The role of numerosity in processing nonsymbolic proportions
Bibliographic record
Abstract
The difficulty in processing fractions seems to be related to the interference between the whole-number value of the numerator and the denominator and the real value of the fraction. Here we assess whether the reported problems with symbolic fractions extend to the nonsymbolic domain, by presenting fractions as arrays of black and white dots representing the two operands. Participants were asked to compare a target array with a reference array in two separate tasks using the same stimuli: a numerosity task comparing just the number of white dots in the two arrays; and a proportion task comparing the proportion of black and white dots. The proportion task yielded lower accuracy and slower response, confirming that even with nonsymbolic stimuli accessing proportional information is relatively difficult. However, using a congruity manipulation in which the greater numerosity of white dots could co-occur with a lower proportion of them, and vice versa, it was found that both task-irrelevant dimensions would interfere with the task-relevant dimension suggesting that both numerosity and proportion information was automatically accessed. The results indicate that the magnitude of fractions can be automatically and holistically processed in the nonsymbolic domain.
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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 | 0.001 | 0.000 |
| 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 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".