algorithme et codage dans les apprentissages

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l'Algorithmie

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Sommaire

Définitions

SI

alors

alors

alors

développer des routines de fonctionnement

formaliser les apprentissages

le savoir être

les savoirs

le savoir faire

Construction des savoirs

Conclusion

Un algorithme apporte une solution effective. C’est une méthode systématique qu’un apprenant peut mettre en œuvre

Un algorithme résout un problème, c’est-à-dire, répond à une question précise posée pour une même famille.

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4 invariants

Preuve et algorithme interagissent. Pour présenter un algorithme et affirmer qu’il résout un problème donné, on en donner une démonstration.

La création d'algorithmes peut s’appuyer sur des modèles théoriques déjà éprouvés.

Un algorithme doit toujours se conclure après un nombre défini d'étapes.

Chaque algorithme a une ou plusieurs entrées

Chaque étape de l'algorithme doit être définie précisemment

5 Définitions

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Il ne s’agit pas tout à fait d’une définition, mais cela soulève les caractéristiques importantes d’un algorithme. La notion de résolution de problème est centrale

Chaque étape de l'algorithme doit être la plus basique possible

Chaque algorithme a une ou plusieurs sortie

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un algorithme est une suite finie et non ambiguë d’opérations ou d’instructions à exécuter dans l’ordre pour résoudre un problème ou obtenir un résultat.

développer des routines de fonctionnement

Quelles formalisations de démarches?

AlgorithmesAlgorigrammes

Un algorigramme, aussi appelé organigramme de programmation, est la représentation visuelle d’un algorithme. Il montre les enchaînements de décisions et d’opérations à faire pour un algorithme donné.

L'algorigramme a de nombreux avantages : il permet de mieux visualiser ces idées, de travailler plus facilement en équipe, d’éviter les erreurs potentielles et il est compréhensible par tous. Il est important, si ce n’est primordial, d’en créer un avant de commencer sa programmation.

• Structure alternative

• boucle et conditions

• Structure linéaire

• L'algorithme le plus simple mais aussi le plus puissant et facile à mettre en oeuvre est l'arbre des choix

• Il permet de mettre en oeuvre des stratégies opératoires et de les confronter afin de mettre en valeur la ou les plus efficientes.

• Visuellement, il explicite des stratégies et amène à faire réfléchir sur l'optimisation.

• Les réseaux de tri sont des exemples d'algortihmes utilisables pour classer et ordonner des informations

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Formaliser des apprentissages

Quelles exploitations par les élèves ?

• Travaux d'élèves sur un algorithme autour du jeu de nim. Attention à la trace mathématique.

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• Coder le déplacement d'un véhicule en valeur absolue et relative.
• Coder en binaire un message

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• Les déplacements aux échec

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• Algorithme et expression écrite

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Construction des savoirs

Quelles traces écrites ?

Algorithmes en maternelle

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• Apprendre à reproduire un algorithme.
• Amener progressivement l’élève à discerner les analogies et des différences, à comparer
• des objets, à les ranger et à affiner son raisonnement logique.
• Développer la pensée logique.
• Suivre une règle, savoir repérer un rythme.
• Apprendre à décoder un modèle : Savoir l’orienter, l’observer et le décrire.
• Apprentissage des notions d’ordre : avant, après, devant, derrière, puis, ensuite, après…

Et notre jeu de Nim alors????

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Algorithmes et scratch

• Conceptualiser un algortihme de résolution de problème, c'est donner aux élèves une situation sur laquelle ils peuvent s'appuyer afin de résoudre une autre situation, qui devient dès lors familière.
• Elle permet également de développer des routines de calcul par la recherche d'un algortihme commun de plus en plus efficient.

Exemple

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Des ressources en ligne

Exerciseurs

Projet 1, 2 ,3 codez

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La notion de résolution de problème est centrale et elle est mise en avant par beaucoup d’auteurs (Garey & Johnson, 1979 ; Beauquier, Berstel, & Chrétienne, 1992 ; Cormen, Leiserson, Rivest, & Cazin, 1994 ; Aho, Hopcroft, & Ullman, 1989). Elle est très liée aux notions d’entrée et de sortie. Les caractéristiques sont d’ailleurs présentes dans la plupart des définitions d’algorithme, mais toutes ne sont pas aussi détaillées. Par exemple, Sedgewick (1988) parle simplement des algorithmes comme des méthodes de résolution de problèmes.

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