The theoretical and methodological tools provided by the first generation of activity theory have been expanded in recent decades by the French community of cognitive ergonomists, followed by a sub-community of researchers working in the didactics of mathematics. The main features are, first, the distinction between tasks and activity and, second, the dialectic between the subject of the activity and the situation within which this activity takes place. The core of the theory is the twofold regulatory loop that reflects both the codetermination of the activity by the subject and by the situation and the developmental dimension of the subject's activity. This individual and cognitive understanding of activity theory mixes aspects of Piaget's and Vygotsky's frameworks. In this paper, it is first explored in association with a methodology for analysing students' mathematical activities. We then present findings that help to understand the complexity of student mathematical activities when working with technology.