Integrating numerical cognition research and mathematics education to strengthen the teaching and learning of early number
Bibliographic record
Abstract
This study reports on the design, implementation, and effects of a 16-week (25-hour) mathematics Professional Development (PD) model for K-3 educators (N=45) and their students (N=180). A central goal of the PD was to better integrate numerical cognition research and mathematics education. The results of the first iteration (Year 1), indicated that compared to a control group, both teachers and students benefitted from the intervention. Teachers demonstrated gains in self-perceived and actual numerical cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on a measure of self-perceived numerical cognition knowledge, but no gains in actual numerical cognition knowledge. At the student level, there was some evidence of gains in numeration. Given the mixed findings, questions remain as to why the model may be effective in one school context but not another.
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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 | 0.004 |
| 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 | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".