Classical test theory, item response theory, and generalizability theory all treat the abilities to be measured as continuous variables, and the items of a test as independent probes of underlying continua. These models are well-suited to measuring the broad, diffuse traits of traditional differential psychology, but not for measuring the outcomes of school learning. Discrete latent structure models offer a powerful and promising alternative. Abilities can be modeled as partially ordered sets of discrete states (at a minimum, "nonmastery" and "mastery") and may be linked according to an asymmetric "prerequisite" relation. Narrower, simpler abilities may be combined into broader, more complex abilities. The various possible outcomes of performing a task can be modeled as a partially ordered set of task performance states. Abilities and task performances are clearly distinguished from one another, and more than one ability pattern may permit successful performance of a given task. Subtasks need not be modeled as conditionally independent given ability. The mapping from ability states to task performance states shows clearly what a given test can and cannot measure, and what may be inferred from a given pattern of test performance. These models for ability and task performance, together with the mapping between them, may be augmented with a suitable model for measurement error (misclassification) to complete an alternative framework for scoring, analyzing, and interpreting test performance. This framework has the potential to solve significant measurement problems inherent in performance testing and other applications. (Contains 12 figures.) (Author/SLD)