Abstract
Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM) as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc) could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults.
Highlights
Numerate societies demand that their members have numerical skills
In the easier type 2×1 and 3×1 problems, medium and high scoring group participants performed at the same level (Medium group: M2x1 = 0.925 and M3x1 = 0.878; High group: M2x1 = 0.963 and M 3x1 = 0.919), but the medium score participants were significantly worse than the high score group in calculating type 4x1 problems (Medium group: M = 0.725; High group: M = 0.850)
Discussion of Experiment 2 The results of Experiment 2 revealed that both MUSpace and MUcalc were the best predictors for the accuracy of the multidigit mental multiplication task (MMM), correlated with MMM, and with harder type 4x1 problems
Summary
Numerate societies demand that their members have numerical skills. Most previous studies have focused on simple arithmetic problems to understand how cognitive factors influence the acquisition of mathematical skills. We focus on multidigit rather than singledigit multiplication because it exemplifies a package of needed skills: understanding the number system and the principles of arithmetic, memory for the retrieval of multiplication facts, procedures for multiplying and adding, and the ability accurately to maintain and update information as needed by the task (e.g., Hunter, 1962; Baddeley and Hitch, 1977; Ericsson and Charness, 1994; Logie et al, 1994; Ericsson and Kintsch, 1995). Competence in this task can be seen as evidence of the possession of important numerical skills
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