Working memory demands of exact and approximate addition

Abstract

We compared the working memory requirements of two forms of mental addition: exact calculation (e.g., 63 + 49 = 112) and approximation (e.g., 63 + 49 is about 110). In two experiments, participants solved two-digit addition problems (e.g., 63 + 49) alone and in combination with a working memory task (i.e., remembering four consonants). In Experiment 1, participants chose an answer from two alternatives (e.g., exact: 112 vs. 122; approximate: 110 vs. 140). In Experiment 2, participants responded verbally with exact or approximate answers. In both experiments, the working memory load impaired exact and approximate addition performance, but exact addition was affected more. Load also impaired performance on problems with a carry operation in the units (e.g., 28 + 59 or 76 + 57) more than on problems without a unit carry (e.g., 24 + 53 or 76 + 52). These results identify the carry operation as the source of the working memory demands in multidigit addition.

This research was funded by the Natural Sciences and Engineering Research Council of Canada through a PGS-A scholarship to DK and a Discovery Grant to JL. We thank the Mathematical Cognition group at Carleton University and Diana DeStefano for their helpful comments on earlier versions of this work. DK is also grateful to Katherine Arbuthnott for her contributions to research that preceded the work reported in this paper. A version of these results were presented at the annual meeting of the Canadian Society for Brain, Behaviour, and Cognitive Science, St. John's, Newfoundland, June 2004.