Synergy between manipulative and digital artefacts: a teaching experiment on axial symmetry at primary school

This paper presents a study aimed at investigating the didactic poten- tiality of the combined use of two di erent kinds of artefacts for the purpose of constructing and conceptualizing mathematical mean- ings related to the notion of axial symmetry. In our view, the process of meanings construction can be fostered by the use of adequate artefacts, but it requires a teaching/learning model, which explic- itly takes care of the evolution of meanings, from those personal, emerging through the activities, to the mathematical ones, aims of the teaching intervention. The main hypothesis of this study is that a potential synergy may occur between the use of di erent arte- facts, synergy that can foster the integration of di erent and comple- mentary meanings providing a rich support to the development of the expected mathematical meaning. The Theory of Semiotic Media- tion o ers the theoretical framework suitable to design the teaching sequence and to analyze the collected data. Speci cally, the construct of semiotic potential provides the tool for describing the potentiali- ties of the two artefacts, while that of didactic cycle o ers a model for the organization of the di erent activities. The paper reports on a teaching sequence and its implementation in a teaching experi- ment, involving pupils at fourth grade level. We describe them, within the chosen theoretical framework, and provide the analysis of key episodes of the teaching sequence. We show evidence supporting our main hypothesis about the combined use of an artefact that can be manipulated (paper and pin), and a digital artefact (Dynamic Geometry Environment) in the development of the notion of axial symmetry and its properties: the combined, intentional and con- trolled use of the two artefacts may develop a synergy, so that each activity enhances the potential of the other.