Parallel individuation supports numerical comparisons in preschoolers
Bibliographic record
Abstract
While the approximate number system (ANS) has been shown to represent relations between numerosities starting in infancy, little is known about whether parallel individuation – a system dedicated to representing objects in small collections – can also be used to represent numerical relations between collections. To test this, we asked preschoolers between the ages of 2 ½ and 4 ½ to compare two arrays of figures that either included exclusively small numerosities (< 4) or exclusively large numerosities (> 4). The ratios of the comparisons were the same in both small and large numerosity conditions. Experiment 1 used a between-subject design, with different groups of preschoolers comparing small and large numerosities, and found that small numerosities are easier to compare than large ones. Experiment 2 replicated this finding with a wider range of set sizes. Experiment 3 further replicated the small-large difference in a within-subject design. We also report tentative evidence that non- and 1-knowers perform better on comparing small numerosities than large numerosities. These results suggest that preschoolers can use parallel individuation to compare numerosities, possibly prior to the onset of number word learning, and thus support previous proposals that there are numerical operations defined over parallel individuation (e.g., Feigenson & Carey, 2003; https://doi.org/10.1111/1467-7687.00313 ).
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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 | 0.002 | 0.012 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".