Primary historical sources in the teaching and learning of mathematics:short and long term effects
Bibliographic record
Abstract
The study of primary historical sources is often described as a rewarding pursuit worth the effort, despite being extremely demanding for both teachers and students.In the present talk, focus shall be on recent empirical research findings from a Danish study and on the short and long term effects for students of having been exposed to readings of historical primary sources.The Danish study revolved around two specially designed, so-called, HAPhmodules, which are teaching modules on aspects of the History, Application, and Philosophy of mathematics.One of these modules concerned the early history of graph theory and its later application to shortest path algorithms, and the other concerned the history of Boolean algebra and its later application to electric circuit design.Upper secondary mathematics students, exposed to readings of primary source material as part of these modules in 2010-11, illustrate the short term effects; while undergraduate mathematics students exposed to the same material in 2012, and interviewed in 2015, illustrate the long term effects.
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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 | 0.017 | 0.079 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.006 |
| Science and technology studies | 0.005 | 0.007 |
| Scholarly communication | 0.010 | 0.008 |
| Open science | 0.002 | 0.014 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.018 | 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".