Processing fractions and proportions: An fMRI study

Number cognition is important both for the society and for the individual. The disorder of number cognition (developmental dyscalculia) can havemajor impact on individual life quality. Several children and adults experience problemswith one aspect of ‘arithmetic syntax’, the representation of place value structure. Here we provide the first cognitive neuroscience investigation of place value representation. Our study systematically contrasted semantic (the numerical distance effect) and syntactic (place value structure) violations in a mental addition verification task. Participants verified additions with fourdigit numbers. Semantic incongruencies elicited theN400 ERP effect. A centro-parietal (putative P600) effect to place-value violationswas not related to arithmetic syntax. Rather, this effect was an enlarged P3b reflecting different surprise values of place value vs. non-place value violations. This potential confound should be considered in numerical cognition experiments. The latency of the N400 and P3a effects were differentially affected byplace-value analysis. The amplitude of the P3a and that of a fronto-central positive effect (FP600) was sensitive to place value analysis and digit content. Results suggest that ERPs can index the syntactical analysis of multi-digit numbers. Both ERP and behavioral data confirmed thatmulti-digit numberswere decomposed into their constituent digits, rather than evaluated holistically. These findings enable the detailed investigation of place value representation in both normal and dyscalculic populations.