Abstract
In Chapter 6, we analyzed didactic phenomena occurring during experiments in integrating symbolic calculators. We then showed how adopting an instrumental approach to analyzing these phenomena helped in understanding the influence of such tools upon mathematical activity and upon knowledge building. It is during the process of instrumental genesis that a calculator becomes a mathematical instrument.In the first part of this chapter, we analyze the different forms that instrumental genesis takes by studying students’ behavior so as to establish a typology of work methods in calculator environments. This typology indicates that the more complex the environment, the more diverse the work methods, and, consequently, the more necessary the intervention of the teacher in order to assist instrumental genesis.In the second part of this chapter, taking this necessity into account, we introduce the notion of instrumental orchestration, defined by a didactical configuration and its modes of exploitation.An orchestration is part of a scenario for didactical exploitation which aims to build, for every student and for the class as a whole, coherent systems of instruments.