Students using programming for pure and applied mathematics investigations
Bibliographic record
Abstract
In this paper, we recount our research on undergraduate mathematics students learning to use programming for mathematics investigation projects. More precisely, we focus on how a particular theoretical perspective (the Instrumental Approach) helps us better understand this student activity. Pulling data from students' and instructors' experiences in a sequence of courses (offered since 2001), our results expose, at the micro and macro levels, how the student activity is organized (through stable 'ways of doing'), and highlights the complexity of this activity (as an intertwined web of 'ways of doing' involving a combination of both mathematics and programming competencies). We end with concrete recommendations to instructors. Dans cet article, nous présentons notre recherche sur les étudiants de premier cycle en mathématiques apprenant à utiliser la programmation pour des projets d'investigation en mathématiques. Plus précisément, nous nous concentrons sur la façon dont une certaine perspective théorique (l'Approche instrumentale) nous aide à mieux comprendre cette activité de l’étudiant. S’appuyant sur des données des expériences d’étudiants et d’instructeurs dans une séquence de cours (offerts depuis 2001), nos résultats décrivent comment l'activité de l’étudiant est organisée (par le biais de «façons de faire» stables), et met en évidence la complexité de cette activité (comme un réseau entrelacé de « manières de faire » impliquant une combinaison de compétences en mathématiques et en programmation). Nous terminons par quelques recommandations concrètes pour les instructeurs.
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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 | 0.005 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.008 | 0.004 |
| Open science | 0.002 | 0.008 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".