An understanding-based approach to teaching arithmetic word problems is used in the Training Arithmetic Problem Solving Skills (TAPS) research project, for which four semantic schemas or problem representations have been revised and adopted: Combine, Compare, Change, and Vary. It is hypothesized that a good problem solver identifies the schema of the problem, instantiates the slots with problem information, verifies the schema identification, executes the appropriate procedural attachment to generate the numerical answer, and checks to see whether the solution is appropriate. In the case of a complex problem, the problem solver also has to recognize the goal of the problem and use memory-management skills to store and retrieve information as required in the solution process. Researchers plan to teach these skills explicitly in the TAPS instructional program, which is designed for use by elementary students who have reading and computational competencies, but perform poorly in solving word problems. An individualized curriculum will be developed for each student on the basis of a diagnostic test which will identify deficient skill areas, and the new skill will be introduced via direct didactic instruction and practiced without speed pressure. Performance will be further improved through intensive drill and practice monitored by an intelligent tutoring system. Seven references are listed. (MES)