Working Memory States Modulate Arithmetic Estimation Strategy Processing: Evidence from Visual and Articulatory...

Arithmetic estimation requires maintaining numerical information while applying rule-based procedures for approximate calculation, yet it remains unclear whether such estimation strategy processing depends on the working memory state in which task-relevant information is maintained. This study examined whether operationally defined online and offline working memory states modulate arithmetic estimation strategy processing, and whether such modulation varies with estimation strategy difficulty sequence and interference condition. Through three behavioral experiments, participants completed a serial probe task requiring estimation strategy consistency judgments for rounding down, rounding up, and mixed rounding strategies. Experiment 1 manipulated presentation duration and revealed distinct temporal profiles: online state performance was highest at the shortest duration and declined thereafter, whereas offline state performance improved and then stabilized. Experiment 2 showed that visual interference did not produce a uniform impairment, but selectively modulated online state estimation strategy judgments in a difficulty-sequence-dependent manner. Experiment 3 showed that articulatory interference produced broader disruption, impairing offline state performance across sequence conditions and reducing online state performance in the difficult-simple sequence. These findings are consistent with the view that arithmetic estimation strategy performance varies with operationally defined working memory representational state, difficulty sequence context, and the task demands imposed by different interference conditions.