In this paper, we describe an educational activity involving the use of a digital artifact, implemented in a visual programming environment, for mediating the learning of axial symmetry in primary school through algorithmics and computer programming. The educational activity was designed with the aim of bringing out increasingly "advanced" utilization schemes and solving strategies by students. We use an instrumental approach for analyzing how the systematic and intentional choice of technological artifacts and tools, i.e. the instrumental orchestration, guided instrumental genesis by the students. The analysis of the case study of Arianna seems to show how her evolution of utilization schemes is related both to the emergence of increasingly time and effort efficient strategies and to a growing understanding of the functionality of the visual programming environment.