Play is critical for children's learning, but there is significant disagreement over whether and how parents should guide children's play. The objective of the current study was to examine how parent-child interaction affected children's engagement and problem-solving behaviors when challenged with similar tasks. Parents and 4- to 7-year-old children in the U.S. (N = 111 dyads) played together at an interactive electric circuit exhibit in a children's museum. We examined how parents and children set and accomplished goals while playing with the exhibit materials. Children then participated in a set of challenges that involved completing increasingly difficult circuits. Children whose parents set goals for their interactions showed less engagement with the challenge task (choosing to attempt fewer challenges), and children whose parents were more active in completing the circuits while families played with the exhibit subsequently completed fewer challenges on their own. We discuss these results in light of broader findings on the role of parent-child interaction in museum settings.