Limit as a challenge: understanding the formal definition through an inquiry-game activity

In this paper we present a teaching experiment centred on the concept of limit. It involved a class of grade-12 students, who worked on inquiry-game activities aimed at promoting the understanding of the formal ε-δ definition of limit for real functions. These activities were designed by the authors basing on the Game Theory Logic by Hintikka and involved two players, Mr. Epsilon and Mrs. Delta. One selected episode from the teaching experiment allows to investigate how a pair of students makes sense of the (logical and dynamical) relationships between ε and δ by playing the game: the analysis of their gestures and utterances reveals the complex evolution of their conceptualisation processes.