Humanizing Proof-based Mathematics Instruction Through Experiences Reading Rich Proofs and Mathematician Stories
Bibliographic record
Abstract
Abstract The Reading and Appreciating Mathematical Proofs (RAMP) project seeks to provide novel resources for teaching undergraduate introduction to proof courses centered around reading activities. These reading activities include (1) reading rich proofs to learn new mathematics through proofs as well as to learn how to read proofs for understanding and (2) reading mathematician stories to humanize proving and to legitimize challenge and struggle. One of the guiding analogies of the project is thinking about learning proof-based mathematics like learning a genre of literature. We want students to read interesting proofs so they can appreciate what is exciting about the genre and how they can engage with it. Proofs were selected by eight professors in mathematics who as curriculum co-authors collected intriguing mathematical results and added stories of their experience becoming mathematicians. As mathematicians of colour and/or women mathematicians, these co-authors speak to the challenges they faced in their mathematical history, how they overcame these challenges, and the key role mentors and community have played in that process. These novel opportunities to learn to read and read to learn in the proof-based context hold promise for supporting student learning in new ways. In this commentary, we share how we have sought to humanize proof-based mathematics both in the reading materials and in our classroom implementation thereof.
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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 | 0.011 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.007 | 0.021 |
| Scholarly communication | 0.009 | 0.007 |
| Open science | 0.002 | 0.013 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 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; 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".