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1. First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals

   https://doi.org/10.1111/cdev.13470  

   Szkudlarek, Emily; Brannon, Elizabeth M. (May 2021, Child Development)

   Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty‐five 6‐ to 8‐year‐old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children’s numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills. 

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2. Predicting children’s math skills from task-based and resting-state functional brain connectivity

   https://doi.org/10.1093/cercor/bhab476  

   Lynn, Andrew; Wilkey, Eric D; Price, Gavin R (December 2021, Cerebral Cortex)

   Abstract A critical goal of cognitive neuroscience is to predict behavior from neural structure and function, thereby providing crucial insights into who might benefit from clinical and/or educational interventions. Across development, the strength of functional connectivity among a distributed set of brain regions is associated with children’s math skills. Therefore, in the present study we use connectome-based predictive modeling to investigate whether functional connectivity during numerical processing and at rest “predicts” children’s math skills (N = 31, Mage = 9.21 years, 14 Female). Overall, we found that functional connectivity during symbolic number comparison and rest, but not during nonsymbolic number comparison, predicts children’s math skills. Each task revealed a largely distinct set of predictive connections distributed across canonical brain networks and major brain lobes. Most of these predictive connections were negatively correlated with children’s math skills so that weaker connectivity predicted better math skills. Notably, these predictive connections were largely nonoverlapping across task states, suggesting children’s math abilities may depend on state-dependent patterns of network segregation and/or regional specialization. Furthermore, the current predictive modeling approach moves beyond brain–behavior correlations and toward building models of brain connectivity that may eventually aid in predicting future math skills. 

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3. Approximate multiplication in young children prior to multiplication instruction

   Chuyan Qu, Emily Szkudlarek (January 2021, Journal of experimental child psychology)

   Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can per-form a true multiplication operation, flexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruc-tion. We presented 5- to 8-year-olds with nonsymbolic multipli-cands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a vis-ible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multipli-cation, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2
   3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between chil-dren’s Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children’s emerging symbolic math competence. These findings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning. 

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4. Network topology of symbolic and nonsymbolic number comparison

   https://doi.org/10.1162/netn_a_00144  

   Conrad, Benjamin N.; Wilkey, Eric D.; Yeo, Darren J.; Price, Gavin R. (January 2020, Network Neuroscience)

   null (Ed.)

   Author Summary Previous studies of local activity levels suggest that both shared and distinct neural mechanisms support the processing of symbolic (Arabic digits) and nonsymbolic (dot sets) number stimuli, involving regions distributed across frontal, temporal, and parietal cortices. Network-level characterizations of functional connectivity patterns underlying number processing have gone unexplored, however. In this study we examined the whole-brain functional architecture of symbolic and nonsymbolic number comparison. Stronger community membership was observed among auditory regions during symbolic processing, and among cingulo-opercular/salience and basal ganglia networks for nonsymbolic. A dual versus unified fronto-parietal/dorsal attention community organization was observed for symbolic and nonsymbolic formats, respectively. Finally, the inferior temporal gyrus and left intraparietal sulcus, both thought to be preferentially involved in processing number symbols, demonstrated robust differences in community membership between formats. 

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5. Short‐term number sense training recapitulates long‐term neurodevelopmental changes from childhood to adolescence

   https://doi.org/10.1111/desc.13524  

   Park, Yunji; Zhang, Yuan; Chang, Hyesang; Menon, Vinod (April 2024, Developmental Science)

   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. 

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