Short-term number sense training recapitulates long-term neurodevelopmental changes from childhood to adolescence

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 HIGHLIGHTS: We 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.

Keywords: arithmetic; individual differences; learning; multivariate neural pattern analysis; number sense; training.

FIGURE 1

Short-term training (STT) and long-term developmental (LTD) study overview and behavioral results from STT. (A) STT and LTD samples. In the current study, we compared training-induced learning in a 4-week training study (STT) to neurodevelopmental differences between children and adolescents in Schwartz et al. (2021) (LTD). (B) STT study design. First, children’s arithmetic fluency was assessed from Math Fluency subtest from Woodcock-Johnson-111 (WJ-III; Woodcock et al., 2001). On a separate day, children underwent an fMRI scan session during which they had to determine which of two quantities (presented in dot arrays [or Arabic numerals] for non-symbolic [or symbolic] condition) is larger. Upon the completion of fMRI scan, children went through intensive 4 weeks of one-on-one number sense training with a tutor, focusing on improving mapping between non-symbolic and symbolic numerical quantity representations. The training occurred three times per week with each session taking ~60 min. After training, children underwent a second fMRI scan session and completed a second WJ-III Math Fluency subtest. (C) fMRI tasks. In the fMRI session, participants performed non-symbolic and symbolic number comparison tasks in separate runs. The figure depicts an example trial of a non-symbolic comparison task. Participants responded which side had the larger quantity after the onset of the presentation of the pair of quantities and before the end of the intertrial interval. Neural representational similarity (NRS) between brain response patterns of the numerical distance effect (near–far distance) in non-symbolic and symbolic number comparison tasks was computed (see details in Methods). (D) Behavioral performance improvements in response to STT. Increased performance efficiency was observed in number comparison task in both non-symbolic (Nonsym) and symbolic (Sym) formats. Performance efficiency was measured by dividing accuracy by median reaction time, with higher scores indicating higher efficiency. p*** < 0.001.

FIGURE 2

Short-term training leads to dissociation between cross-format (non-symbolic-symbolic) neural representational similarity (NRS) in parietal and frontal regions and arithmetic fluency in children. Before training (blue dots and regression lines), cross-format NRS significantly correlates with arithmetic fluency in children in the left intraparietal sulcus/lateral occipital cortex (IPS/LOC), precentral gyrus (PreCG), premotor cortex (premotor), insula and the right central operculum (COper) (Bayes factors [BF₁₀s] > 3). In contrast, after training (red triangles and regression lines), cross-format NRS does not significantly correlate with arithmetic fluency in children in these regions of interest (ROIs) (BF₁₀s < 3). Correlation coefficients were significantly different between pre- and post-training in these six ROIs (ps < 0.04), which were among the ROIs defined from Schwartz et al. (2021) (see also Figure 4a). Results from the other nine ROIs also showed significant brain-behavior correlations before, but not after, short-term training (Supplementary Results), p* < 0.05, p** < 0.01, p*** < 0.001. Statistically significant r-values and their corresponding p-values, as well as BF₁₀ values that provide evidence for test hypothesis are bolded. L, left; R, right.

FIGURE 3

Association between cross-format (non-symbolic-symbolic) neural representational similarity (NRS) and arithmetic fluency in children after training is comparable to that of adolescents from a long-term developmental (LTD) sample. Cross-format NRS of children at post-training from the short-term training (STT) sample (red triangles and regression lines) and that of adolescents group from the LTD sample (purple triangles and regression lines; see details in Figure 1 and Methods) do not significantly correlate with arithmetic fluency in the left intraparietal sulcus/lateral occipital cortex (IPS/LOC), precentral gyrus (PreCG), premotor cortex (premotor), insula and the right central operculum (COper) (Bayes factors [BF₁₀s] < 3). Correlation coefficients were not significantly different between children at post-training from STT and adolescents from LTD in these 6 ROIs (ps > 0.36), which were among the ROIs defined from Schwartz et al. (2021) (see also Figure 4a). Results from the other nine ROIs also showed no significant brain-behavior correlations at post-training in children in the STT sample and in adolescents in the LTD sample (Supplementary Results). L, left; R, right.

FIGURE 4

Cross-format (non-symbolic–symbolic) neural representational similarity (NRS) in multiple brain regions jointly contributes to arithmetic fluency in children before, but not after, short-term training, (a) Regions of interest (ROIs). A total of 15 ROIs were defined from Schwartz et al. (2021). (b) Short-term training (STT) sample. Cross-format NRS in all ROIs jointly significantly predicted arithmetic fluency In children at pre-training (adjusted R² = 0.486, p = 0.003), but not at post-training (adjusted R² = −0.039, p = 0.572). (c) Long-term developmental (LTD) sample. Cross-format NRS in all ROIs jointly significantly predicted arithmetic fluency In children (adjusted R² = 0.423, p = 0.003), but not in adolescents (adjusted R² = −0.191, p = 0.894). Each adjusted R² value was obtained from a multilinear regression analysis predicting arithmetic fluency with cross-format NRS values of all 15 ROIs In each group of each sample included as predictors (see details in Methods), p** < 0.01, p*** < 0.001. COper, central operculum; HIPP, hippocampus; IPS, intraparietal sulcus; L, left; MFG, middle frontal gyrus; PreCG, precentral gyrus; preMotor, premotor cortex; R, right.