Continuous visual properties of number influence the formation of novel symbolic representations
Bibliographic record
Abstract
Numerical symbols are thought to be mapped onto preexisting nonsymbolic representations of number. A growing body of evidence suggests that nonsymbolic numerical processing is significantly influenced by the associated visual properties of continuous quantity (e.g., surface area, density), but their role in the acquisition of novel symbols is unknown. Forty undergraduate students were trained to associate novel abstract symbols with numerical magnitudes. Half of the symbols were associated with nonsymbolic arrays in which total surface area and numerosity were correlated ("congruent"), and the other symbols were associated with arrays in which total surface area was equated across numerosities ("incongruent"). As numbers are represented in multiple formats (words, digits, nonsymbolic arrays), we also tested whether providing auditory nonword labels facilitated symbol learning. Following training, participants engaged in speeded comparisons of the newly learnt symbols. Comparisons were affected by the ratio between the numerosities associated with each symbol, a characteristic marker of numerical processing. Furthermore, comparisons were hardest for large-ratio comparisons of symbols associated with incongruent area and numerosity pairing during learning. In turn, these findings call for the further investigation of visual parameters on the development of numerical cognition.
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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 | 0.000 | 0.005 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".