Bibliographic record
Abstract
The phrase "opportunities to learn" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed.
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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 | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 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".