Children can map precise number words to approximate arithmetic prior to formal instruction.
Bibliographic record
Abstract
as the correct answer. Here, we show that once children have mapped number words to their intuitive number sense, they can perform approximate arithmetic estimation: that is, they can attach precise number words to approximate division operations. Forty-five 5- to 8-year-olds completed an approximate division task in which they were given a unit of one, three, or five objects and had to then estimate between five and 110 briefly presented dots. Children provided highly accurate estimates and flexibly switched their responses according to the divisor provided. We further show that they did so without relying on various possible "cheats" and discuss three possible mechanisms for this competency. These findings highlight how the interface between number words and intuitive numerical capacities can support rich mathematical reasoning, including helping children arrive at a single approximate answer despite the inherent uncertainty of the underlying representations. (PsycInfo Database Record (c) 2025 APA, all rights reserved).
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".