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Impact des formulations sur la résolution de problèmes additifs chez l’enfant de 6 a 10 ans

How the wording of problems works on solving additive problems in children from 6 to 10

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Résumé

Nous avons conduit une expérience afin d’étudier l’impact des formulations des énoncés sur la résolution de problèmes arithmétiques additifs chez des enfants de 6 à 10 ans. Trois variables ont été contrôlées, toutes inter-sujets. Tous les problèmes suivaient le même patron sous-jacent — un état initial (Ei), deux transformations (T1 et T2), un état final (Ef) — mais l’inconnue était tantôt Ef (problèmes S1) tantôt Ei (S2). Les transformations étaient soit formulées en second (01) soit en premier (02). Enfin, la question se trouvait en position soit finale (Q1) soit initiale (Q2).

Cent quatre vingt douze sujets (64 six, huit et dix ans) ont été soumis chacun à huit problèmes de la même modalité. Les difficultés de calcul numérique étaient contrôlées de manière à les rendre approximativement «proportionnelles» à l’âge.

Les résultats obtenus à partir d’une analyse des scores puis des procédures mettent en évidence que: a) Les problèmes portant sur la recherche de l’état final (S1) sont facilement et précocement résolus alors qu’une nette progression se manifeste avec ceux S2. b) Le placement en tête des transformations (02) et de la question (Q2) entraîne un accroissement systématique et très significatif des scores. c) Les procédures utilisées pour la résolution sont, à 6 et 8 ans, très dépendantes des formulations.

Nous proposons une interprétation en termes de connaissances disponibles en M.L.T. et de limitations de la capacité de traitement en mémoire de travail.

Abstract

An experiment was carried out concerning arithmetical problem solving in children. Three between sujects variables were manipulated. All problems followed the same underlying pattern with an initial state (Ei), two additive transformations (T1 and T2), and a final state (Ef); yet the unknown state concerned either Ef (S1 problems) or Ei (S2 problems). The order of introducing the transformations was counterbalanced: either state first (O1 order) or transformations first (O2). Finally, the question was located either at the end of the problem (Q1) or at its beginning (Q2).

One hundred and ninety two subjects (64 six, eight, and ten year-olds) were submitted to 8 different problems of the same type. The difficulties of the numerical series were tentatively controlled on an atempt to render the computations roughly «proportional» to ages.

Quantitative and qualitative analysis were conducted. Results show that: a) Problems with final state unknown (S1) are solved more easily and early, whereas problems with initial state unknown (S2) are better solved as the children grow older. b) Introducing the transformations first (O2) and placing the question at the beginning of the problem-text (Q2) yields better performances c) The procedures used to solve the problems are clearly dependant on the wording of the problems.

An interpretation is proposed which takes in account both the knowledge available in L.T.M. and the limitations of working memory.

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Authors and Affiliations

  1. Laboratoire de Psychologie, 36, Rue Chabot-Charny, 21000, Dijon, France

    Michel Fayol & Hervé Abdi

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  1. Michel Fayol
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  2. Hervé Abdi
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Additional information

Cette recherche a pu être conduite grâce à une subvention de l’Etablissement Public Régional de Bourgogne (Contrat EPR 1982–1984) et à l’aide consécutive à la Recommandation par la Direction de la Recherche du Ministère de l’Education Nationale. Nous remercions C. Bastien et J. Brun pour eurs commentaires à propos d’une première version de cet article.

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Fayol, M., Abdi, H. Impact des formulations sur la résolution de problèmes additifs chez l’enfant de 6 a 10 ans. Eur J Psychol Educ 1, 41–58 (1986). https://doi.org/10.1007/BF03177410

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  • DOI: https://doi.org/10.1007/BF03177410

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