Developmental Changes in Nonsymbolic and Symbolic Fractions Processing: A Cross-Sectional fMRI study
Bibliographic record
Abstract
A substantial body of research has found that human and nonhuman animals are capable of processing the magnitudes of nonsymbolic ratios. Lewis, Mathews and Hubbard (2015) hypothesized that this ability may depend on a neurocognitive architecture called the ratio processing system (RPS). They further hypothesized 1) that the RPS might serve as a neurocognitive startup tool—an evolutionarily conserved cognitive architecture—and 2) that it can be recycled to support the acquisition of symbolic fractions knowledge. We tested these two predictions of the RPS account by comparing neural signatures of the RPS in 2nd-graders, who have not yet received formal symbolic fraction instruction, and 5th-graders, who have. During fMRI scanning, children performed ratio comparison tasks in which they determined which of two ratios or symbolic fractions was larger. Both cohorts showed behavioral and neural evidence of processing symbolic and nonsymbolic fractions magnitudes, with performance modulated by the numerical distance between stimuli. Consistent with our predictions, 2nd-grade children reliably recruited a right parietal-frontal network for nonsymbolic ratio comparisons but not symbolic fractions, and 5th-grade children recruited a bilateral parietal-frontal network for both nonsymbolic and symbolic fractions that overlapped with, but extended beyond, that found for 2nd-graders. These results present the first neuroimaging evidence that neural substrates for nonsymbolic ratios exist prior to formal learning and that this nonsymbolic foundation may be recycled to process symbolic fractions. These findings open the door for pedagogical strategies that focus on supporting this recycling process to improve 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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".