Gaming the system: An opportunity to analyse difficulties in arithmetical problem solving

International audienceGaming the system is a behaviour that must be avoided when interactive learning environments are designed. However, from the point of view of the research in mathematics education, the observation of this behaviour may bring to light the students' knowledge. In this paper, we provide results of a study in which primary education students (10–11 years old), grouped in pairs, solved problems in an arithmetical way using an intelligent tutoring system. We analyse cases in which the students were able to refine a fuzzy idea of how to calculate a quantity based on the belief that they necessarily had to use certain quantities, operations or conceptual schemes. We also provide examples of how sometimes such students' certainties can become obstacles