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Abstract Number sense is fundamental to the development of numerical problem‐solving skills. In early childhood, children establish associations between non‐symbolic (e.g., a set of dots) and symbolic (e.g., Arabic numerals) representations of quantity. The developmental estrangement theory proposes that the relationship between non‐symbolic and symbolic representations of quantity evolves with age, with increased dissociation across development. Consistent with this theory, recent research suggests that cross‐format neural representational similarity (NRS) between non‐symbolic and symbolic quantities is correlated with arithmetic fluency in children but not in adolescents. However, it is not known if short‐term training (STT) can induce similar changes as long‐term development. In this study, children aged 7–10 years underwent a theoretically motivated 4‐week number sense training. Using multivariate neural pattern analysis, we investigated whether short‐term learning could modify the relation between cross‐format NRS and arithmetic skills. Our results revealed a significant correlation between cross‐format NRS and arithmetic fluency in distributed brain regions, including the parietal and prefrontal cortices, prior to training. However, this association was no longer observed after training, and multivariate predictive models confirmed these findings. Our findings provide evidence that intensive STT during early childhood can promote behavioral improvements and neural plasticity that resemble and recapitulate long‐term neurodevelopmental changes that occur from childhood to adolescence. More generally, our study contributes to our understanding of the malleability of number sense and highlights the potential for targeted interventions to shape neurodevelopmental trajectories in early childhood. Research HighlightsWe tested the hypothesis that short‐term number sense training induces the dissociation of symbolic numbers from non‐symbolic representations of quantity in children.We leveraged a theoretically motivated intervention and multivariate pattern analysis to determine training‐induced neurocognitive changes in the relation between number sense and arithmetic problem‐solving skills.Neural representational similarity between non‐symbolic and symbolic quantity representations was correlated with arithmetic skills before training but not after training.Short‐term training recapitulates long‐term neurodevelopmental changes associated with numerical problem‐solving from childhood to adolescence. 

Number sense is essential for early mathematical development but it is compromised in children with mathematical disabilities (MD). Here we investigate the impact of a personalized 4-week Integrated Number Sense (INS) tutoring program aimed at improving the connection between nonsymbolic (sets of objects) and symbolic (Arabic numerals) representations in children with MD. Utilizing neural pattern analysis, we found that INS tutoring not only improved cross-format mapping but also significantly boosted arithmetic fluency in children with MD. Critically, the tutoring normalized previously low levels of cross-format neural representations in these children to pre-tutoring levels observed in typically developing, especially in key brain regions associated with numerical cognition. Moreover, we identified distinct, ‘inverted U-shaped’ neurodevelopmental changes in the MD group, suggesting unique neural plasticity during mathematical skill development. Our findings highlight the effectiveness of targeted INS tutoring for remediating numerical deficits in MD, and offer a foundation for developing evidence-based educational interventions. Significance StatementFocusing on neural mechanisms, our study advances understanding of how numerical problem-solving can be enhanced in children with mathematical disabilities (MD). We evaluated an integrated number sense tutoring program designed to enhance connections between concrete (e.g. 2 dots) and symbolic (e.g. “2”) numerical representations. Remarkably, the tutoring program not only improved these children’s ability to process numbers similarly across formats but also enhanced their arithmetic skills, indicating transfer of learning to related domains. Importantly, tutoring normalized brain processing patterns in children with MD to resemble those of typically developing peers. These insights highlight the neural bases of successful interventions for MD, offering a foundation for developing targeted educational strategies that could markedly improve learning outcomes for children facing these challenges. 

Abstract Efficient memory-based problem-solving strategies are a cardinal feature of expertise across a wide range of cognitive domains in childhood. However, little is known about the neurocognitive mechanisms that underlie the acquisition of efficient memory-based problem-solving strategies. Here we develop, to the best of our knowledge, a novel neurocognitive process model of latent memory processes to investigate how cognitive training designed to improve children’s problem-solving skills alters brain network organization and leads to increased use and efficiency of memory retrieval-based strategies. We found that training increased both the use and efficiency of memory retrieval. Functional brain network analysis revealed training-induced changes in modular network organization, characterized by increase in network modules and reorganization of hippocampal-cortical circuits. Critically, training-related changes in modular network organization predicted performance gains, with emergent hippocampal, rather than parietal cortex, circuitry driving gains in efficiency of memory retrieval. Our findings elucidate a neurocognitive process model of brain network mechanisms that drive learning and gains in children’s efficient problem-solving strategies. 

