Learning programming for mathematical investigations: an instrumental and community of practice approach
Bibliographic record
Abstract
In this article, we seek to understand how university students learn to use programming for mathematical investigations; our precise focus is on how the analysis of social elements in operational knowledge elucidates this learning. We propose a framework coordinating the instrumental approach and communities of practice (CoP) theory. We apply it in the context of project-based university courses (MICA courses), where the CoP of mathematicians using programming for their research is a reference. We investigate the schemes associated with the programming language and its environment developed by students along trajectories of legitimate peripheral participation. We focus on the scheme developed for the goal “validating the programmed mathematics.” Our results indicate that for the same goal, common rules-of-action are developed by students, but differences can appear concerning theorems-in-action. This study also suggests theoretical developments linked with the coordination of the instrumental approach and CoP theory.
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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 | 0.023 | 0.037 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.002 |
| Science and technology studies | 0.006 | 0.054 |
| Scholarly communication | 0.012 | 0.015 |
| Open science | 0.004 | 0.017 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.007 | 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".