Arithmetic skills are associated with left fronto-temporal gray matter volume in 536 children and adolescents

The study addresses why individuals differ widely in arithmetic skill and whether these differences are linked to brain structure. Prior functional neuroimaging implicates parietal areas (intraparietal sulcus, IPS; left angular gyrus, AG) in number representation and arithmetic, as well as temporal (left MTG) and frontal (left IFG) regions and the hippocampus. However, findings about how individual differences in arithmetic relate to neural measures are inconsistent, partly due to small samples in prior brain-wide association studies. The purpose here is to test, in a large sample of children and adolescents, whether arithmetic skill relates to gray matter volume (GMV) in key regions implicated by prior work, controlling for language and intelligence, to clarify reliable structural correlates of arithmetic ability.

Functional studies suggest IPS supports numerical magnitude manipulation, while left AG supports retrieval of memorized arithmetic facts. Additional evidence implicates left MTG (phonological processes and fact retrieval), left IFG (verbal working memory, increased demand/complexity), and hippocampus (encoding/retrieval of problem-answer associations early in learning). Structural studies with small samples have linked arithmetic skills to GMV in parietal, frontal, temporal, fusiform, hippocampal, and ventrotemporal regions, but with heterogeneous loci and directions. Recent larger work found minimal concurrent GMV associations after adjusting for total brain volume, highlighting power/reliability issues. Thus, evidence spans parietal, frontal, temporal, and hippocampal regions, but robust, well-powered associations remain unclear.

Design: Cross-dataset voxel-based morphometry (VBM) brain-wide association study of arithmetic skill. Six independent structural MRI datasets were merged, yielding N=536 children/adolescents aged 7.5–15 years (mean 10.58, SD 1.60) from France (sets #1–#2) and the US (sets #3–#6). ADHD diagnoses were present only in sets #3–#6; stimulant medication was withheld ≥24 h before testing. Behavioral measures: Arithmetic skill assessed with WJ-III Calculation or CMAT Basic Calculations Composite (untimed paper-pencil; mixed operations: addition, subtraction, multiplication, division). Additional covariates: vocabulary (NEMI-2 or WASI), reading (Alouette CM for sets #1–#2; TOWRE SWE for sets #3–#6), verbal IQ (NEMI-2 Comparison or WASI Similarities), non-verbal IQ (NEMI-2 or WASI Matrix). Scores were z-transformed within each dataset due to differing instruments. MRI acquisition: Sets #1–#2 on Siemens 3T Prisma (64-channel coil; T1 MPRAGE-like: TR=3500 ms, TE=2.24 ms, flip=8°, 0.875 mm isotropic). Sets #3–#6 on Siemens 3T Trio-Tim (16/32-channel coils; TR=2300 ms, TE=3.36 ms, flip=9°, 1 mm isotropic). Preprocessing: CAT12 within SPM12. Segmentation into GM/WM/CSF; DARTEL normalization to MNI; quality checks; total intracranial volume (TIV) estimation; 8 mm FWHM smoothing. Mean voxel intensity within ROIs used as proxy for GMV. Regions of interest: Seven anatomically defined ROIs (to avoid circularity): bilateral IPS (hIP1–hIP3, Anatomy Toolbox), left AG, left MTG, left IFG (opercular + triangular parts), bilateral hippocampus (AAL3). Statistical analysis: Linear mixed-effects models per ROI with GMV (mean intensity) as outcome; fixed effects: arithmetic score, TIV, age, sex, ADHD; random intercepts: arithmetic test (WJ-III vs CMAT) and scanning site (France vs US). Parsimonious models with random intercepts only (random slopes did not improve fit >5%). Additional models added reading, vocabulary, verbal IQ, and non-verbal IQ separately and jointly to test specificity. Bayesian mixed-effects models (BayesFactor in R) compared models with vs without arithmetic score to compute Bayes factors (BF) quantifying evidence for relation (H1) vs no relation (H0). Exploratory whole-brain VBM regression was also run (not accounting for nesting), with FWE correction. Exploratory cortical thickness analysis (CAT12 SBM pipeline; whole-brain regression including TIV, age, sex, ADHD, site, language, IQ covariates) assessed CT–arithmetic relations; none were significant.

