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The development of mathematical skills in early childhood relies on number sense, the foundational ability to discriminate among quantities. Number sense in early childhood is predictive of academic and professional success, and deficits in number sense are thought to underlie lifelong impairments in mathematical abilities. Despite its importance, the brain circuit mechanisms that support number sense learning remain poorly understood. Here, we designed a theoretically motivated training program to determine brain circuit mechanisms underlying foundational number sense learning in female and male elementary school-age children (7–10 years). Our 4 week integrative number sense training program gradually strengthened the understanding of the relations between symbolic (Arabic numerals) and nonsymbolic (sets of items) representations of quantity. We found that our number sense training program improved symbolic quantity discrimination ability in children across a wide range of math abilities including children with learning difficulties. Crucially, the strength of pretraining functional connectivity between the hippocampus and intraparietal sulcus, brain regions implicated in associative learning and quantity discrimination, respectively, predicted individual differences in number sense learning across typically developing children and children with learning difficulties. Reverse meta-analysis of interregional coactivations across 14,371 fMRI studies and 89 cognitive functions confirmed a reliable role for hippocampal–intraparietal sulcus circuits in learning. Our study identifies a canonical hippocampal–parietal circuit for learning that plays a foundational role in children's cognitive skill acquisition. Findings provide important insights into neurobiological circuit markers of individual differences in children's learning and delineate a robust target for effective cognitive interventions.SIGNIFICANCE STATEMENTMathematical skill development relies on number sense, the ability to discriminate among quantities. Here, we develop a theoretically motivated training program and investigate brain circuits that predict number sense learning in children during a period important for acquisition of foundational cognitive skills. Our integrated number sense training program was effective in children across a wide a range of math abilities, including children with learning difficulties. We identify hippocampal–parietal circuits that predict individual differences in learning gains. Our study identifies a brain circuit critical for the acquisition of foundational cognitive skills, which will be useful for developing effective interventions to remediate learning disabilities.

Mathematical knowledge is constructed hierarchically from basic understanding of quantities and the symbols that denote them. Discrimination of numerical quantity in both symbolic and non-symbolic formats has been linked to mathematical problem-solving abilities. However, little is known of the extent to which overlap in quantity representations between symbolic and non-symbolic formats is related to individual differences in numerical problem solving and whether this relation changes with different stages of development and skill acquisition. Here we investigate the association between neural representational similarity (NRS) across symbolic and non-symbolic quantity discrimination and arithmetic problem-solving skills in early and late developmental stages: elementary school children (ages 7-10 years) and adolescents and young adults (AYA, ages 14-21 years). In children, cross-format NRS in distributed brain regions, including parietal and frontal cortices and the hippocampus, was positively correlated with arithmetic skills. In contrast, no brain region showed a significant association between cross-format NRS and arithmetic skills in the AYA group. Our findings suggest that the relationship between symbolic-non-symbolic NRS and arithmetic skills depends on developmental stage. Taken together, our study provides evidence for both mapping and estrangement hypotheses in the context of numerical problem solving, albeit over different cognitive developmental stages.

Highlights • We examined neurocognitive mechanisms underlying learning and near transfer in elementary school children. • A five-day tutoring led to marked differentiation of behavioral and brain responses between trained and novel problems. • Children who learned trained problems faster transferred their learnt knowledge to novel problems better. • Faster learners showed greater overlap in local neural representations between trained and novel problems. • More efficient learning led to greater differentiation of functional brain circuits engaged by trained and novel problems., Why some children learn, and transfer their knowledge to novel problems, better than others remains an important unresolved question in the science of learning. Here we developed an innovative tutoring program and data analysis approach to investigate individual differences in neurocognitive mechanisms that support math learning and “near” transfer to novel, but structurally related, problems in elementary school children. Following just five days of training, children performed recently trained math problems more efficiently, with greater use of memory-retrieval-based strategies. Crucially, children who learned faster during training performed better not only on trained problems but also on novel problems, and better discriminated trained and novel problems in a subsequent recognition memory task. Faster learners exhibited increased similarity of neural representations between trained and novel problems, and greater differentiation of functional brain circuits engaged by trained and novel problems. These results suggest that learning and near transfer are characterized by parallel learning-rate dependent local integration and large-scale segregation of functional brain circuits. Our findings demonstrate that speed of learning and near transfer are interrelated and identify the neural mechanisms by which faster learners transfer their knowledge better. Our study provides new insights into the behavioral, mnemonic, and neural mechanisms underlying children’s learning.

Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low—compared to high—math anxious individuals perform better when they activate this network less—a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently.

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.

Anxiety about mathematics — highly prevalent across the globe — is associated with poor math performance. Why is math anxiety related to poor math performance and how can we reduce this link? Current behavioral and psychophysiological research reveals that the math anxiety-math performance link is related to both individual (cognitive, affective/physiological, motivational) and environmental (social/contextual) factors. Several interventions have recently been developed to alleviate the relation between math anxiety and math performance. To lower math anxiety and reduce its relation to poor math performance, future interventions may benefit from focusing on both math-anxious individuals themselves and those around them.

Even at young ages, children self-report experiencing math anxiety, which negatively relates to their math achievement. Leveraging a large dataset of first and second grade students' math achievement scores, math problem solving strategies, and math attitudes, we explored the possibility that children's math anxiety (i.e., a fear or apprehension about math) negatively relates to their use of more advanced problem solving strategies, which in turn relates to their math achievement. Our results confirm our hypothesis and, moreover, demonstrate that the relation between math anxiety and math problem solving strategies is strongest in children with the highest working memory capacity. Ironically, children who have the highest cognitive capacity avoid using advanced problem solving strategies when they are high in math anxiety and, as a result, underperform in math compared with their lower working memory peers.

The odd–even effect in numerical processing has been explained as the easier processing of even numbers compared with odd numbers. We investigated this effect in Sudoku puzzles, a reasoning problem that uses numbers but does not require arithmetic operations. Specifically, we asked whether the odd–even effect occurred with Sudoku puzzles and whether individual differences in working memory (WM), aging, and experience with Sudoku modulated this effect. We manipulated the presence of odd and even numbers in Sudoku puzzles, measured WM with the Wisconsin Card Sorting Test and backward digit span task, tested older and younger adults, and collected Sudoku experience frequency. Performance on Sudoku was more accurate for even puzzles than odd ones. Younger, experienced, and higher-WM participants were more accurate on Sudoku, but these individual difference variables did not interact with the odd–even effect. Odd numbers may impose more cognitive load than even numbers, but future research is needed to examine how age, experience, or WM may influence the odd–even effect.

Metabolic syndrome is prevalent in older adults and increases the risk of cardiovascular disease. Second-generation antipsychotics (aripiprazole, clozapine, olanzapine, quetiapine, risperidone, and ziprasidone) increase the risk of metabolic syndrome and present many challenges for psychiatrists. In this article, we review the relationships between second-generation antipsychotics and metabolic syndrome with a focus on older adults. Because few studies focus exclusively on older adults, we augment this review with relevant findings from younger adults. The differential risk factors of each medication are reviewed, as are recent findings in monitoring and treating metabolic syndrome. Olanzapine and clozapine are more strongly associated with metabolic risks, whereas aripiprazole and ziprasidone are less associated. Although lifestyle modifications can help to reduce some aspects of metabolic syndrome, lifestyle modifications in conjunction with metformin therapy appear to be most effective.