The purpose of this study was to investigate the effects of coopreative learning instructional strategy on the achievement. Subjects of the study consisted of 209 four grade of elementary school boys and girls. Independent variables were the four types of learning, which was cooperative learning with reward, cooperative learning without reward, competitive learning with reward, and competitive learning without reward. Dependent vatiable was mathematic achievement that was used to experimental materials. ANOVA method was applied to analyze the data. The major findings were as follows : 1) There was no difference learning effects between type of cooperative learning and that of competitive learning on mathematics achievement in fourth grade of elementary school. 2) There was no difference learning effects between cooperative incentive structure and cooperative task structure on the achievement. There was no interaction effects between cooperative, competitive learning and incentive task structure. 3) There was no interaction effects between the ability level of learner and the types of cooperative and competitive. 4) There was no interaction effect between sex difference of learners and types of cooperative and competitive learning. 5) There was interaction effects between sex difference and reward structure. That is, more high achievement was shown in girls in cooperative incentive structure, whereas, more high achievement was shown in boys in competitive or cooperative task structure.