- Across ROIs, arithmetic skill positively related to GMV only in left IFG and left MTG. - Left IFG (without language/IQ covariates): Arithmetic estimate ~0.004, t=2.79, p=0.01; age and TIV significant covariates. With all language and IQ covariates included, the arithmetic effect remained significant (estimate ~0.004, t=2.30, p=0.02; Table 5). Results also robust when adding each covariate separately (e.g., with reading: β=0.004, t=3.169, p=0.002; with vocabulary: β=0.004, t=2.459, p=0.014; with non-verbal IQ: β=0.003, t=2.258, p=0.024; with verbal IQ: β=0.004, t=2.304, p=0.022). - Left MTG (without language/IQ covariates): Arithmetic estimate ~0.004, t=3.54, p<0.001. With all language and IQ covariates included, the arithmetic effect remained significant (estimate ~0.003, t=2.57, p=0.01; Table 6). Also robust with each covariate alone (e.g., with reading: β=0.004, t=3.604, p<0.001; with vocabulary: β=0.004, t=2.741, p=0.006; with non-verbal IQ: β=0.003, t=2.688, p=0.007; with verbal IQ: β=0.003, t=2.569, p=0.010). - Bayesian evidence: Substantial evidence for relation in left IFG (BF10=4.95) and very strong in left MTG (BF10=37.61). Evidence for lack of relation in left AG (BF01=11.58), left IPS (BF01=7.10), and hippocampus (left: BF01=10.38; right: evidence favored H0). Right IPS: anecdotal evidence against a relation (BF01=2.82). - Exploratory whole-brain analysis corroborated left IFG and left MTG clusters (supplementary). Exploratory cortical thickness analyses found no significant associations with arithmetic.

Findings indicate that individual differences in arithmetic skill in children and adolescents are associated with structural variation in left fronto-temporal cortex, specifically the left IFG and left MTG, rather than parietal cortex or hippocampus. This pattern partially diverges from prior BWAS emphasizing parietal regions. The left MTG result aligns with proposals that phonological processes and fact retrieval support arithmetic fluency. The left IFG association may reflect contributions of verbal working memory, interference suppression, sequential/syntactic processing shared with language, or attentional control; however, these functional interpretations are tentative. Importantly, the associations remained after controlling for reading, vocabulary, and IQ, suggesting specificity beyond general language and cognitive abilities. Results underscore the value of adequately powered samples for reliable brain–behavior associations in educational neuroscience.

This large-scale BWAS (n=536) demonstrates that higher arithmetic skill is linked to greater GMV in left IFG and left MTG in school-age children and adolescents, with no evidence for associations in parietal cortex or hippocampus. The work clarifies structural correlates of arithmetic beyond general language and IQ effects and emphasizes the need for large samples in brain–behavior research. Future studies should: (1) examine operation-specific associations (addition, subtraction, multiplication, division); (2) use alternative morphometric measures (e.g., deformation-based, surface-based metrics such as cortical folding and surface area) to pinpoint the structural features driving VBM effects; (3) conduct well-powered, age-stratified longitudinal analyses to track developmental changes; and (4) integrate functional measures to specify the cognitive mechanisms linking left IFG/MTG structure to arithmetic.

- Arithmetic skill measured by aggregate calculation scores (WJ-III or CMAT) combining operations, preventing operation-specific analyses. - VBM used as the structural metric; other measures (deformation-based morphometry, surface-based metrics like cortical thickness, folding, surface area) may reveal different associations. Exploratory cortical thickness analyses found no significant relations, suggesting the VBM effects may relate more to surface area/folding than thickness. - Despite the large overall sample, power was insufficient for reliable subgroup analyses (e.g., narrow age bands), and exploratory whole-brain/CT analyses did not account for the nested data structure. - Scanner/site differences existed (France vs US, different MRI systems), though modeled as random effects.