What metrics of participation balance predict outcomes of collaborative learning with a robot?

One of the keys to the success of collaborative learning is balanced participation by all learners, but this does not always happen naturally. Pedagogical robots have the potential to facilitate balance. However, it remains unclear what participation balance robots should aim at; various metrics have been proposed, but it is still an open question whether we should balance human participation in human-human interactions (HHI) or human-robot interactions (HRI) and whether we should consider robots' participation in collaborative learning involving multiple humans and a robot. This paper examines collaborative learning between a pair of students and a teachable robot that acts as a peer tutee to answer the aforementioned question. Through an exploratory study, we hypothesize which balance metrics in the literature and which portions of dialogues (including vs. excluding robots' participation and human participation in HHI vs. HRI) will better predict learning as a group. We test the hypotheses with another study and replicate them with automatically obtained units of participation to simulate the information available to robots when they adaptively fix imbalances in real-time. Finally, we discuss recommendations on which metrics learning science researchers should choose when trying to understand how to facilitate collaboration.