This article gives a comprehensive description of a theory for efficient assessment of knowledge. The essential concept is that the knowledge state of a subject, with regard to a specified field of information, can be represented by a particular subset of problems that the subject is capable of solving. (SLD)

A three-level multivariate statistical modeling strategy is presented that resolves the question of whether the unit of analysis should be the teacher or the student. A reanalysis of U.S. high school data (51 Catholic and 59 public schools from the High School and Beyond survey) illustrates the model. (SLD)