The refinement of a Q-matrix: Assessing methods to validate tasks to skills mapping.
Why this work is in the frame
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Bibliographic record
Abstract
The objective of specifying which skills are required in a given task is fundamental for the accurate assessment of a student’s knowledge and for personalizing tutor interaction towards more relevant and effective assessment and learning. We compare three data driven techniques for the validation of skills-to-tasks mappings. All methods start from a given mapping, typically obtained from domain experts, and use optimization techniques to suggest a refined version of the skills-to-task mapping. To validate the different techniques, we inject perturbations in the Q-matrix and verify whether the original Q-matrix can be recovered. Tests are run over both simulated and real data. The analysis of the Q-matrix refinements of each technique over ten data sets shows that, in general, around 1/2 to 2/3 of the perturbations can be restored to their original values, but a number of poten-tially wrong perturbations are also introduced. The number of correctly restored and falsely switched values vary across the three techniques and between synthetic and real data. For 1 to 10 perturbations injected, simulated data recov-ery rate is around 2/3, and invalid alterations introduced vary around 2 to 3. For real data, the two best techniques generally recover about half the perturbations injected, but introduce between 5 and 7 alterations inconsistent with the original, expert defined Q-matrix, although some of them may be real improvements.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it