  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.
