For learning to take place in digital learning environments, learners need to use educational software – more or less – as intended. However, previous studies show that some school children, instead of trying to learn and master a skill, choose to systematically exploit or outsmart the system to gain progress. But what about preschoolers? The present study explores the presence of this kind of behavioral patterns among preschoolers who use a teachable agent-based play-&-learn game in early math. We analyzed behavioral data logs together with interviews and observations. We also analyzed action patterns deviating from the pedagogical design intentions in terms of non-harmful gaming, harmful gaming, and wheel-spinning. Our results reveal that even if pedagogically not intended use of the game did occur, harmful gaming was rare. Interestingly, the results also indicate an unexpected awareness in children of what it means to learn and to teach. Finally, we present a series of possible adjustments of the used software in order to decrease gaming-like behavior or strategies that signalize insufficient skills or poor learning.