Three studies were conducted in order to determine the source and frequency of children's difficulties in subtraction and to examine different approaches to remediation. In the first study, third-grade children were asked to solve subtraction problems and were observed and questioned about their solution processes. Children who had difficulty either attempted to borrow incorrectly or made inversion errors. The second study examined the efficacy of two minimally intrusive methods of remediation. Third-grade children were given either instructions to borrow, promised rewards for accurate performance or no intervention and were asked to solve a series of subtraction problems requiring borrowing. Neither experimental condition resulted in a significant increase in the number of problems solved correctly, and error patterns again indicated that children had difficulty with the borrowing process. In the third study, third- and fourth-grade children were assigned to one of three conditions: training in the component skills required for borrowing; feedback in the form of correctly worked solutions; or a regular classroom control condition. Both treatment conditions resulted in a significant increase in the number of problems solved correctly, and these increases were accompanied by a reduction of errors in the borrowing process. (Author)