Distinct neural representational changes following cross-format number tutoring in children with mathematical difficulties

Abstract

Children with mathematical difficulties (MD) often struggle to connect abstract numerical symbols with corresponding nonsymbolic quantities, a foundational skill for mathematical development. We evaluated a 4-week personalized cross-format number (CFN) tutoring program designed to strengthen these symbolic-nonsymbolic mappings in children with MD aged 7-10 years. CFN tutoring was associated with significant improvements in numerical and arithmetic fluency. Neural representational similarity (NRS) analysis revealed that deficient cross-format NRS in children with MD was normalized following tutoring, aligning with pre-tutoring levels of typically-developing (TD) peers. This normalization was most pronounced in parietal and parahippocampal regions known to support quantity and spatial representation. We observed a distinctive pattern of neural plasticity across groups-children with MD showed increased cross-format NRS following tutoring, while TD children showed a decrease-suggesting a nonlinear, skill-dependent plasticity. These findings underscore the need for developmentally tailored interventions to support children with MD through targeted, evidence-based strategies.

Fig. 1. Study design, analysis steps, and key hypotheses.

a Study design. Children with mathematical difficulties (MD) and typically developing (TD) peers underwent pre-tutoring assessments and fMRI scans, followed by a 4-week cross-format number (CFN) tutoring program and post-tutoring assessments and fMRI scans. b fMRI task and analysis. Participants performed nonsymbolic and symbolic number comparison tasks during fMRI scans. We examined whether CFN tutoring induced changes in cross-format neural representational similarity (NRS) between nonsymbolic and symbolic numbers. c Neural normalization hypothesis. We posited that CFN tutoring would enhance cross-format NRS in children with MD at post-tutoring, reaching levels similar to TD peers at pre-tutoring. d Linear and nonlinear model hypotheses. Expected outcomes illustrate similar or distinct effects of CFN tutoring across MD and TD groups. A linear model predicts universal decreases in cross-format NRS across MD and TD groups, consistent with the symbolic estrangement account, which suggests increases in dissociation between symbolic and nonsymbolic number representations across math skill development. Alternatively, a nonlinear model predicts divergent neural plasticity: children with MD would exhibit increased cross-format NRS following tutoring, reflecting enhanced mapping between symbolic and nonsymbolic number representations; in contrast, TD children would show decreased cross-format similarity post-tutoring, reflecting a shift toward more distinct symbolic number representations. e Linear and nonlinear models of association and dissociation of number formats. Schematic models are presented to illustrate potentially similar or distinct trajectories of changes in cross-format NRS as a function of short-term learning in response to tutoring in MD and TD groups. ** hypothetical significant difference. n.s. hypothetical non-significant difference.

Fig. 2. Behavioral normalization of weak cross-format similarity and transfer of learning to arithmetic skills in children with MD following cross-format number tutoring.

a Behavioral normalization of weak cross-format similarity between nonsymbolic and symbolic numbers in children with MD. As a measure of cross-format similarity in numerical processing, a metric of between-format dissimilarity was obtained as the absolute difference between nonsymbolic and symbolic number comparison task efficiency. Lower scores on between-format dissimilarity represented higher cross-format similarity in numerical processing. Pre-tutoring, the MD group had higher behavioral between-format dissimilarity (lower cross-format similarity in numerical processing), compared to TD peers. Post-tutoring, this dissimilarity was reduced, aligning with pre-tutoring TD levels. b Transfer of learning to arithmetic fluency in children with MD. Tutoring led to a significant transfer of learning to arithmetic fluency in the MD group, narrowing the pre-existing gap with TD peers. ^†p < 0.10, ^**p < 0.01, ^***p < 0.001, d = Cohen’s d. MD = children with mathematical difficulties, TD = typically developing children.

Fig. 3. Neural normalization in children with MD following cross-format number tutoring.

a Whole-brain analysis revealed pre-tutoring differences in cross-format NRS between the MD and TD groups in key brain regions implicated in memory and visuospatial numerical processing, including the PHG, SPL/IPS, LOC/IPS, PreCG, and Premotor. Figure represents the significant voxels overlaid onto the pediatric T1-weighted brain template. b Tutoring led to normalization of cross-format NRS in children with MD at post-tutoring, which was comparable to the pre-tutoring level in TD children (Supplementary Table 4). Effect sizes illustrate a reduction in neural disparity of the MD group following CFN tutoring, when compared to the TD group at pre-tutoring, across all brain regions. c Support-vector machine (SVM)-based classification was performed on 10 brain regions identified from the whole-brain analysis where children with MD exhibited lower pre-tutoring cross-format NRS, compared to their TD peers (Fig. 3a; see Supplementary Table 3 for details). d SVM classifier revealed significant difference in cross-format NRS between the MD and TD groups at pre-tutoring (p = 0.004), but not between the MD group at post-tutoring and the TD group at pre-tutoring (p = 0.232). ^**p < 0.01, ^***p < 0.001. d = Cohen’s d. MD = children with mathematical difficulties, NRS = neural representational similarity, TD = typically developing children, L = Left, R = Right.

Fig. 4. Differential neurodevelopmental trajectories of math skill development in the MD and TD groups following cross-format number tutoring.

a Time (pre-tutoring, post-tutoring) x Group (MD, TD) ANOVA revealed a significant Time x Group interaction on cross-format NRS in 5 brain regions, including the parahippocampal gyrus (PHG), occipital fusiform gyrus (FG), and cerebellum. Figure represents the significant voxels overlaid onto the pediatric T1-weighted brain template. b Time x Group interaction effect was characterized by relative increases in cross-format NRS in the MD group and relative decreases in cross-format NRS in the TD group in observed brain regions. c The observed changes across the two groups aligned with distinct patterns of cross-format association and dissociation of numbers: on average, children with MD showed enhanced cross-format NRS at post-tutoring, reaching levels similar to pre-tutoring TD levels; TD children shifted towards more specialized, distinguishable neural representations between the two number formats, aligned with their increased proficiency in symbolic numbers. See Supplementary Table 6 and Supplementary Table 8 for details. ^*p < 0.05. d = Cohen’s d. MD = children with mathematical difficulties, NRS = neural representational similarity, TD = typically developing children, L = Left, R = Right.