MathCHOPS: A Platform for Developing Collaborative Higher Order Problem Solving in Mathematics
Bibliographic record
Abstract
We describe an exploratory pilot study and a collaborative platform designed to engage novice learners in higher-order thinking processes.The theoretical motivation for and facets of novel item design are described.The pilot study took place in a high-school enrichment classroom in Shanghai.Gain scores in higher-order problem solving tests were higher than those in a control classroom, but differences were not statistically significant.Pre-and post-measures of expert-like attitudes towards mathematics problem solving and perceptions of collaboration were also used, and overall differences were also not statistically significant.Preliminary evidence, however, suggests that higher perceived benefits/enjoyment of collaboration may have been offset by higher perceived challenges/costs of collaboration.
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How this classification was reachedexpand
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 | 0.010 | 0.002 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.000 |
| Bibliometrics | 0.002 | 0.024 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.006 |
| Insufficient payload (model declined to judge) | 0.001 | 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; both teacher heads agree on what is shown here.
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".