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Although behavioral studies show large improvements in arithmetic skills in elementary school, we do not know how brain structure supports math gains in typically developing children. While some correlational studies have investigated the concurrent association between math performance and brain structure, such as gray matter volume (GMV), longitudinal studies are needed to infer if there is a causal relation. Although discrepancies in the literature on the relation between GMV and math performance have been attributed to the different demands on quantity vs. retrieval mechanisms, no study has experimentally tested this assumption. We defined regions of interests (ROIs) associated with quantity representations in the bilateral intraparietal sulcus (IPS) and associated with the storage of arithmetic facts in long-term memory in the left middle and superior temporal gyri (MTG/STG), and studied associations between GMV in these ROIs and children's performance on operations having greater demands on quantity vs. retrieval mechanisms, namely subtraction vs. multiplication. The aims of this study were threefold: First, to study concurrent associations between GMV and math performance, second, to investigate the role of GMV at the first time-point (T1) in predicting longitudinal gains in math skill to the second time-point (T2), and third, to study whether changes in GMV over time were associated with gains in math skill. Results showed no concurrent association between GMV in IPS and math performance, but a concurrent association between GMV in left MTG/STG and multiplication skill at T1. This association showed that the higher the GMV in this ROI, the higher the children's multiplication skill. Results also revealed that GMV in left IPS and left MTG/STG predicted longitudinal gains in subtraction skill only for younger children (approximately 10 years old). Whereas higher levels of GMV in left IPS at T1 predicted larger subtraction gains, higher levels of GMV in left MTG/STG predicted smaller gains. GMV in left MTG/STG did not predict longitudinal gains in multiplication skill. No significant association was found between changes in GMV over time and longitudinal gains in math. Our findings support the early importance of brain structure in the IPS for mathematical skills that rely on quantity mechanisms., Competing Interests: Declaration of Competing Interest The authors declare that they have no conflict of interest., (Copyright © 2021. Published by Elsevier Inc.)

Models of the neural basis of arithmetic argue that left inferior frontal cortex is involved in cognitive control of verbal representations of math facts in left lateral temporal cortex, whereas bilateral intra-parietal cortex is involved in numerical calculation. Lower levels of math competence for multiplications is associated with greater effortful retrieval because of less robust verbal representations and the engagement of numerical operations as a back-up strategy. Previous studies on multiplication have focused on brain activation in isolated nodes of the network, so we do not know how functional connectivity between these nodes is related to competence. Moreover, previous studies have not employed longitudinal designs, so we do not know how changes in multiplication performance over time is related to changes in its neural basis. The objective of this study was to investigate how changes in multiplication task performance is associated with changes in functional connectivity of temporal cortex with frontal and parietal cortices. Longitudinal data was collected from 45 children, with an average 2.2-year interval between the two sessions, when they were about 11 years old at time 1 (T1) and 13 years old at time 2 (T2). A Psychophysiological Interaction (PPI) analysis was carried out by defining the seed in the temporal cortex (i.e. posterior superior and middle temporal gyri) and examining changes in connectivity with frontal cortex (i.e. left inferior frontal gyrus) as well as parietal cortex (i.e. left and right inferior and superior parietal lobules). We found that children who did not improve in a multiplication task showed greater levels of functional connectivity of left temporal cortex with left inferior frontal gyrus (IFG) and left intraparietal sulcus (IPS) at T2, as compared to their peers who improved. The cluster showing greater levels of connectivity in the left IFG at T2 for the Non-improvers overlapped a cluster independently identified by a verbal localizer task and the cluster showing greater levels of connectivity in the left IPS Non-improvers overlapped a cluster independently identified by a numerosity localizer task. These results suggest that lack of improvement in multiplications are associated with greater cognitive control of verbal representations and greater engagement of numerical operations., (Copyright © 2018 Elsevier Inc. All rights reserved.)

This study uses event-related brain potentials to investigate the difficulties that high math anxious individuals face when processing dramatically incorrect solutions to simple arithmetical problems. To this end, thirteen high math-anxious (HMA) and thirteen low math-anxious (LMA) individuals were presented with simple addition problems in a verification task. The proposed solution could be correct, incorrect but very close to the correct one (small-split), or dramatically incorrect (large-split). The two groups did not differ in mathematical ability or trait anxiety. We reproduced previous results for flawed scores suggesting HMA difficulties in processing large-split solutions. Moreover, large-split solutions elicited a late positive component (P600/P3b) which was more enhanced and delayed in the HMA group. Our study proposes that the pattern of flawed scores found by previous studies (and that we replicate) has to do with HMA individuals'difficulties in inhibiting an extended processing of irrelevant information (large-split solutions)., (Copyright © 2013 Elsevier B.V. All rights reserved.)

This paper focuses on the capacity to solve numerical incongruities in high- and lower-skilled arithmetic problem-solvers by investigating event-related brain potentials elicited by incorrect solutions to additions. Fifteen high-skill and fifteen low-skill individuals were presented with simple addition problems in a verification task. The proposed solution was manipulated by presenting correct solutions and incorrect solutions very close to the correct ones. Incorrect solutions elicited a negative component followed by a late positive component (LPC/P3b), whose amplitude was smaller for the low-skill group than for the high-skill group. Because the LPC/P3b amplitude has been taken as an indicator of the plausibility of the stimulus, this result suggests that incorrect solutions close to the correct ones appear more plausible to low-skilled individuals than to their high-skilled counterparts. This result is interpreted in terms of differences in the strength of association between problems and potential solutions depending on arithmetical skill.