Abstract
This study investigates the development of an adaptive strategy for the estimation of numerosity from the theoretical perspective of “strategic change” (Lemaire & Siegler, 1995; Siegler & Shipley, 1995). A simple estimation task was used in which participants of three different age groups (20 university students, 20 sixth-graders and 10 second-graders) had to estimate 100 numerosities of (colored) blocks presented in a 10x10 rectangular grid. Generally speaking, this task allows for two distinct estimation procedures: either repeatedly adding estimations of groups of blocks (=addition procedure) or subtracting the estimated number of empty squares from the (estimated) total number of squares in the grid (=subtraction procedure). A rational task analysis indicates that the most efficient overall estimation strategy consists of the adaptive use of both procedures, depending on the ratio of the blocks to the empty squares. The first hypothesis was that there will be a developmental difference in the adaptive use of the two procedures, and according to the second hypothesis this adaptive use will result in better estimation accuracy. Converging evidence from different kinds of data (i.e., response times, error rates, and retrospective reports) supported both hypotheses. From a methodological point of view, the study shows the potential of Beem’s (1995a, 1995b) “segmentation analysis” for unravelling subjects’ adaptive choices between different procedures in cognitive tasks, and for examining the relationship between these adaptive choices and performance.
Résumé
Les auteurs adoptent la perspective théorique nommée “strategic chance” développée par siegler pour étudier le développement et l’utilisation d’une stratégie adaptative concernant l’estimation de la numérosité. Des sujets de trois groupes d’âge (20 étudiants universitaires, 20 élèves de sixième et 10 élèves de deuxième année d’école primaire) ont été soumis à une tâche simple d’estimation de numérosité comportant 100 blocs présentés dans une grille de 10x10. En principe, cette tâche peut susciter deux procédures d’estimation différentes: 1) estimation et addition de tous les groupes de blocs colorés que le sujet a distingué dans la totalité des blocs présentés (procédure additive); 2) soustraction du nombre estimé des carrés vides de la totalité des blocs dans la grille (procédure soustractive). Une analyse rationnelle de la tâche indique que la plus efficace de toutes stratégies d’estimation consiste en une utilisation adaptée des deux procédures liée à la comparaison des blocs colorés et des carrés vides. La première hypothèse prévoyait l’existence de différences liées à l’âge dans l’utilisation adaptée des deux procédures, et la seconde hypothèse que cette utilisation adaptée permettrait des estimations plus précises. Les données relatives à plusieurs variables (réponses, temps de réaction, verbalisations) ont confirmé les deux hypothèses. D’un point de vue méthodologique, cette recherche montre l’intérêt de la méthode de I “analyse segmentée” proposée par Beem (1995a, 1995b) pour l’étude des choix adaptatifs entre des procédures différents dans une tâche cognitive, et également pour l’étude des relations entre choix adaptatifs et les performances des sujets.
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Verschaffel, L., De Corte, E., Lamote, C. et al. The acquisition and use of an adaptive strategy for estimating numerosity. Eur J Psychol Educ 13, 347–370 (1998). https://doi.org/10.1007/BF03172950
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DOI: https://doi.org/10.1007/BF03172950