Learning with the logic of inquiry: game-activities inside Dynamic Geometry Environments

The paper describes a game-activity proposed to 7 th grade students with the goal to make them discover the geometric property concerning the mutual relationship between two circles. The activity, called "the game of the two circles" , is composed of a strategic game that students play in GeoGebra and an investigative task which requires conjecturing and generalization. The aim of the activity is to trigger an approach to mathematics based on the logic of inquiry. We analyse students' dialogues and actions paying particular attention to the additional values the game confers to the more traditional exploratory activities with dynamic geometry software.