Sur le rôle de l’ordre en analyse à la transition secondaire – supérieur
In France, current curricular choices tend to make the role of order in analysis invisible. They implicitly favour a topological point of view related to metric spaces, which we find in the notion of absolute value, generalised to that of distance. These choices lead us to leave aside a complementar...
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| Publicado en: | URI:https://journals.openedition.org/adsc, |
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| Autores principales: | , , |
| Formato: | Article ou chapitre numérique |
| Lenguaje: | Français |
| Publicado: |
Annales de Didactique et de Sciences Cognitives
2025
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| Materias: | |
| Acceso en línea: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| Sumario: | In France, current curricular choices tend to make the role of order in analysis invisible. They implicitly favour a topological point of view related to metric spaces, which we find in the notion of absolute value, generalised to that of distance. These choices lead us to leave aside a complementary perspective that emphasises ordered sets, in which the connected parts of ℝ, which are intervals, play a central role. In our epistemological study and using two examples from the secondary-tertiary transition, we show that considering the relationship between connectedness and completeness in the set of real numbers encourages an explicit consideration of the role of order in analysis, especially in proofs. Finally, we suggest some avenues of research opened up by this work to help take into account the dual nature of this transition. |
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