A Role for Attentional Reorienting During Approximate Multiplication and Division

Abstract

When asked to estimate the outcome of arithmetic problems, participants overestimate for addition problems and underestimate for subtraction problems, both in symbolic and non-symbolic format. This bias is referred to as operational momentum effect (OM). The attentional shifts account holds that during computation of the outcome participants are propelled too far along a spatial number representation. OM was observed in non-symbolic multiplication and division while being absent in symbolic multiplication and division. Here, we investigate whether (a) the absence of the OM in symbolic multiplication and division was due to the presentation of the correct outcome amongst the response alternatives, putatively triggering verbally mediated fact retrieval, and whether (b) OM is correlated with attentional parameters, as stipulated by the attentional account. Participants were presented with symbolic and non-symbolic multiplication and division problems. Among seven incorrect response alternatives participants selected the most plausible result. Participants were also presented with a Posner task, with valid (70%), invalid (15%) and neutral (15%) cues pointing to the position at which a subsequent target would appear. While no OM was observed in symbolic format, non-symbolic problems were subject to OM. The non-symbolic OM was positively correlated with reorienting after invalid cues. These results provide further evidence for a functional association between spatial attention and approximate arithmetic, as stipulated by the attentional shifts account of OM. They also suggest that the cognitive processes underlying multiplication and division are less prone to spatial biases compared to addition and subtraction, further underlining the involvement of differential cognitive processes.