The view of learning that underlies standard test theory is inconsistent with the view rapidly emerging from cognitive and educational psychology. Learners become more competent not simply by learning more facts and skills, but by reconfiguring their knowledge; by "chunking" information to reduce memory loads; and by developing strategies and models that help them discern when and how facts and skills are important. Neither classical test theory nor item response theory is designed to inform educational decisions conceived from this perspective. This paper sketches the outlines of a test theory built around models of student understanding, as inspired by the substance and the psychology of the domain of interest. The ideas are illustrated with a simple numerical example based on the balance beam tasks of R. S. Siegler. Directions in which the approach must be developed to be broadly useful in educational practice are discussed. An appendix gives equations for the latent class model. (Contains 2 tables, 8 figures, and 48 references.) (Author/SLD)