Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what constitutes a complete, satisfactory solution to a modeling problem--has a shaping influence on its members' participation in modeling activities. Devising a means of assessing classroom modeling cultures is thus a crucial task for both research and praxis. In this article, we present an approach to operationally defining and assessing classroom modeling cultures, which is (a) based in quantitative analyses of discourse during whole-class presentations of modeling solutions, and (b) grounded in research in individual modeling competencies. We show how our assessment distinguishes the classroom modeling cultures of different classrooms and how it captures shifts over time in the modeling culture of a given classroom. Finally, we accompany our quantitative results with interpretive analyses of presentation discourse, to triangulate and to attribute meaning to the patterns our assessment detects. Our primary data sources include video recorded presentation and Q&A sessions for three modeling activities in each of two US middle school (Grades 5-8) classrooms. Our assessment approach is a significant contribution because it operationalizes the construct of a classroom's modeling culture, in terms that highlight potential connections with the research literature of individual modeling competencies. It therefore invites modeling research that coordinates learning and development across individual and social levels.