Some drivers of test item difficulty in mathematics : an analysis of the competency rubric
Bibliographic record
Abstract
This paper is concerned with the empirical validation of the competency rubric described in another paper presented at the same conference: Turner, Ross (April 2012). Some drivers of test item difficulty in mathematics. Paper presented at the Annual Meeting of the American Educational Research Association (AERA), Vancouver, 13-17 April 2012 http://research.acer.edu.au/pisa/4/ Using items developed for the PISA 2012 survey, and data collected as part of an extensive field trial of the PISA tasks conducted during 2011 in some 67 countries, the authors use multidimensional Rasch modelling and latent regression to examine the following three questions: 1. What is the level of agreement among raters when they apply the competency rubric? 2. Does each of the competencies capture different dimensions of cognitive complexity in the tasks? 3. To what extent do ratings of the cognitive complexity account for (predict) the difficulty of the tasks for students?
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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 | 0.037 | 0.200 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.008 | 0.006 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".