Le discret et le continu dans l’enseignement des suites et des fonctions en fin de collège et au lycée
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...
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| Publicado no: | URI:https://journals.openedition.org/adsc, |
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| Autor principal: | |
| Formato: | Article ou chapitre numérique |
| Idioma: | Français |
| Publicado em: |
Annales de Didactique et de Sciences Cognitives
2022
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| Assuntos: | |
| Acesso em linha: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| Resumo: | 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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