An Open Architecture to Improve Mathematical Competence in High School
Bibliographic record
Abstract
This paper presents the development of an intelligent tutoring system called TURING (French acronym of «TUtoRiel INtelligent en Geometrie») in a multidisciplinary project, that joint recent research in didactic of mathematics with the possibilities of computer-based learning environments. From the educational point of view, the system is helpful for the student to improve problem solving aptitudes, mathematical reasoning abilities and communication skills using natural and mathematical language. In addition, the system is helpful to assist the teacher in his responsibility of attending the diversity of the development of mathematical competences in a whole class. From the technical point of view, the TURING architecture is a multi-agent system conceived in a flexible approach so that a teacher can adjust the heuristic and discursive features according to specific practices with real students. In particular, for the discovery of a conjecture or for the realization of a mathematical proof, the system consents to adapt, in the problem solving process, the space of meaningful actions and, in argumentative process, the set of strategic message with pedagogical agents. The TURING is a client-server application that is in its phase of implementation in Java programming language.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.006 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".