This study consisted of two experiments. Experiment 1 was designed to examine the effects of the transfer and reinforcement contingency on addition performance in retarded and non-retarded children. Eighty-eight retarded children selected from special classes, and 88 non-retarded children, selected from regular classes, both in elementary school level in Taipei City, participated in the experiment. A 2(IQ) ×2(transfer model) × 2(reinforcement) factorial design was used.　 　　Experiment 2 was particularly designed to instruct the 15 retarded subjects who did not obtain any gains during Experiment 1, with emphasis on systematic intervention of computational tasks and instructional strategies as a means of helping individual retarded children acquire some level of addition skills. An ABA reversal design was used in this experiment. Each subject participated in the experiment for 10 to 13 weeks according to his performance. The major findings of the study were as follows: 1) The transfer effects either forward (A→B model) or Backward (B→A model) had occurred for both retarded and non-retarded children. 2) There were significant differences between A→B and B→A groups, with B→A taking more high Percentage Correct and Correct Rate in every condition. 3) The reinforcement contingencies facilitated a larger amount of transfer than did the no reinforcement contingencies. 4) A single model of instructional strategy was not approprate in teaching all levels of retarded children to acquire the computational skills.