Lack of improvement in multiplication is associated with reverting from verbal retrieval to numerical operations.

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.