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.
more »
« less
Short‐term number sense training recapitulates long‐term neurodevelopmental changes from childhood to adolescence
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.
more »
« less
- Award ID(s):
- 2024856
- PAR ID:
- 10559627
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Developmental Science
- Volume:
- 27
- Issue:
- 5
- ISSN:
- 1363-755X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Bortfeld, Heather; de Haan, Michelle; Nelson, Charles A.; Quinn, Paul C. (Ed.)Abstract Children's ability to discriminate nonsymbolic number (e.g., the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest that it may be due to a sharpening numerical representation or an improved ability to pay attention to number and filter out non‐numerical information. We investigate this issue by studying change in children's performance (N = 65) on a nonsymbolic number comparison task, where children decide which of two dot arrays has more dots, from the middle to the end of 1st grade (mean age at time 1 = 6.85 years old). In this task, visual properties of the dot arrays such as surface area are either congruent (the more numerous array has more surface area) or incongruent. Children rely more on executive functions during incongruent trials, so improvements in each congruency condition provide information about the underlying cognitive mechanisms. We found that accuracy rates increased similarly for both conditions, indicating a sharpening sense of numerical magnitude, not simply improved attention to the numerical task dimension. Symbolic number skills predicted change in congruent trials, but executive function did not predict change in either condition. No factor predicted change in math achievement. Together, these findings suggest that nonsymbolic number processing undergoes development related to existing symbolic number skills, development that appears not to be driving math gains during this period.Children's ability to discriminate nonsymbolic number improves throughout development. Competing theories suggest improvement due to sharpening magnitude representations or changes in attention and inhibition.The current study investigates change in nonsymbolic number comparison performance during first grade and whether symbolic number skills, math skills, or executive function predict change.Children's performance increased across visual control conditions (i.e., congruent or incongruent with number) suggesting an overall sharpening of number processing.Symbolic number skills predicted change in nonsymbolic number comparison performance.more » « less
-
Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic and non-symbolic approximate division. Subjects were presented with non-symbolic (dot array) or symbolic (Arabic numeral) dividends ranging from 32 to 185, and non-symbolic divisors ranging from 2 to 8. Subjects compared their imagined quotient to a visible target quantity. Both children (Experiment 1 N = 89, Experiment 2 N = 42) and adults (Experiment 3 N = 87) were successful at the approximate division tasks in both dots and numeral formats. This was true even among the subset of children that could not recognize the division symbol or solve simple division equations, suggesting intuitive division ability precedes formal division instruction. For both children and adults, the ability to divide non-symbolically mediated the relation between Approximate Number System (ANS) acuity and symbolic math performance, suggesting that the ability to calculate non-symbolically may be a mechanism of the relation between ANS acuity and symbolic math. Our findings highlight the intuitive arithmetic abilities children possess before formal math instruction.more » « less
-
Abstract Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic‐like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function‐like structure, like symbolic arithmetic. Children (n =74 4‐ to ‐8‐year‐olds in Experiment 1;n =52 7‐ to 8‐year‐olds in Experiment 2) first solved two nonsymbolic arithmetic problems. We then showed children two unequal sets of objects, and asked children which of the two derived solutions should be added to the smaller of the two sets to make them “about the same.” We hypothesized that, if nonsymbolic arithmetic follows similar function rules to symbolic arithmetic, then children should be able to use the solutions of nonsymbolic computations as inputs into another nonsymbolic problem. Contrary to this hypothesis, we found that children were unable to reliably do so, suggesting that these solutions may not operate as independent representations that can be used inputs into other nonsymbolic computations. These results suggest that nonsymbolic and symbolic arithmetic computations are algorithmically distinct, which may limit the extent to which children can leverage nonsymbolic arithmetic intuitions to acquire formal mathematics knowledge.more » « less
-
Spatial skills in early childhood are key predictors of mathematical achievement. Previous studies have found that training mental rotation can transfer to arithmetic skills; however, some studies have failed to replicate this transfer effect, or observed transfer effects only in certain types of arithmetic problems. Even in studies where transfer effects were observed, the underlying mechanisms of this transfer have not been explored. This study focused on the effect of short-duration (i.e., single-session) spatial training on arithmetic skills, and tested two underlying mechanisms. First, based on the spatial modeling account, short-duration spatial training may prime spatial processing, leading to a reduction in the use of counting strategies and an increase in spatially-related strategies following spatial training. Second, from a social-psychological account, short-duration spatial training may reduce children’s state anxiety, thus allowing them more cognitive resources in spatial and arithmetic tasks. We tested these mechanisms among 80 U.S. second- and third-graders using a pretest-intervention-posttest design, with 40 children in the spatial training group and 40 in an active control group. Short-duration spatial training improved children’s overall arithmetic performance; this effect did not differ by problem type (conventional, missing-term, or two-step problems). Spatial training also reduced children’s use of counting strategies. However, we did not find a significant increase in spatially-related strategies, nor did we observe a significant reduction in state anxiety. This study makes an important contribution to understanding the mechanisms underlying the transfer effects of short-duration spatial training on arithmetic skills, providing partial support for the spatial modeling account.more » « less
An official website of the United States government

