Trois problÈmes semblables de moyenne
pas si semblables que ça ! l’influence de la

structure d’un problÈme sur les rÉponses des

ÉlÈves

 

THREE SIMILAR MEAN PROBLEMS: ARE THEY REALLY

THAT SIMILAR? RESEARCH ON THE INFLUENCE OF THE

STRUCTURE OF THE PROBLEM ON STUDENTS’

RéSPONSES

 

Claudine Mary

Université de Sherbrooke

Claudine.Mary@Usherbrooke.ca

 

Linda Gattuso

Université du Québec à Montréal

gattuso.linda@uqam.ca

 

RÉsumÉ

 

Les résultats sont tirés d’une étude plus large sur les stratégies de résolution que des élèves de 2e, 3e et 4e secondaires (14 à 16 ans) utilisent pour résoudre des problèmes de moyenne. Dans ce texte, les résolutions de trois problèmes seront analysées. Ces problèmes ont été composés de telle sorte que nous puissions distinguer entre la capacité des élèves de calculer une moyenne et celle de saisir les liens qu’il y a entre la modification de l’effectif et d’une donnée et celle de la moyenne. Les problèmes visaient aussi à tester l’influence d’une donnée égale à zéro, influence signalée dans les études précédentes. Les résultats de la présente étude font voir que, dans le contexte choisi, le type et le sens des modifications effectuées influencent les comportements des élèves et que des conceptions inadéquates ou des glissements de sens apparaissent dans certaines situations et pas dans d’autres. Note: Un long resume en anglais precede l’article qui est ecrit en francais.

 

Mots-clés: Recherche en enseignement de la statistique; Moyenne arithmétique; Enseignement secondaire

 

Abstract

 

The results are taken from a much larger study on the strategies that pupils in the 2nd, 3rd and 4th stages at secondary school (ages 14-16) use for solving problems concerning the mean. In this paper the solutions of three problems are analysed. These problems have been formulated to be of such a kind that we can distinguish between the ability of pupils to calculate a mean, and that of realising the effect of a change in the number of observations or in the value of an observation, on the mean. The problems were also seen to test the influence of a value equal to zero on the mean, drawn attention to in earlier research studies. The results of the current study show us, in the chosen context, the type and sense of the modifications exerting influence on the manipulations of the pupils, and that inadequate conceptions or a change of meaning appeared in certain situations and not in others. Note: An extended summary in English is provided at the beginning of this paper, which is written in French.

Keywords: Statistics education research; Arithmetic mean; High school

 

 

__________________________

Statistics Education Research Journal, 4(2), 82-102, http://www.stat.auckland.ac.nz/serj

Ó International Association for Statistical Education (IASE/ISI), Nov, 2005

 

 

 

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Claudine Mary

Département d’études sur l’adaptation scolaire et sociale

Université de Sherbrooke

Sherbrooke, J1K 2R1

Canada