Symbiotic Symbols: Symbolic (but not Nonsymbolic) Number Representation Predicts Calculation Fluency in Adults
Bibliographic record
Abstract
There is debate in the numerical cognition literature concerning symbolic and nonsymbolic number representation systems as foundations for more complex mathematical skills.The purpose of this study was to investigate the relation between these number representation systems and calculation fluency.The present study used 51 university students.Participants completed symbolic and nonsymbolic magnitude comparison and ordinality tasks on an iPad as well as a penand-paper version of the addition and subtractionmultiplication subtest of the Kit of Factor-Referenced Cognitive Tests (French, Ekstron, & Price, 1963).Data reductions were performed and a symbolic and a nonsymbolic factor were constructed.A multiple regression analysis revealed that the symbolic factor was a significant predictor of calculation fluency, but the nonsymbolic factor was not.Two separate repeated measures ANOVAs revealed 3-way interactions between task, distance, and format for both accuracy and response time.These results support the view that the two systems develop separately.
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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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".