Identification and remediation of children's subtraction errors: A comparison of practical approaches

Three studies were conducted to determine the sources and frequency of children's subtraction errors and to examine four approaches to remediation. In Study 1, 56 third-grade children were asked to solve subtraction problems requiring borrowing (regrouping) and were questioned about their solution procedures. Ghildren who had difficulty either attempted to borrow incorrectly or made inversion errors. In Study 2, 80 third graders were promised rewards for correct solutions or were instructed to borrow on subtraction problems. Neither condition produced an increase in correct solutions, and instructions inflated incorrect attempts to borrow. In Study 3, 67 third-and fourth-grade children were assigned to one of three conditions: component skills for borrowing; feedback for performance; no training (control). Both treatment conditions resulted in a significant increase in the number of borrowing problems correctly solved, but neither condition produced a significant reduction in the number of computational, inversion, borrowing, or other errors. The results are discussed in terms of cost efficiency and constraints imposed by realities of today's classrooms. Future directions also are considered.