A theory of how people learn certain procedural skills is presented. It is based on the idea that the teaching and learning that goes on in a classroom is like an ordinary conversation. The speaker (teacher) compresses a non-linear knowledge structure (the target procedure) into a linear sequence of utterances (lessons). The listener (student) constructs a knowledge structure (the learned procedure) from the utterance sequence (lesson sequence). Speakers unknowingly obey certain constraints, called felicity conditions or conversational postulates, which help listeners construct an appropriate knowledge structure. This research has shown that there are felicity conditions on lesson sequences that help students learn procedures. Three felicity conditions were discovered, forming the central hypotheses in the learning theory, which was embedded in a model, a large computer program using artificial intelligence (AI) techniques. The model's performance was compared to data from several thousand students learning to subtract multidigit numbers, add fractions, and solve simple algebraic equations. A key criterion for the theory is that the set of procedures that the model "learns" should exactly match the set of procedures that students actually acquire. Both testing the predictions and arguing for the validity of the theory are included in the report. (Author/MNS)