Notice bibliographique
Résumé
In this research, we analysed two didactic situations in order to study the functioning of arithmetic knowledge in the context of the transition from arithmetic to algebra, considering intellectual validation as a fundamental issue in this change of practice. These situations were tested in four classes, two classes in Argentina (level corresponding to the 1st year of secondary education in Quebec) and two classes in Quebec (2nd year of secondary education). The aim of our study was to highlight some of the limitations of arithmetic practices and the associated validation practices, when it comes to resolving a contradiction and validating the general nature of an algebraic formula. We were also interested in analysing the development of situations in the context of classes characterised by different didactic contracts: efforts to adapt the pupils' knowledge in order to provoke a change in practice (change of contract); the teacher's work within the constraints imposed by the situations.The design of the situations was based on the theory of situations and on several studies in the didactics of algebra. The problematic of our research led us to a more detailed analysis of certain aspects of these theorisations. Taking into account the need to develop a practice of intellectual validation, as a problematic in itself and as a possible source for giving meaning to algebraic practices, led to a closer examination of the notion of adidacticity and validation situations, in the theory of didactic situations developed by Brousseau (1998).Our attempt to set up a validation practice enabled us to observe a different way in which arithmetical knowledge functioned, by making it possible to give meaning to the pupils' entry into algebraic practices, and then to develop a particular language. At the same time, the development of this language has encouraged new objects to enter the classroom - 'numerical expressions', which were previously a means of calculation, are now becoming objects of reflection. But recognition of the explanatory and operative nature of writing requires a different use of the properties of operations, which are the fruit of social agreements and cultural conventions specific to a new practice. Our research has enabled us to characterise this change in practice and contract, and to realise the complexity of the teacher's role in this context.The development of social agreements and cultural conventions specific to a new practice involves the production of situational knowledge. Our research has characterised the nature of this production and the nature of the knowledge involved, by identifying different levels of knowledge in play. We have analysed this knowledge and the conditions of its production in the light of existing theorising; finally, we have formulated questions that have not yet been addressed in research into the didactics of mathematics.
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.
Comment cette classification a été obtenuedéplier
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 | 0,022 | 0,009 |
| Méta-épidémiologie (sens strict) | 0,001 | 0,001 |
| Méta-épidémiologie (sens large) | 0,001 | 0,000 |
| Bibliométrie | 0,000 | 0,001 |
| Études des sciences et des technologies | 0,001 | 0,001 |
| Communication savante | 0,001 | 0,000 |
| Science ouverte | 0,001 | 0,000 |
| Intégrité de la recherche | 0,001 | 0,001 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,003 | 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 découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule tête enseignante, pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».