We developed a novel Proactive Reactive and Attentional Dynamics (PRAD) computational model designed to dissect the latent mechanisms of inhibitory control in human cognition. Leveraging data from over 7,500 participants in the NIH Adolescent Brain Cognitive Development study, we demonstrate that PRAD surpasses traditional models by integrating proactive, reactive, and attentional components of inhibitory control. Employing a hierarchical Bayesian framework, PRAD offers a granular view of the dynamics underpinning action execution and inhibition, provides debiased estimates of stop-signal reaction times, and elucidates individual and temporal variability in cognitive control processes. Our findings reveal significant intra-individual variability, challenging conventional assumptions of random variability across trials. By addressing nonergodicity and systematically accounting for the multi-componential nature of cognitive control, PRAD advances our understanding of the cognitive mechanisms driving individual differences in cognitive control and provides a sophisticated computational framework for dissecting dynamic cognitive processes across diverse populations. 

Nonergodicity and Simpson’s paradox present significant, yet underappreciated challenges in neuroscience. Leveraging brain imaging and behavioral data from over 4,000 children and a Bayesian computational model of cognitive dynamics, we investigated brain-behavior relationships underlying cognitive control at both between-subjects and within-subjects levels. Strikingly, we observed a reversal of associations of inhibitory control brain activations with dynamic behavioral measures when comparing between-subjects and within-subjects analyses, revealing the nonergodic nature of these processes. This nonergodicity was pervasive throughout the brain but most pronounced in the salience network. Additionally, within-subjects analysis uncovered dissociated brain representations of reactive and proactive control processes, as well as distinct brain-behavior associations for individuals who adaptively versus maladaptively regulated cognitive control. Our findings offer insights into dynamic neural mechanisms of cognitive control during a critical developmental period. This work highlights the importance of embracing nonergodicity in human neuroscience, with implications for both theoretical understanding and applications to AI and psychopathology. 

Learning disabilities affect a significant proportion of children worldwide, with far-reaching consequences for their academic, professional, and personal lives. Here we develop digital twins – biologically plausible personalized Deep Neural Networks (pDNNs) – to investigate the neurophysiological mechanisms underlying learning disabilities in children. Our pDNN reproduces behavioral and neural activity patterns observed in affected children, including lower performance accuracy, slower learning rates, neural hyper-excitability, and reduced neural differentiation of numerical problems. Crucially, pDNN models reveal aberrancies in the geometry of manifold structure, providing a comprehensive view of how neural excitability influences both learning performance and the internal structure of neural representations. Our findings not only advance knowledge of the neurophysiological underpinnings of learning differences but also open avenues for targeted, personalized strategies designed to bridge cognitive gaps in affected children. This work reveals the power of digital twins integrating AI and neuroscience to uncover mechanisms underlying neurodevelopmental disorders. 

Abstract Number sense, the ability to decipher quantity, forms the foundation for mathematical cognition. How number sense emerges with learning is, however, not known. Here we use a biologically-inspired neural architecture comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS) to investigate how neural representations change with numerosity training. Learning dramatically reorganized neuronal tuning properties at both the single unit and population levels, resulting in the emergence of sharply-tuned representations of numerosity in the IPS layer. Ablation analysis revealed that spontaneous number neurons observed prior to learning were not critical to formation of number representations post-learning. Crucially, multidimensional scaling of population responses revealed the emergence of absolute and relative magnitude representations of quantity, including mid-point anchoring. These learnt representations may underlie changes from logarithmic to cyclic and linear mental number lines that are characteristic of number sense development in humans. Our findings elucidate mechanisms by which learning builds novel representations supporting number sense.