An overview is presented of information processing analyses of knowledge and performance in three areas of the elementary mathematics curriculum. These include basic addition and subtraction facts, complex procedures such as multicolumn subtraction, and the solution of word problems. Theories are presented of the knowledge associated with “expert” performance. We show how such theories can be applied to practical problems such as the analysis of lower levels of expertise and the acquisition of skill. The emphasis is on diagnostic analysis of the knowledge underlying the less than expert performances exhibited by younger and/or less able children. Several specific research questions are identified. Answers to these questions should help provide a basis for understanding and effectively remediating the specific problems experienced by learning disabled children in elementary mathematics.
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