Making School Math Messy: Deepening Mathematical Appreciation in Gifted High School Students
Bibliographic record
Abstract
The literature and our experiences suggest that gifted students believe doing mathematics is fi nding the right answer and learning mathematics involves memorizing isolated procedures. These beliefs are asynchronous with reform efforts predicated by a socio-cultural view of the teaching of mathematics and with the discipline of mathematics described within the philosophy of mathematics literature. We developed a philosophy of mathematics unit based on a notion of ’messiness’ and implemented it with gifted high school students during a philosophy course. Messiness highlights the uncertain, social, and contextual aspects of school mathematics. Preliminary analyses suggest that while most students did not engage with alternative visions of mathematics, some did, and their appreciation of mathematics seemed to grow. We conclude that high school math for all gifted students, not just those taking philosophy, should be infused with messiness.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.004 | 0.008 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.001 | 0.007 |
| Research integrity | 0.001 | 0.003 |
| 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".