Re-thinking ‘normal’ development in the early learning of number
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
In this article we suggest that, notwithstanding noted differences, one unmarked similarity across psychology and mathematics education is the continued dominance of the view that there is a ‘normal’ path of development. We focus particularly on the case of the early learning of number and point to evidence that puts into question the dominant narrative of how number sense develops through the concrete and the cardinal. Recent neuroscience findings have raised the potential significance of ordinal approaches to learning number, which in privileging the symbolic—and hence the abstract—reverse one aspect of the ‘normal’ development order. We draw on empirical evidence to suggest that what children can do, and in what order, is sensitive to, among other things, the curriculum approach—and also the tools they have at their disposition. We draw out implications from our work for curriculum organisation in the early years of schooling, to disrupt taken-for-granted paths.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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