A central assumption within the embodied cognition paradigm is that particular action experiences are instrumental in providing children with sensorimotor contingencies that form the foundation for conceptualisation of and, later, communication of mathematical ideas. Digital technology designs that foster specific movements offer promising foundations for young children's mathematical learning, together with haptic technologies that newly bring tactile sensorimotor experiences for children to draw on. This article reports on a qualitative study examining the role of a haptic learning environment supporting 7-8-year-old children's embodied exploration of 3D shape. It examined the in situ dynamic unfolding of interaction of pairs of children, as they engaged with a haptic device. Multimodal analysis was focused on the process of how the prescribed enaction of the device-mediated interaction, the kinds of action experiences and action schemes it elicited and the strategies children collaboratively developed to complete tasks. Findings show how specific action experiences and, later, communication experiences, were shaped, not only by the prescribed enaction of the design, but also by embodied participatory sense-making, and demonstrate the potential for haptic technology in mediating new learning experiences for mathematics.