The research described here explores the idea of using Supreme Court oral arguments as pedagogical examples in first year classes to help students learn the role of hypothetical reasoning in law. The article presents examples of patterns of reasoning with hypotheticals in appellate legal argument and in the legal classroom and a process model of hypothetical reasoning that relates them to work in cognitive science and Artificial Intelligence. The process model describes the relationships between an advocate’s proposed test for deciding a case or issue, the facts of the hypothetical and of the case to be decided, and the often conflicting legal principles and policies underlying the issue. The process model of hypothetical reasoning has been partially implemented in a computerized teaching environment, LARGO (“Legal ARgument Graph Observer”) that helps students identify, analyze, and reflect on episodes of hypothetical reasoning in oral argument transcripts. Using LARGO, students reconstruct examples of hypothetical reasoning in the oral arguments by representing them in simple diagrams that focus students on the proposed test, the hypothetical challenge to the test, and the responses to the challenge. The program analyzes the diagrams and provides feedback to help students complete the diagrams and reflect on the significance of the hypothetical reasoning in the argument. The article reports the results of experiments evaluating instruction of first year law students at the University of Pittsburgh using the LARGO program as applied to Supreme Court personal jurisdiction cases. The learning results so far have been mixed. Instruction with LARGO has been shown to help law student volunteers with lower LSAT scores learn skills and knowledge regarding hypothetical reasoning better than a text-based approach, but not when the students were required to participate. On the other hand, the diagrams students produce with LARGO have been shown to have some diagnostic value, distinguishing among law students on the basis of LSAT scores, posttest performance, and years in law school. This lends support to the underlying model of hypothetical argument and suggests using LARGO as a pedagogically diagnostic tool.