Robotic learning environments may benefit if combined with intelligent tutoring technologies, but it is unclear how best to integrate the two types of systems. We explore this integration using a tangible teachable agent paradigm, where students teach a robot about geometry concepts. To identify potential design directions, we employ a user-centered method called Speed Dating, involving construction of several scenarios probing student needs, and then orchestration of user enactments of the scenarios. We found that students seek activities that provide them with an appropriate level of challenge, feelings of discovery, opportunity for physicality, and a sense of responsibility for the robot. We discuss the implications of these findings with respect to building a tangible teachable robot. By employing HCI methods underutilized in learning, we gain traction on an important research challenge in education technology.