Can children represent and compute over mixed sets with the Approximate Number System?
Bibliographic record
Abstract
Considerable debate exists over the kinds of numbers the Approximate Number System (ANS) can represent and compute over. Across three experiments (N = 218), we show that children can represent and add large mixed sets (i.e., large collections that include two types of items) with the ANS. In Experiment 1, 5-7-year-olds completed a replication of a large non-symbolic number addition task using an online asynchronous format. In Experiments 2 and 3, 5-7-year-olds completed a variation of that addition task with mixed sets of stimuli either area-controlled or area-correlated and again performed above chance level. Taken together, these findings are a crucial first step in examining whether the ANS can represent all positive rational numbers (i.e., fractions or ratios), as opposed to exclusively integers. In sum though, our findings suggest that children can represent and compute over large mixed sets of stimuli with the ANS.
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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 | 0.010 |
| 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 | 0.003 | 0.006 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".