Arithmetic in the Child and Adult Brain

Abstract

This review examines brain and cognitive processes involved in arithmetic. I take a distinctly developmental perspective because neither the cognitive nor the brain processes involved in arithmetic can be adequately understood outside the framework of how developmental processes unfold. I review four basic neurocognitive processes involved in arithmetic, highlighting (1) the role of core dorsal parietal and ventral temporal-occipital cortex systems that form basic building blocks from which number form and quantity representations are constructed in the brain; (2) procedural and working memory systems anchored in the basal ganglia and frontoparietal circuits, which create short-term representations that allow manipulation of multiple discrete quantities over several seconds; (3) episodic and semantic memory systems anchored in the medial and lateral temporal cortex that play an important role in long-term memory formation and generalization beyond individual problem attributes; and (4) prefrontal cortex control processes that guide allocation of attention resources and retrieval of facts from memory in the service of goal-directed problem solving. Next I examine arithmetic in the developing brain, first focusing on studies comparing arithmetic in children and adults, and then on studies examining development in children during critical stages of skill acquisition. I highlight neurodevelopmental models that go beyond parietal cortex regions involved in number processing, and demonstrate that brain systems and circuits in the developing child brain are clearly not the same as those seen in more mature adult brains sculpted by years of learning. The implications of these findings for a more comprehensive view of the neural basis of arithmetic in both children and adults are discussed.

Mechanisms of interactive specialization and emergence of functional brain circuits supporting cognitive development in children

“…35 Our results highlight the contribution of a previously neglected dorsal-ventral stream circuit to the development of numerical cognition, and add to the growing body of evidence for the importance of the FG and its interactions with the IPS. [50][51][52][53] This is in line with previous work demonstrating the maturation of representations of arithmetic problems in both IPS and VTOC in adults relative to children.…”

“…Then, based on heuristic model comparison measures, i.e., AIC (Akaike Information Criterion), we selected the best fitting model at each voxel. Our analysis focused on the left hIP3, the posterior most cytoarchitectonic subdivision of the IPS, based on its extensive role in numerical cognition 35,[37][38][39][40][41] as determined by meta-analysis of previously published tasks in the domain (see Methods).…”

“…[31][32][33][34] Together, the IPS and the VTOC facilitate the efficient manipulation of numerical quantity necessary for numerical problem solving. 35 In addition, frontal systems anchored in the insula, dorsolateral and ventrolateral prefrontal cortex (PFC) support working memory and other cognitive control functions important for effortful problem solving. 26,36 Cross-sectional studies have suggested that IPS and VTOC activity increase with age, while PFC activity decreases with age, reflecting decreasing demands on the working memory system accompanied by increasing utilization of mature problem solving abilities.…”

“…To better understand the mechanisms underlying IS, we examined whether longitudinal developmental changes would be associated with: (1) selective strengthening of specialized functional circuits, (2) selective weakening of PFC circuits that scaffold development, and (3) increases and decreases in activity within brain areas that show targeted changes in connectivity. 1,6 Based on extensive evidence for its prominent role in quantity representation and manipulation, 35,40,41 we focused on IPS connectivity to characterize longitudinal developmental changes in functional brain circuits and test-specific hypotheses about the mechanisms underlying IS. Specifically, we hypothesized that over time the IPS would show: (1) increased effective connectivity within local parietal cortical circuits; (2) increased connectivity with VTOC regions involved in basic number form processing; (3) decreased connectivity with PFC cognitive control and working memory systems.…”

The principles and practices of educational neuroscience: Comment on Bowers (2016).

“…These authors specifically considered the case of dyscalculia, which they argued is a deficit in number sense, and offered suggestions based on pedagogical theory about how this condition could be remediated. Their argument is supported by a localized abnormality in one neural area (intraparietal cortex) consistently activated during reasoning about number and set size, part of the large-scale neural network for arithmetic (e.g., (Andres, Pelgrims, Michaux, Olivier, & Pesenti, 2011;Menon, 2015;Zago et al, 2001).…”