social phenomenon (Lave, 1997; Matos, 2010). As a social participation, it is the process of being an active participant in the practice of social communities and constructing identities in relation to those communities (Wenger, 1998). “Such participation shapes not only what we do, but also who we are and how we interpret what we do” (Wenger, 1998, p. 4). The social theory of learning includes components that are interrelated and characterize the social participation as a process of learning and of knowing: (a) community, (b) identity, (c) practice, and (d) meaning. The construct of community of practice is a central one in this theory. The basic structure of a community of practice is composed of three elements: (1) the domain of knowledge that defines the area or the set of shared topics; (2) the community of people, concerned with the domain, creating relationships and a sense of belonging; and (3) the shared practice developed by people to deal with the domain, consisting of the body of shared knowledge and resources that enables the community to