Developmental dissociation in the neural responses to simple multiplication and subtraction problems.

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a cross-sectional design to measure the neural activity associated with single-digit subtraction and multiplication in 34 children from 2nd to 7th grade. The neural correlates of language and numerical processing were also identified in each child via localizer scans. Although multiplication and subtraction were undistinguishable in terms of behavior, we found a striking developmental dissociation in their neural correlates. First, we observed grade-related increases of activity for multiplication, but not for subtraction, in a language-related region of the left temporal cortex. Second, we found grade-related increases of activity for subtraction, but not for multiplication, in a region of the right parietal cortex involved in the procedural manipulation of numerical quantities. The present results suggest that fluency in simple arithmetic in children may be achieved by both increasing reliance on verbal retrieval and by greater use of efficient quantity-based procedures, depending on the operation.

Fractionating the neural substrates of transitive reasoning: task-dependent contributions of spatial and verbal representations.

It has long been suggested that transitive reasoning relies on spatial representations in the posterior parietal cortex (PPC). Previous neuroimaging studies, however, have always focused on linear arguments, such as "John is taller than Tom, Tom is taller than Chris, therefore John is taller than Chris." Using functional magnetic resonance imaging (fMRI), we demonstrate here that verbal representations contribute to transitive reasoning when it involves set-inclusion relations (e.g., "All Tulips are Flowers, All Flowers are Plants, therefore All Tulips are Plants"). In the present study, such arguments were found to engage verbal processing regions of the left inferior frontal gyrus (IFG) and left PPC that were identified in an independent localizer task. Specifically, activity in these verbal regions increased as the number of relations increased in set-inclusion arguments. Importantly, this effect was specific to set-inclusion arguments because left IFG and left PPC were not differentially engaged when the number of relations increased in linear arguments. Instead, such an increase was linked to decreased activity in a spatial processing region of the right PPC that was identified in an independent localizer task. Therefore, both verbal and spatial representations can underlie transitive reasoning, but their engagement depends upon the structure of the argument.

Distinct representations of subtraction and multiplication in the neural systems for numerosity and language.

It has been proposed that recent cultural inventions such as symbolic arithmetic recycle evolutionary older neural mechanisms. A central assumption of this hypothesis is that the degree to which a preexisting mechanism is recycled depends on the degree of similarity between its initial function and the novel task. To test this assumption, we investigated whether the brain region involved in magnitude comparison in the intraparietal sulcus (IPS), localized by a numerosity comparison task, is recruited to a greater degree by arithmetic problems that involve number comparison (single-digit subtractions) than by problems that involve retrieving number facts from memory (single-digit multiplications). Our results confirmed that subtractions are associated with greater activity in the IPS than multiplications, whereas multiplications elicit greater activity than subtractions in regions involved in verbal processing including the middle temporal gyrus (MTG) and inferior frontal gyrus (IFG) that were localized by a phonological processing task. Pattern analyses further indicated that the neural mechanisms more active for subtraction than multiplication in the IPS overlap with those involved in numerosity comparison and that the strength of this overlap predicts interindividual performance in the subtraction task. These findings provide novel evidence that elementary arithmetic relies on the cooption of evolutionary older neural circuits.

Attentional network deficits in children with autism spectrum disorder.

STATEMENT OF PURPOSE: Individuals with autism spectrum disorder (ASD) often demonstrate deficient attentional ability, but the specific nature of the deficit is unclear. The Attention Networks model provides a useful approach to deconstruct this attentional deficit into its component parts. METHOD: Fifty-two neurotypical (NT) children and 14 children with ASD performed the child version of the Attention Network Test (ANT). The latter requires participants to indicate the direction of a centre target stimulus, which is presented above/below fixation and sometimes flanked by either congruent or incongruent distractor stimuli. RESULTS: Relative to NT children, those with ASD were: (1) slower to react to spatially cued trials and (2) more error prone on executive (conflict) attention trials. CONCLUSIONS: Young children with ASD have intact alerting attention, but less-efficient orienting and executive attention.

Spatial and visuospatial working memory tests predict performance in classic multiple-object tracking in young adults, but nonspatial measures of the executive do not.

An individual-differences approach was used to investigate the roles of visuospatial working memory and the executive in multiple-object tracking. The Corsi Blocks and Visual Patterns Tests were used to assess visuospatial working memory. Two relatively nonspatial measures of the executive were used: operation span (OSPAN) and reading span (RSPAN). For purposes of comparison, the digit span test was also included (a measure not expected to correlate with tracking). The tests predicted substantial amounts of variance (R (2) = .33), and the visuospatial measures accounted for the majority (R (2) = .30), with each making a significant contribution. Although the executive measures correlated with each other, the RSPAN did not correlate with tracking. The correlation between OSPAN and tracking was similar in magnitude to that between digit span and tracking (p < .05 for both), and when regression was used to partial out shared variance between the two tests, the remaining variance predicted by the OSPAN was minimal (sr ( 2 ) = .029). When measures of spatial memory were included in the regression, the unique variance predicted by the OSPAN became negligible (sr ( 2 ) = .000004). This suggests that the executive, as measured by tests such as the OSPAN, plays little role in explaining individual differences in multiple-object tracking.