The Temporal Dynamics of Information Flow in Working Memory when Executing a Mental Algorithm: the Case of Multi-Digit Arithmetic

The importance of working memory (WM) in executing mental algorithms is well-established in cognitive theories and empirical evidence. However, many of the precise ways in which WM operates during a mental algorithm are still poorly understood. Here, we used the classical example of mental arithmetic to examine how information is managed in WM during the algorithm execution. Participants added, in their head, pairs of two-digit numbers with a decade crossing either at the decades (82+74) or at the units (28+47). They used either of two 3-stage algorithms: [1] add the decades, [2] add the units, [3] merge their sums (20+40; 8+7; 60+15=75); or [1] add-units, [2] add-decades, [3] merge. Addition (stages 1-2) was harder when the sum of the two digits exceeded 10, a situation that increases the WM demands. Importantly, this decade crossing effect was larger in stage 1 than in stage 2. We conclude that the addends of stage-1 were removed from WM once this stage was completed and they were no longer needed; this reduced the WM load in stage 2, leading to better performance. Additionally, the performance in stage 3 (merge) was modulated by the order of the preceding stages (1-2): stage 3 was faster in the decades-then-units case than in the units-then-decades case. We conclude that WM stores data (the decade and unit sums) in an ordered manner by default, even when this is not needed for the task. We discuss the importance of WM management processes, of the kind shown here, for mental algorithms.