A comparison of self-instructional checking procedures for remediating mathematical deficits

We examined the relative effectiveness of three procedures for teaching long multiplication/division to seven adolescents with learning disabilities: no-checking, end-checking, and multi-checking. During training, each subject was taught by modelling and imitation to verbalize self-instructions in the form of a strategy while solving the problems. The relative effects of the checking and no-checking procedures on accuracy and rate of problems completed were examined in an alternating treatments design. The best treatment was then given alone and a reversal was implemented six weeks later, followed by a return to the best treatment during a final phase. Irrespective of the procedure used, the subjects' accuracy improved while the rate of problems completed decreased. These effects were greatest with the multi-checking procedure for six of the seven subjects. Generalization to untaught problems of various levels of complexity occurred under all procedures. Though maintenance effects were seen during the follow-up, accuracy was generally higher and more reliable when the subject's best checking procedure was reinstated. It is suggested that error detection and correction were important for maintaining high levels of accuracy and that these operated differentially in the three procedures to produce the differing levels of accuracy. The role of other factors such as pre-skill knowledge, complexity of the problem and prior reinforcement history are also considered.