Le discret et le continu dans l’enseignement des suites et des fonctions en fin de collège et au lycée
Bibliographic record
Abstract
Notions pertaining to the Calculus field in France, up to the end of Seconde (10th grade), are mainly functions and their graphical representations. Curricula, followed by textbooks, integrate these notions into “the continuous”. This appears to be self-evident since “the discrete” is not explicitly addressed. Sequences, which are a priori part of “the discrete”, are first studied in Première.However, “the discrete” and “the continuous” have mathematical aspects and constitute two worlds (in a sense that we will define) between which it is difficult to delineate a boundary. Students’ activities on tasks which mobilize continuous functions may be carried out in the discrete world as much as in the continuous one. Furthermore, sequences and functions in secondary school count numerous interactions and correct or incorrect analogies. Textbooks make choices in the graphical and algebraical registers which differ from one book series to another, which testifies to the existence of objective difficulties. Lastly, in secondary school and MEEF master, students’ work shows a number of confusions between sequences and functions. This leads us to reflect on a possible introduction of sequences prior to functions.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.016 |
| Scholarly communication | 0.009 | 0.009 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".