How children interface number words with perceptual magnitudes
Bibliographic record
Abstract
How do children map symbolic number words to continuous and noisy perceptual magnitudes? We explore how 5- to 12-year-olds attach novel units to number, length, and area by examining whether verbal estimation performance is primarily predicted by access to number words, the precision of children’s underlying perceptual systems, or a more general process in structurally aligning number words with perceptual magnitudes. We find that from age five onward, children can readily form novel mappings between number words and perceptual magnitudes, including dimensions they have no experience estimating in (e.g., length, area), and even when faced with completely novel units (e.g., mapping a collection of three dots to “one” unit for number). Additionally, estimation performance was poorly predicted by the noise in their underlying perceptual magnitudes and number word access. Instead, we show that individual differences in children’s abilities to translate continuous perceptual signals into discrete categories underlie verbal estimation performance.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".