Kindergarteners’ symbolic number abilities predict nonsymbolic number abilities and math achievement in grade 1.
Bibliographic record
Abstract
Research has shown that two different, though related, ways of representing magnitude play foundational roles in the development of numerical and mathematical skills: a nonverbal approximate number system and an exact symbolic number system. While there have been numerous studies suggesting that the two systems are important predictors of math achievement, there has been substantial debate regarding whether and how these basic numerical competencies may be developmentally interrelated. Specifically, the causal direction of their relation has been the subject of debate: whether children's approximate number abilities predict later symbolic number abilities (the mapping account) or the other way around (the refinement account). Our sample included 622 kindergarten children (mean age = 62 months, SD = 3.5, 279 females, 75 born outside Canada), whose dot comparison, number comparison, and mixed comparison skills were assessed over three time-points and math achievement assessed over four time-points. We contrasted multiple theoretical predictions of the interrelations between the variables of interest posited by these two developmental accounts using longitudinal random intercept cross-lagged models. Results were most consistent with the refinement account, suggesting that earlier symbolic number ability is consistently the strongest predictor of approximate number ability, mixed-comparison ability, and arithmetic skills. Notably, our results demonstrated that, when individual models are examined in isolation, model fit was adequate or near adequate for all models tested. This highlights the need for future research to contrast competing accounts, as our results suggest the examination of any one account in isolation may not reveal the best fitting developmental model. (PsycInfo Database Record (c) 2021 APA, all rights reserved).
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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 | 0.001 | 0.005 |
| 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 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 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".