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Strategic aspects of children’s numerosity judgement

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Abstract

A previous study (Luwel, Verschaffel, Onghena, & De Corte, 2000) revealed that 2nd and 6th graders use at least 3 different kinds of strategies for determining different numerosities of blocks presented in square grids: (a) an addition strategy by means of which (groups of) blocks are counted (and added), (b) a subtraction strategy in which the number of empty squares is subtracted from the total number of blocks in the grid (i.e. the anchor), and (c) an estimation strategy, whereby the number of blocks is determined in a quick but imprecise way. Although 6th as well as 2nd graders used the clever subtraction strategy, the majority of 2nd graders had serious trouble with the correct determination of the anchor, resulting in huge numerosity judgement errors. Since this finding seriously complicated the testing of a number of hypotheses in that study, we replicated the above study but presented the children information about the grid size. This manipulation led to a substantial increase in the proportion of appropriate subtraction strategy users and made it possible to investigate the effect of several subject and task variables on the frequency, accuracy, and adaptiveness with which the different strategies were applied. Results are discussed in terms of the conceptual framework of Lemaire and Siegler (1995) regarding strategic change.

Résumé

Une étude antérieure (Luwel, Verschaffel, Onghena, & De Corte, 2000) a démontré que des élèves en deuxième et en sixième année (de l’école primaire) se servent d’au moins 3 différents types de stratégies pour déterminer différentes quantités de blocs représentés dans une grille carrée: (a) une stratégie d’ addition par laquelle des (groupes de) blocs sont comptés (et additionnées), (b) une stratégie de soustraction par laquelle on soustrait le nombre de carrés vides de la totalité des blocs représentés dans la grille (i.e., l’ancre) et (c) une stratégie d’estimation dans laquelle on détermine assez rapidement le nombre de blocs, mais de façon imprécise. Quoique tant les élèves de la deuxième année que ceux de la sixième utilisent la stratégie de soustraction de manière intelligente, la majorité des élèves de la deuxième année éprouvent toutefois de sérieuses difficultés dans la détermination correcte de l’ancre, ce qui aboutit à un taux très élevé d’erreurs dans la determination des quantités.

Comme ces résultats ont considérablement compliqué le contrôle d’un certain nombre d’hypothèses dans ladite étude, nous avons repris cette expérience tout en fournissant aux élèves des informations supplémentaires sur la taille de la grille.

Cette manipulation a abouti à une hausse substantielle de la proportion des élèves qui optaient pour la stratégie de soustraction, qui était la plus appropriée. Elle a également permis l’examen de l’effet de plusieurs variables (liées au sujet et à la tâche) sur la fréquence, la précision et la faculté d’adaptation par laquelle les différentes stratégies ont été mises en œuvre. Les résultats sont discutés suivant le cadre conceptuel de Lemaire et Siegler (1995) concernant le changement de stratégie.

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Authors and Affiliations

  1. Center for Instructional Psychology and Technology, University of Leuven, Vesaliusstraat 2, B-3000, Leuven, Belgium

    Koen Luwel, Lieven Verschaffel, Patrick Onghena & Erik De Corte

Authors
  1. Koen Luwel
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  2. Lieven Verschaffel
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  3. Patrick Onghena
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  4. Erik De Corte
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Corresponding author

Correspondence to Koen Luwel.

Additional information

This study is supported by the grant G. 0157.98 from the Fund of Scientific Research.

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Luwel, K., Verschaffel, L., Onghena, P. et al. Strategic aspects of children’s numerosity judgement. Eur J Psychol Educ 16, 233–255 (2001). https://doi.org/10.1007/BF03173028

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  • DOI: https://doi.org/10.1007/BF03173028

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