Abstract
Using the game to teach mathematics to pupils became increasingly an obvious standard pedagogical practice in the scholastic institution. This generic term also reflects very different implementations that do not result in the same experience according to pupils. The objective of our work is to explore some of these practices and to determine the conditions in order for the pupils to play and develop mathematical competence during the same learning sequence. In the first instance, we are trying to define the activities that can be in-class games, keeping in mind that the school environment strongly and negatively influences the ability to experience real playing periods. We suggest a characterisation of these activities from four conceptual tools: the game (the structure of the game), the play (the game attitude), the playful potential and the learning potential. Then, we will draw two main conditions of in-class use of games: the “gameifying” of a didactic situation or the exploitation of an existing game. Assuming that the second possibility is more likely to lead to a gaming attitude for pupils, we are designing a learning sequence based on the strategy board game “go” in a junior division classroom at an elementary school, in order to study mathematical learning impacts. To do so, we are introducing a method of game analysis that, applied to Go, can extract two important learning potentials: the heuristic argumentation (Duval, 1992) for problem-solving and the sequential apprehension of figures (Duval, 1994) for geometry. This analysis method is implemented as part of the current constraints of the scholastic institution. The sequence, made of ten sessions, is implemented by experimenter teachers who are not Go specialists. We will then analyse the actual sequence in order to determine if the pupils have experienced gaming periods according to their own game understanding and if mathematical learning has emerged. We ultimately ask the question: how these skills, built as part of the Go game, have been deployed in other mathematical fields? From this experimentation, we want to clear the conditions and constraints of a boarding game implementation at the elementary school.