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Atten Percept Psychophys. 2009 May;71(4):803-21. doi: 10.3758/APP.71.4.803.

Dynamic representations underlying symbolic and nonsymbolic calculation: evidence from the operational momentum effect.

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  • 1INSERM, Unité 562, Gif-sur-Yvette, France.


When we add or subtract, do the corresponding quantities "move" along a mental number line? Does this internal movement lead to spatial biases? A new method was designed to investigate the psychophysics of approximate arithmetic. Addition and subtraction problems were presented either with sets of dots or with Arabic numerals, and subjects selected, from among seven choices, the most plausible result. In two experiments, the subjects selected larger numbers for addition than for subtraction problems, as if moving too far along the number line. This operational momentum effect was present in both notations and increased with the size of the outcome. Furthermore, we observed a new effect of spatial-numerical congruence, related to but distinct from the spatial numerical association of response codes effect: During nonsymbolic addition, the subjects preferentially selected numbers at the upper right location, whereas during subtraction, they were biased toward the upper left location. These findings suggest that approximate mental arithmetic involves dynamic shifts on a spatially organized mental representation of numbers. Supplemental materials for this study may be downloaded from

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