This study investigated the effects of the nature of the algorithm, reinforcement, and level of problem difficulty on the ability of fourth graders to solve addition problems as measured by the number of problems correctly solved and the number of columns attempted. Subjects were selected for high scores on a test of basic addition facts; only subjects with recorded scores on the Metropolitan Achievement Tests were included. Half of the subjects were trained on Hutchings'"low fatigue" addition algorithm, and the other half on the conventional algorithm. Subjects were then assigned to one of three reinforcement conditions for posttesting; posttests contained items of three difficulty levels. Data were submitted to an analysis of variance which revealed that subjects trained to use Hutchings' algorithm scored higher on both criteria. A significant effect for problem difficulty was also found. Inspection of the data revealed that the superiority of Hutchings' algorithm decreased as problems grew more difficult. Although there was no main effect for reinforcement, children receiving reinforcement after each column of addition seemed to have attempted fewer problems, and added fewer correctly, than those in the other reinforcement conditions. (SD)