The application of a linear learning model, which combines learning theory with a structural analysis of the exercises given to students, to an elementary mathematics curriculum is examined. Elementary arithmetic items taken by about 100 second-grade students on 26 weekly tests form the data base. Weekly predictions of group performance on addition items are made, based upon earlier observations. The model is tested by studying the accuracy of the predictions, by varying parameters of the model, and by comparing its predictions with those made from a regression analysis. The study indicates that the most important skill to consider in making predictions of performance on addition items is carrying. The skill of adding two digits made a much smaller contribution. (MP)