Multiplication is thought to be primarily solved via direct retrieval from memory. Two of the main factors known to influence the retrieval of multiplication facts are problem size and interference. Because these factors are often intertwined, we sought to investigate the unique influences of problem size and interference on both performance and neural responses during multiplication fact retrieval in healthy adults. Behavioral results showed that both problem size and interference explained separate unique portions of RT variance, but with significantly stronger contribution from problem size, which contrasts with previous work in children. Whole-brain fMRI results relying on a paradigm that isolated multiplication fact retrieval from response selection showed highly overlapping brain areas parametrically modulated by both problem size and interference in a large network of frontal, parietal, and subcortical brain areas. Subsequent analysis within these regions revealed problem size to be the stronger and more consistent “unique” modulating factor in overlapping regions as well as those that appeared to respond only to problem size or interference at the whole-brain level, thus underscoring the need to look beyond anatomical overlap using arbitrary thresholds. Additional unique contributions of interference (beyond problem size) were identified in right angular gyrus and subcortical regions associated with procedural processing. Together, our results suggest that problem size, relative to interference, tends to be the more dominant factor in driving behavioral and neural responses during multiplication fact retrieval in adults. Nevertheless, unique contributions of both factors demonstrate the importance of considering the overlapping and unique contributions of each in explaining the cognitive and neural bases of mental multiplication.

Although significant insights into the neural basis of numerical and mathematical processing have been made, the neural processes that enable abstract symbols to become numerical remain largely unexplored in humans. In the present study, adult participants were trained to associate novel symbols with nonsymbolic numerical magnitudes (arrays of dots). Functional magnetic resonance imaging was used to examine the neural correlates of numerical comparison versus recognition of the novel symbols after each of two training stages. A left-lateralized fronto-parietal network, including the intraparietal sulcus, the precuneus, and the dorsal prefrontal cortex, was more active during numerical comparison than during perceptual recognition. In contrast, a network including bilateral temporal–occipital regions was more active during recognition than comparison. A whole-brain three-way interaction revealed that those individuals who had higher scores on a postscan numerical task (measuring their understanding of the global numerical organization of the novel symbols) exhibited increasing segregation between the two tasks in the bilateral intraparietal sulci as a function of increased training. Furthermore, whole-brain regression analysis showed that activity in the left intraparietal sulcus was systematically related to the effect of numerical distance on accuracy. These data provide converging evidence that parietal and left prefrontal cortices are involved in learning to map numerical quantities onto visual symbols. Only the parietal cortex, however, appeared systematically related to the degree to which individuals learned to associate novel symbols with their numerical referents. We conclude that the left parietal cortex, in particular, may play a central role in imbuing visual symbols with numerical meaning.

There exists a long-standing debate regarding whether small and large numerosities engage different networks of processing. The ability to rapidly enumerate small (1–4) numerosities is referred to as “subitizing” and is thought to be qualitatively different from large numerosity processing. Functional neuro-imaging studies have attempted to dissociate neural correlates of small and large number processing by contrasting subitizing with counting of numerosities just outside the subitizing range. In the present study, we used functional magnetic resonance imaging (fMRI) to contrast the processing of numerosities in the “subitizing range” with numerosities requiring estimation. Participants compared sequentially presented slides of either dots or Arabic numerals for their relative magnitude. We show that comparison of nonsymbolic numerosities in the subitizing range led to activation of the right temporo-parietal junction, while at the same time this region was found to be suppressed during large numerosity processing. Furthermore, relative suppression of this region was strongly associated with faster response times. In previous studies, this region has been implicated in stimulus-driven attention.We therefore contend that activation of the temporo-parietal junction during small number processing and the suppression thereof during large numerosity comparisons reflects differential reliance on stimulus-driven versus goal-directed attentional networks in the brain.