Simulation games for learning geometry are learning environments purposely designed, and are being experimented within a research project, that has been demonstrating their effectiveness. They offer a different learning and teaching system, that opens interesting spaces to be explored relating the role of the conductor and the implications for teacher’s training. The paper presents the theoretical and methodological aspects used as a basis to design the simulation games within a research project Similandia and describes their procedural architecture. On the basis of their specificity, it sketches the role of the conductor and analyses the principal functions of the leading for each phase. Task-oriented and relationship-oriented leadership are kept strictly integrated.