Interference and problem size effect in multiplication fact solving: Individual differences in brain activations and arithmetic performance

Abstract

In the development of math ability, a large variability of performance in solving simple arithmetic problems is observed and has not found a compelling explanation yet. One robust effect in simple multiplication facts is the problem size effect, indicating better performance for small problems compared to large ones. Recently, behavioral studies brought to light another effect in multiplication facts, the interference effect. That is, high interfering problems (receiving more proactive interference from previously learned problems) are more difficult to retrieve than low interfering problems (in terms of physical feature overlap, namely the digits, De Visscher and Noël, 2014). At the behavioral level, the sensitivity to the interference effect is shown to explain individual differences in the performance of solving multiplications in children as well as in adults. The aim of the present study was to investigate the individual differences in multiplication ability in relation to the neural interference effect and the neural problem size effect. To that end, we used a paradigm developed by De Visscher, Berens, et al. (2015) that contrasts the interference effect and the problem size effect in a multiplication verification task, during functional magnetic resonance imaging (fMRI) acquisition. Forty-two healthy adults, who showed high variability in an arithmetic fluency test, participated in our fMRI study. In order to control for the general reasoning level, the IQ was taken into account in the individual differences analyses. Our findings revealed a neural interference effect linked to individual differences in multiplication in the left inferior frontal gyrus, while controlling for the IQ. This interference effect in the left inferior frontal gyrus showed a negative relation with individual differences in arithmetic fluency, indicating a higher interference effect for low performers compared to high performers. This region is suggested in the literature to be involved in resolution of proactive interference. Besides, no correlation between the neural problem size effect and multiplication performance was found. This study supports the idea that the interference due to similarities/overlap of physical traits (the digits) is crucial in memorizing arithmetic facts and in determining individual differences in arithmetic.

Keywords: Arithmetic fact; Individual differences; Interference; Learning; Mathematics; Numerical cognition.