The RaPID approach for teaching mathematics: An effective, evidence-based model
Bibliographic record
Abstract
The use of systematic variance and invariance has been identified as a critical aspect of mathematics lessons in many countries with top results in international assessments; however, the literature on teaching strategies is less frequent. In particular, the use of systematic variation to inform teachers’ continuous decision-making during class is uncommon. We elaborate on the five-year longitudinal results from an initiative targeted at elementary level and involving collaboration among two school districts and a university in Alberta along with a resource developer. Data for this study include students’ performance in mathematics, classroom observation, interviews with student and teachers, and analysis of video-recorded lessons. Based on this data, we proposed the Raveling, Prompting, Interpreting, and Deciding (RaPID) model for teaching mathematics, which is informing our efforts to scale up teacher professional learning for teachers across the province. In this presentation, we describe the model and the data supporting its development.
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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 | 0.084 | 0.111 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.012 | 0.006 |
| Science and technology studies | 0.003 | 0.006 |
| Scholarly communication | 0.007 | 0.012 |
| Open science | 0.009 | 0.006 |
| Research integrity | 0.005 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 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".