Working Memory States Modulate Arithmetic Estimation Strategy Processing: Evidence From Visual and Phonological Interference

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 online and offline working memory states modulate arithmetic estimation strategy processing and whether such modulation varies with estimation strategy difficulty sequence and interference modality. Across 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 estimation strategy judgments in a difficulty sequence dependent manner. Experiment 3 showed that phonological interference produced broader disruption, impairing offline performance across sequence conditions and reducing online performance in the difficult–simple sequence. These findings suggest that arithmetic estimation strategy processing is shaped by dynamic working memory states, difficulty sequence related load, and modality specific interference.