Simple mental addition in children with and without mild mental retardation.

The speeded performance on simple mental addition problems of 6- and 7-year-old children with and without mild mental retardation is modeled from a person perspective and an item perspective. On the person side, it was found that a single cognitive dimension spanned the performance differences between the two ability groups. However, a discontinuity, or "jump," was observed in the performance of the normal ability group on the easier items. On the item side, the addition problems were almost perfectly ordered in difficulty according to their problem size. Differences in difficulty were explained by factors related to the difficulty of executing nonretrieval strategies. All findings were interpreted within the framework of Siegler's (e.g., R. S. Siegler & C. Shipley, 1995) model of children's strategy choices in arithmetic. Models from item response theory were used to test the hypotheses.