Informal learning environments such as science centers and museums are instrumental in the promotion of science, technology, engineering, and mathematics (STEM) education. These settings provide children with the chance to engage in self-directed activities that can create lifelong interest and persistence in STEM. In addition, the participation of parents in these settings can engage children in conversations that can boost understanding and enhance learning of STEM topics. To date, a considerable amount of research has focused on adult-child dialogue. Findings from those studies revealed that children experience more elaborate scientific thinking when parents facilitate learning. Given the need for engineers to have computer science skills, academic discourse has placed emphasis on studying computational thinking (CT) in children. While some recent studies have focused on the roles parents play to promote children's engineering thinking, very few studies have explored parents' influence on children's engagement in CT. Therefore, in this study, we investigate the roles that parents play in promoting computational thinking in their young children. In this study, families of 5-7 year-old children were invited to a science center. The families were asked to interact with an exhibit, “Computing for the Critters,” that was designed to promote engineering and computational thinking in children. We conducted a qualitative case study to closely examine child-parent interactions during one portion of the exhibit that is a computer-based coding game. Drawing on previous literature from engineering education and informal science education, a coding scheme was developed with the essential roles that parents play in science centers and museums. The roles include Supervising, Co-learning, Facilitating, Encouragement and Student of the Child. In this study, we have observed that parents take multiple roles in which some of them resulted in children's enactment of CTs. The findings of this study advance our understanding of how parents can support computational thinking while engaging in conversations during engineering activities.