CIEAEM 59 CONGRESS DOBOGÓKŐ 2007 1 WHAT STUDENTS WANT: AN ENVIRONMENT WHERE LEARNING TO BE IN MATHEMATICS Ornella Robutti*, Maria Teresa Ravera, Silvia Ghirardi^, Marialuisa Manassero° * Università di Torino, ^IIS Eula di Savigliano, °Liceo scientifico Vasco di Mondovì, Italy Abstract: In this paper we analyse an ongoing teaching experiment with students of secondary school, working within the new technological environment provided by the TI-Navigator. Our purpose is to investigate students’ processes from a semiotic point of view, particularly referred to signs and meanings supported by this environment. Here we present examples of some activities with excerpts of video-taped discussions. Our results suggest that this new technology offers to didactical practice something more than an usual environment. INTRODUCTION AND THEORETICAL FRAME Our research project is framed on a semiotic-cultural approach, referring to the theory of objectification (Radford, 2006). This theory gives rise to an anthropological conception of thinking on the one hand, and a socio-cultural conception of learning on the other. According to Radford’s perspective, thinking is characterized by way of its existence as a reflexive praxis (praxis cogitans), which is a practical reflection on the external world, practical because it takes the forms and the modes of the activities of the individuals. This concept of reflection differs both from empiricism and rationalism. Thinking as re-flection is a dialectical process between a historically and culturally constituted reality and an individual who receives it, as well as revises it, according to his/her own subjective feelings and interpretations. Thinking is not only a reflexive practice, but also a mediated one, if we refer to the role played by artefacts and signs used in order to carry the cognitive praxis itself. Artefacts and signs are not simple aids or catalysts to achieve knowledge, but rather constitutive and consubstantial parts of thinking. The individual thinks with and through semiotic means, which are bearers of an “embodied intelligence” and hide cultural-historical experiences in themselves, conceptions and meanings of the past generations’ cognitive activity. The importance of the role and the mediation of the artefacts is an important theme of many recent researches, following a common direction framed in a post-Vygotskijan perspective. According to this theoretical perspective, learning is a matter of endowing the mathematical objects that the student finds in his/her culture with meaning, it’s a matter of making visible something that was invisible. Then, learning mathematics is not so much a matter of learning to do mathematics; rather it is a matter of learning to be in mathematics. This re-conceptualization of learning implies a re-organization of the class itself and of the roles that students and teachers play within it. What is important is to learn how to live in the classroom as a community, to interact with others, namely: to be-with-others. Learning is considered as a social praxis, based on a common and active reflection about the environment students are living in. What we study as researchers is when and how the students are making visible something that was not before, and in doing this we observe and analyse not only speech but also gestures and whatever sign is introduced by the students in their activity: symbols, drawings, graphics, actions, bodily movements and glances. Recent research (Arzarello, 2006; Robutti, 2006) has stressed the