This study investigated how preschool children processed and understood critical information in Magical Garden, a teachable agent-based play-&-learn game targeting early math. We analyzed 36 children's (ages 4-6 years) real-time behavior during game-use to explore whether children: (i) processed the information meant to support number sense development; (ii) showed an understanding of the teachable agent as an entity with agency. An important methodological goal was to go beyond observable behavior and shed some light on how cognitive processing and understanding in children of such young age can be studied. First, the children played Magical Garden for three weeks to get acquainted with the game. Second, in an experimental part of the study, the children's gaze behaviors were measured during 5 rounds of interaction with an experimental version of one of the sub-games. The analyses suggest that two of the gaze behaviors were positively correlated with the game performance measure, as hypothesized. Another result was that children looked at the teachable agent significantly more often when the teachable agent had been in charge of gameplay than when it had not. This can be interpreted as an indication that the children had an understanding of their teachable agent as an entity that, like themselves and unlike other dynamic visual elements in the game, made decisions based on own 'knowledge'. In a broader context, the findings are important in showing the potential gains of combining log data with eye-tracking data for developing and refining AI algorithms for adaptive individual feedback and scaffolding.

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