In this paper, we investigate children's learning of reflectional symmetry in a dynamic geometry environment. Through a classroom-based intervention involving two 1-h lessons, we analyse the changes in the children's thinking about reflectional symmetry: first, they developed dynamic and embodied ways of thinking about symmetry after working with a pre-constructed sketch called the "symmetry machine". Secondly, they moved from distinguishing symmetrical and asymmetrical figures statically to generalising about properties of symmetry. This was evident in the way children expressed symmetric movement through words, gestures and diagrams during the computer-based lessons as well as in the follow-up paper-and-pencil tasks. We highlight the specific roles of the teacher and of the digital technology in supporting the process of semiotic mediation through which the children learned symmetry.