Task analysis as a tool in the design of instruction is the subject of this paper. Some of the major historical approaches (associationist/behaviorist, gestalt, and Piagetian) are described using examples from mathematics. The usefulness of these approaches to instructional design is evaluated on the basis of four criteria: instructional relevance, psychological formulation, instructability, and recognition of stages of competence. A detailed discussion of rational and empirical information-processing analyses for instructional purposes follows. It includes descriptions of empirical studies carried out to validate and elucidate formal and informal task analyses of mathematical skills, such as addition and subtraction, and generalized "learning-to-learn" abilities. (Author/JBW)