An orchestra of mathematical instruments. Mathematical machines, dynamic geometry software and interactive multimedia whiteboards in middle school

Abstract

This article describes the intentional use of multiple instruments (instrumental orchestration) such as a pantograph, a dynamic geometry software and an interactive whiteboard (IWB), for introducing 7th grade students to the idea of axial symmetry as one-to-one correspondence between points in the plane, overcoming the naïve concept one of figures transformation. The chosen frame of reference is the theory of semiotic mediation (Bartolini Bussi & Mariotti, 2009) and its didactical structure: small group activity with artifact, individual activity and class discussion. Moreover, the instrumental approach (Rabardel, 1995) based on the distinction between artifact and instrument has been taken into account. The IWB has been used as an action place (Didoni & Di Palma, 2009) in order to show individual actions to the whole class.