The authors examine current textbook representations of Coase's analysis of negative externalities [Coase, 1960]. Standard treatments identify Coase's ideas with Stigler's Coase Theorem: a zero transaction cost world in which efficient solutions emerge automatically, regardless of legal rules and the initial allocation of rights. Yet Coase's seminal paper breaks from this mode of analysis. The authors use this intellectual history to distinguish two approaches to negative externalities: blackboard (Pigou, Stigler, Samuelson) and Coasean. They survey 45 microeconomics textbooks and find that 80 percent misrepresent Coase's arguments. They argue that a Coasean approach increases students' critical thinking skills by challenging them to move beyond simple laissez faire or interventionist solutions.