The purposes of the study were to investigate the effects of the combination of a trained teacher and a planned program on the problem solving abilities of mentally handicapped children, to develop measures of verbal problem solving (IDES) and arithmetic understanding (PUT), and to analyze the interrelationships among primary mental abilities and various combinations of achievement tests. A teacher training workshop presented for 10 evenings focused on the organization and use of 86 lessons in nine units for 18 weeks. Teaching methods concentrated on developing understanding through the solution of problems which originated in the classroom. Trained teachers used the prepared program with 161 retarded children; untrained teachers used the program with 58 retarded children; and there were 132 retarded and 89 average-ability controls. The results showed that the IDES and the PUT appear to be stable and consistent measures of the arithmetic performance of mentally handicapped children, and that the teacher training program and the prepared program of arithmetic curriculum were effective. Measures of primary mental abilities and academic achievement were highly interrelated. The study supports the contention that problem solving and concept development among the mentally handicapped can be influenced by education. (LE)