The study investigated arithmetic achievement and attitude changes of five institutionalized emotionally disturbed children, age 7 to 11 years. The children participated in a diagnostic teaching program involving diagnosis of mathematics skills and instruction based upon the diagnosis. Emphasized were mathematical patterns, manipulation of physical objects, and problem solving understanding of mathematical actions. A hierarchy of behaviorally defined skills for addition and subtraction was developed. A diagnostic achievement test required Ss to manipulate objects illustrating number sentences, write number sentences describing actions performed on objects by tester, and solve paper and pencil problems. Ss received an average of 38 days of approximately 25-minute instructional periods. At the study's conclusion, both the diagnostic achievement test and a semantic differential attitude scale were administered to the Ss. An educational case study format was adopted as the most feasible method of studying a small number of emotionally disturbed children. At the study's beginning, Bart and David lacked mastery of many tasks concerning addition and subtraction and expressed negative attitudes toward mathematics; both their mathematical skills and attitudes showed improvement. Karen, Cinthia, and Michael also showed skill and attitude improvement. (CB)