The use of social robots as a tool for language learning has been studied quite extensively recently. Although their effectiveness and comparison with other technologies are well studied, the effects of the robot’s appearance and the interaction setting have received less attention. As educational robots are envisioned to appear in household or school environments, it is important to investigate how their designed persona or interaction dynamics affect learning outcomes. In such environments, children may do the activities together or alone or perform them in the presence of an adult or another child. In this regard, we have identified two novel factors to investigate: the robot’s perceived age (adult or child) and the number of learners interacting with the robot simultaneously (one or two). We designed an incidental word learning card game with the Furhat robot and ran a between-subject experiment with 75 middle school participants. We investigated the interactions and effects of children’s word learning outcomes, speech activity, and perception of the robot’s role. The results show that children who played alone with the robot had better word retention and anthropomorphized the robot more, compared to those who played in pairs. Furthermore, unlike previous findings from human-human interactions, children did not show different behaviors in the presence of a robot designed as an adult or a child. We discuss these factors in detail and make a novel contribution to the direct comparison of collaborative versus individual learning and the new concept of the robot’s age.