On tasks that lead to praxeologies’ formation: a case in vector calculus
Bibliographic record
Abstract
A praxeology comprises a type of task, a technique to accomplish it, a discourse (technology) explaining this technique and a theory supporting this discourse. We consider a situation where a praxeology was presented to students in a lecture, but they discovered an alternative one while working on a routine exercise. This exercise was then followed by a more challenging question related to immediate results obtained by the students. We analyzed this student experience in view of Chevallard’s six steps of constructing a praxeology. We suggest that observing students’ work on standard exercises may give some productive and innovative ideas for the design of tasks that help students deepen their understanding and encourage theoretical justifications of their solutions. We also comment about possible effects of the explicit requirement to search for the most efficient solution on the formation of praxeologies by students.
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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 | 0.010 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.006 | 0.010 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.004 | 0.004 |
| 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".