Many national curricula at all grades suggest involving students in the manipulation of (real or virtual) materials. The current great diffusion of ICT in all aspects of everyday life pushes towards a massive use of such tools in the school. Their practices introduce an “experimental” dimension into mathematics, as well as a dynamic tension between the empirical nature of activities with them, which encompasses perceptual and operational components, and the deductive nature of the discipline, which entails a rigorous and sophisticated formalization. The talk illustrates the pedagogical possibilities offered by the tension between these two aspects when ICT are introduced into the classroom. Some short video clips from the classroom life make palpable this dynamic tension.