Numerical Order Processing in Children: From Reversing the Distance‐Effect to Predicting Arithmetic
Why this work is in the frame
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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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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 | 0.000 | 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