Young Children's Mental Arithmetic Errors: A Working-Memory Analysis

Abstract

BRAINERD, CHARLES J. Young Children's Mental Arithmetic Errors: A Working-Memory Analysis. CHILD DEVELOPMENT, 1983, 54, 812-830. A stochastic model is presented that seeks to distinguish mental arithmetic errors that are caused by failures in arithmetical processing from mental arithmetic errors that are caused by either failures to retain the essential problem infonnation in short-term storage or failures to retrieve this information at appropriate times. In Experiments I and 2, questions of goodness of fit and model validity were studied by administering probed arithmetic items to 4and 5-year-olds. It was found that the ordinal relationships among certain joint probabilities were in line with the model's predictions (i.e., there was statistical evidence of goodness of fit), and the model's parameters reacted in appropriate ways to manipulations designed to affect the rates of processing failure and short-term memory failure, respectively. In Experiments 3 and 4, the model was used to measure the relative contributions of decreases in the failure rate for processing and the failure rate for short-term memory to age changes in mental arithmetic during early elementary school. During this age range, it appeared that improvements in short-term memory functioning were more important sources of developmental changes in arithmetic performance than were improvements in the accuracy of arithmetical processing.