The purpose of this study was to test several hypotheses from self-efficacy theory in the area of children's arithmetic achievement. Fifty-six elementary school children showing low arithmetic achievement were assigned to one of four treatment groups of 12 subjects each (modeling-attribution, modeling-no attribution, didactic-attribution, didactic-no attribution) or to a nontreated control group of 8 subjects. In the cognitive-modeling treatment, children observed as an adult verbalized aloud the solution strategies to division problems contained in the explanatory pages of their packet. In the didactic treatment, children studied the same explanatory pages on their own, after which they worked the practice problems. For children assigned to the modeling-attribution and didactic-attribution conditions, the trainer attributed their successes to high effort and their difficulties to low effort on the average of once every 5 minutes during the practice phase of each of the training sessions. Results showed that both instructional treatments enhanced division persistence, accuracy, and perceived efficacy, but cognitive modeling was more effective in promoting skill development. In the context of competency development, effort attribution had no significant effect either on perceived efficacy or on arithmetic performance. Perceived efficacy was an accurate predictor of arithmetic performance across levels of task difficulty and modes of treatment. The treatment combining modeling with effort attribution produced the highest agreement between efficacy judgment and performance. (Author/JMB)