Numerical Order Processing in Children: From Reversing the Distance‐Effect to Predicting Arithmetic
Bibliographic record
Abstract
ABSTRACT Recent work has demonstrated that how we process the relative order—ordinality—of numbers may be key to understanding how we represent numbers symbolically, and has proven to be a robust predictor of more sophisticated math skills in both children and adults. However, it remains unclear whether numerical ordinality is primarily a by‐product of other numerical processes, such as familiarity with overlearned count sequence, or is in fact a fundamental property of symbolic number processing. In a sample of nearly 1,500 children, we show that the reversed distance effect—a hallmark of symbolic ordinal processing—obtains in children as young as first grade, and is larger for less familiar sets of numbers. Furthermore, we show that the children's efficiency in evaluating the simplest ordered sequences (e.g., 2‐3‐4, 6‐7‐8) captures more unique variance in mental arithmetic than any other type of numerical sequence, and that this result cannot be accounted for by counting ability. Indeed, performance on just five such trials captured more unique mental arithmetic variance than any of several other numerical tasks assessed here. In sum, our results are consistent with the notion that ordinality is a fundamental property of how children process numerical symbols, that this property helps underpin more complex math processing, and that it shapes numerical processing even at the earliest stages of elementary education.
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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 | 0.002 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".