Ten Tips for Successful Creation of Contextualized Problems for Secondary School Students with Maple
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Notice bibliographique
Résumé
Students at all levels of schooling in all countries of the world need to practice mathematical problem solving to develop competencies that they will apply in real-life scenarios. On the other hand, concerning solving, problem posing refers to both the generation of new problems and the re-formulation of given problems. Teaching mathematics from a problem posing and problem-solving perspective entails more than solving non-routine problems or typical textbook types of problems. It is a way for students to exercise all aspects of problem solving: exploring, conjecturing, examining, testing, and generalizing. Tasks should be accessible and extend students’ knowledge. Even students should formulate problems from given situations and create new problems by modifying the conditions of a given problem. The quality of problems submitted to students is an issue that needs to be carefully considered. This work presents different ways to apply good practices when designing a problem-solving activity with students. It is based on the experience of Digital Math Training, a project whose aim is to develop and strengthen Mathematics and Computer Science skills through problem solving activities using the Advanced Computing Environment (ACE) Maple. After initial training in the laboratories of the schools, 3 students per class - the most skilled or motivated ones - participate in online training. They are asked to solve a problem every 10 days and to submit their solution. Meanwhile, students can participate in weekly synchronous tutoring on the use of Maple and collaborate with their colleagues through forum discussions. Students are selected in an intermediate competition and a final one. In this setting it is important to carefully plan and present the activity to the students, the text of the problem should be clear, and concise, with little storytelling to enter the setting of the problem. The problems should not be too theoretical, although they may inspect specific aspects of the related theory. They need to be solved by starting with simpler requests until the most difficult ones, close to the edge of students' knowledge, are reached. The solutions can make use of a calculator, in our case the ACE Maple. Precise design principles are based on both the adoption of suitable practice and the use of Maple. These principles can be adapted to different situations. The paper describes all these features with examples, according to the literature.
Récupéré en direct depuis OpenAlex et désinversé. Les résumés ne sont pas conservés dans cette base de données : les index inversés représentent 8,6 Go des 9,3 Go de texte de la base, et le serveur dispose de 13 Go libres.
Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,001 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,001 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,002 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découle