The article presents a model of understanding that takes into account interaction, cultural knowledge, and the constraints of organizations and institutions. It analyzes discourse and cognition in high school biology classes and clinical consultations involving discussions of genetics. The analytical lenses of constraint satisfaction, coherence-based reasoning, and collective cognition reveal multilayered social, cultural, and interactional components of authority and agency that influence understanding. The analysis reveals similarities across settings in discourse structure and the ways that participants relate to local constraints. (...) In both types of settings, participants attempt to develop process narratives that present a sequential or causal relationship between information and lead to remembered understandings of concepts. However, the absence of certain process information that links terms or concepts functions like a missing plot point in a story, hindering the development of process narratives and understandings. In order to cover such information gaps, students and patients construct and display grey boxes. In addition to talk and text, these consist of various actions and resources specific to a local discourse framework such as pointing at graphics, tabular information, and symbols. Grey boxes satisfy the organizational constraints of time, resources, and task structure that affect interaction related to understanding concepts and procedures, but their connection to a particular discourse framework restricts the transfer of knowledge between settings. The power of medical practitioners and teachers to enhance or restrict understandings relates to the ways that they accommodate the use of grey boxes during interactions with clients and students. Professional frames of reference that teachers or practitioners apply to task interactions may constrain the ways students or clients apply grey boxes and process narratives. Awareness of the functions of process narratives and grey boxes presents opportunities to modify local discourse frameworks and increase understandings of concepts, medical conditions, and treatment options. (shrink)