The role of short-term working memory in mental arithmetic

Abstract

A series of experiments explored the role of information storage in working memory in performing mental arithmetic. Experiment 1 assessed the strategies people report for solving auditorily presented multidigit problems such as 325 + 46. As expected, all subjects reported breaking down the problems into a series of elementary stages, though there were considerable individual differences with regard to the order of their execution. Strategies of this type necessitate both the temporary storage of information and the mobilization of long-term knowledge. Experiments 2 and 3 examined the effects of delaying the output of individual partial results on calculation accuracy and showed that interim information is forgotten if it is not utilized immediately. Experiment 4 showed that forgetting the initial information is also a source of error and suggested that forgetting increases as a function of the number of calculation stages intervening between initial presentation and subsequent utilization of information. Two simple quantitative models were derived from a general task analysis, one of which assumed a decay process in working storage and the other no decay. The decay model gave a reasonable fit to data from Experiments 2–4, and in doing so it coped appreciably well with the effects of a large variety of task variables (e.g., carrying, the provision of written notes, calculation strategy, output order). The decay model is a tractable analysis of a complex task, and it is suggested that similar analyses may prove fruitful for other problem-solving activities which involve the use of working memory.