The concept of engagement across the learning sciences and in museums draws from research on visitor interests, motivations, and behaviors. Such involvement by museum visitors reveals institutional and field expectations about museum efficacy and demonstrated impact. However, engagement is a concept with different uses and interpretations across institutions and fields. If we are going to talk about visitor engagement in museums specifically, it is incumbent on museum educators to understand and address the values that are associated with this idea. What does engagement look like and sound like in a museum's exhibitions, programs, and visitor studies? In this paper we present critical questions to frame a discussion on the assumptions, values and cautions that come with the concept of engagement in a museum setting. We present practical examples from research in a children's museum and discuss the implications of using engagement concepts in museum work. We argue that the ways in which museum staff observe and measure visitor behaviors are guided by assumptions and values, institutional goals and values, and the visitor's assumptions and values. Understanding learning sciences research can aid in the articulation of what visitor engagement looks like for an institution. (Contains 10 notes.)