Developmental Changes in Nonsymbolic and Symbolic Fractions Processing: A Cross‐Sectional fMRI Study
Bibliographic record
Abstract
A substantial body of research has demonstrated that human and nonhuman animals have perceptually-based abilities to process magnitudes of nonsymbolic ratios (e.g., ratios composed by juxtaposing two-line segments). In prior work, we have extended the neuronal recycling hypothesis to include neurocognitive architectures for nonsymbolic ratio processing, proposing that these systems might support symbolic fractions acquisition. We tested two key propositions: (1) children should show neural sensitivity to nonsymbolic fractions before receiving formal fractions instruction, and (2) they should leverage this foundation by recruiting neural architectures for nonsymbolic fractions processing for symbolic fractions. We compared nonsymbolic and symbolic fractions processing among 2nd-graders (n = 28, ages 7.5-8.8), who had not yet received formal symbolic fractions instruction, and 5th-graders (n = 33, ages 10.3-11.9), who had. During fMRI scanning, children performed ratio comparison tasks, determining which of two nonsymbolic or symbolic fractions was larger. Both cohorts showed behavioral and neural evidence of processing nonsymbolic and symbolic fractions magnitudes, with performance modulated by numerical distance between stimuli. Consistent with our predictions, 2nd-graders recruited a right parietal-frontal network for nonsymbolic fractions but not for symbolic fractions, whereas 5th-graders recruited a bilateral parietal-frontal network for both, overlapping with but extending beyond that of 2nd-graders. Furthermore, nonsymbolic-symbolic neural similarity in the intraparietal sulcus was greater for 5th-graders than for 2nd-graders. These results present the first developmental neuroimaging evidence that neural substrates for nonsymbolic ratios exist before formal learning, which may be recycled to process symbolic fractions. SUMMARY: 2nd-graders, prior to formal fractions instructions, already recruit a right parietal-frontal network when comparing nonsymbolic fractions. 5th-graders, who have received some formal fractions instruction, recruit this same network not only for nonsymbolic fractions, but also for symbolic fractions. These findings are consistent with the neuronal recycling account, which posits that symbolic fraction processing builds on neural substrates originally used for nonsymbolic fraction processing. These findings suggest that pedagogical strategies focus on supporting this recycling process may enhance students' understanding of symbolic fractions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".