Instrumental and documentational approaches: from technology use to documentation systems in university mathematics education
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In this article we present an instrumental approach in mathematics education, which focuses on the interactions between students, teachers, and artefacts. This approach analyses mediations attached to the use of a given artefact and instruments developed by the subjects from this artefact along instrumental geneses. We draw on three Research Cases at university to illustrate the use of this approach: the first is about students' geneses with a programming technology; the second about students' and teachers' geneses with a virtual learning environment; and the third about textbooks and teachers professional development. We also introduce the documentational approach, which draws on the instrumental approach, but takes into account the broader range of available resources. It distinguishes resources and documents developed by teachers from these resources, and studies teachers' documentation systems. We present a fourth Research Case concerning the documentation system of a mathematics teacher, and focusing on the place of technologies within this system.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it