The relation between subitizable symbolic and non‐symbolic number processing over the kindergarten school year
Bibliographic record
Abstract
A long-standing debate in the field of numerical cognition concerns the degree to which symbolic and non-symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and non-symbolic quantities may be processed more similarly within, relative to outside of, the subitizing range. However, it remains unclear whether this unique link exists in young children at the outset of formal education. Further, no study has yet taken numerical size into account when investigating the longitudinal influence of these skills. To address these questions, we investigated the relation between symbolic and non-symbolic processing inside versus outside the subitizing range, both cross-sectionally and longitudinally, in 540 kindergarteners. Cross-sectionally, we found a consistently stronger relation between symbolic and non-symbolic number processing within versus outside the subitizing range at both the beginning and end of kindergarten. We also show evidence for a bidirectional relation over the course of kindergarten between formats within the subitizing range, and a unidirectional relation (symbolic → non-symbolic) for quantities outside of the subitizing range. These findings extend current theories on symbolic and non-symbolic magnitude development by suggesting that non-symbolic processing may in fact play a role in the development of symbolic number abilities, but that this influence may be limited to quantities within the subitizing range.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".