Proof and proving in the classroom : Dynamic Geometry Systems as tools of Semiotic Mediation

The objective of this paper is to discuss the didactic potential offered by the use of a Dynamic Geometry System (DGS) in introducing students to theoretical thinking and specifically to the practice of proof. Starting from a discussion about what constitutes the general objective in developing students' sense of proof, the notion of Theorem is introduced as a system consisting of a statement, a proof, and a theory within which such a proof make sense. The paper discusses how the use of Dynamic Geometry Systems may support the teacher's intent to achieve her educational goal. The Theory of Semiotic Mediation provides the main theoretical reference for describing and explaining the role of Dynamic Geometry Systems in fostering the development of students' sense of theorems. Examples will be presented drawn from teaching experiments involving 9th and 10th grade students, illustrating how semiotic potential may unfold in the solution of specific tasks. The didactical focus consists in exploiting the semiotic potential of a DGS, especially the use of Cabri tools and particular dragging modalities that may function as tools of semiotic mediation.