This paper contributes to the existing body of knowledge on the co-design of novel technologies with children. As part of a three year research project aiming to design and develop a robot tutee for use in mathematics education, we present the initial phases of our design approach with children, in which we draw on principles of Participatory Design and Co-design. As part of the early stages of this process, we included a demystifying phase (I), and a gradual introduction to the robot’s capabilities (II), in order to foster reasonable expectations in children and gather feasible design input. Drawing on the Time-Space-Structure framework, two primary schools were involved in the co-design process, where children in grades 2 and 4 participated in a set of workshops. We discuss the benefits and tensions of our approach, and reflect on its implications for mutual learning, hoping to inspire further exploration in this field.