Representing quantity beyond whole numbers: Some, none, and part.
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Previous research has demonstrated how children develop the ability to use notational representations to indicate simple quantities. These studies have shown a developmental shift from the use of idiosyncratic, to analogical, to conventional, numerical notations. The present paper extends these findings by reporting the results from a study in which children from 3 to 7 years old were asked to write a representation to indicate a quantity presented in a game-like scenario. Three kinds of quantities were included: whole numbers, zeros, and fractions. The children's notations were shown to them shortly after they were produced and then again two weeks later to see if children could interpret them. The results showed the familiar developmental pattern towards increased use of conventional notations for all quantities. The ability to read the notations was greatest for conventional numbers where performance was at ceiling, lower for analogue representations, and very poor for idiosyncratic global recordings. Children's choice of a notational format was influenced almost entirely by their age and not by the quantity being represented. Children were able to solve the zero problems almost as well as they could the whole numbers, but their understanding and use of representations for fractions was very limited.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 it