This study is a collaborative project between university researchers and museum practitioners investigating ways to advance STEM learning opportunities for young children and their families in museums. The focus of the work is on how the knowledge resources that are available to families (e.g., prior knowledge, information provided by the museum staff) can support talk about STEM during and after hands-on problem-solving activities in a museum exhibit. More specifically, we asked whether and how associations between parent–child talk about STEM during tinkering, and the STEM content of the children’s reflections on their learning afterward, might vary based on the knowledge that is available to families to make sense of their experiences. One hundred and eleven families with 5- to 10-year-old children (M = 7.23 years) were observed in a tinkering exhibit in a children’s museum. Results indicated that the more parents and children talked about STEM during tinkering, the more the children talked about STEM in their reflections. This association was moderated by children’s knowledge based on prior tinkering experiences, and knowledge that was acquired through a pre-tinkering, facilitated orientation by museum staff about engineering, but not by children’s age or parents’ educational attainment. Implications for museum research and practice are discussed.