ORIGINAL ARTICLE Introducing students to geometric theorems: how the teacher can exploit the semiotic potential of a DGS Maria Alessandra Mariotti Accepted: 15 February 2013 / Published online: 3 March 2013 Ó FIZ Karlsruhe 2013 Abstract Since their appearance new technologies have raised many expectations about their potential for inno- vating teaching and learning practices; in particular any didactical software, such as a Dynamic Geometry System (DGS) or a Computer Algebra System (CAS), has been considered an innovative element suited to enhance mathematical learning and support teachers’ classroom practice. This paper shows how the teacher can exploit the potential of a DGS to overcome crucial difficulties in moving from an intuitive to a deductive approach to geometry. A specific intervention will be presented and discussed through examples drawn from a long-term teaching experiment carried out in the 9th and 10th grades of a scientific high school. Focusing on an episode through the lens of a semiotic analysis we will see how the tea- cher’s intervention develops, exploiting the semiotic potential offered by the DGS Cabri-Ge ´ome `tre. The semi- otic lens highlights specific patterns in the teacher’s action that make students’ personal meanings evolve towards the mathematical meanings that are the objective of the intervention. 1 Introduction Introducing students to theoretical thinking is a key edu- cational issue that teachers are asked to face at different school levels and in relation to different mathematical domains. The complexity of this issue as well the variety of possible approaches has been discussed in the wide liter- ature on this topic (Mariotti 2006, 2012a; Hanna and de Villiers 2012). The content of this paper concerns this specific educational issue and discusses how a particular didactic intervention may be effective in overcoming cer- tain difficulties related to enabling students to enter a theoretical world. We will consider the crucial moment when students are expected to move from intuitive geom- etry to theoretical geometry, that is, geometry as a deductive system. This didactic issue was the basis of a long-term teaching experiment lasting for many years and involving a number of teachers and classes. Outcomes of such long-standing research work have been of different natures, both theoretical and empirical. A general trend in the Italian research context has been that research work has been conceived as ‘‘research for innovation’’ (Arzarello and Bartolini Bussi 1998), in which action in the classroom is both a means and a result of the evolution of research analysis. Teaching experiments of this type allow one to generate at the same time possible didactic sequences, a theoretical background that supports them and a rich database of possible outcomes. Consis- tently, one of the outcomes of the teaching experiments carried out by our teams has been the development of a theoretical framework according to a spiral process where theoretical constructs emerged from results coming from the classrooms and at the same time inspired the design of new didactical interventions. As far as our teaching experiments are concerned, such a theoretical frame is centred on the seminal idea of semiotic mediation introduced by Vygotsky (1978), which in the following will be referred to as the Theory of Semiotic Mediation (TSM) (Bartolini Bussi and Mariotti 2008). After a short description of the TSM and according to the theme of the Special Issue to which this paper belongs, I will discuss a classroom-based intervention aimed at addressing difficulties met by students in moving from an M. A. Mariotti (&) University of Siena, Siena, Italy e-mail: mariotti.ale@unisi.it 123 ZDM Mathematics Education (2013) 45:441–452 DOI 10.1007/s11858-013-0495-5