Two experiments investigated the extent to which children's mental arithmetic is constrained by working memory rather than their arithmetical competence. A span procedure was used to measure the limit on English- and German-speaking children's ability to add together pairs of multidigit numbers. The children's ages ranged from 7 years 7 months to 11 years 5 months. Spans for mental addition were higher when the numbers to be added were visible throughout calculation than when they were not, consistent with a working memory constraint. Variation in addition span with children's age and with difficulty of the arithmetical operations approximated to a linear function of the speed of adding integers. A similar speed/span relationship has previously been observed for counting span, an artificial task designed to load working memory by combining separate processing and storage subtasks. We conclude that the natural task of mental addition, which combines processing and storage as intrinsic components, reflects working memory in a similar way. Results were remarkably similar both between cultures and across age groups, consistent with the notion of working memory as a general-purpose resource with dynamics that are indifferent to the detailed nature of operations.

Copyright 1997 Academic Press.