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) for executing mental algorithms is well-established, but several of the precise ways in which WM operates during mental algorithms are still poorly understood. Here, we show how a simple behavioral method can track, step by step, these WM processes. We used the classical example for a mental algorithm, multi-digit addition, to examine how information is handled in WM during the algorithm execution. Participants added, in their heads, pairs of two-digit numbers with a decade crossing either at the decades (82+74) or at the units (28+47). They used a three-stage algorithm: either [1] add the decades, [2] add the units, [3] merge their sums (20+40; 8+7; 60+15=75); or [1] add the units, [2] add the decades, [3] merge. We measured errors (Experiment 1) or reaction times (Experiment 2) in each stage. Addition (stages 1-2) was harder/slower when the sum of the two digits exceeded 10. Critically, this decade-crossing cost was higher when the crossing occurred in stage 1 than in stage 2. We conclude that the addends of stage 1 were removed from memory once this stage was completed and they were no longer needed, even before the algorithm ended; this reduced the memory load in stage 2, leading to a lower decade-crossing cost. The performance in stage 3 (merge) was faster in decades-then-units calculation than in units-then-decades calculation. We conclude that memory stored the interim results (decade and unit sums) as an ordered pair by default, although their order was irrelevant to the task.