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Cognitive Processing

, Volume 18, Issue 4, pp 447–459 | Cite as

Configured-groups hypothesis: fast comparison of exact large quantities without counting

  • Sébastien Miravete
  • André Tricot
  • Slava Kalyuga
  • Franck Amadieu
Research Report

Abstract

Our innate number sense cannot distinguish between two large exact numbers of objects (e.g., 45 dots vs 46). Configured groups (e.g., 10 blocks, 20 frames) are traditionally used in schools to represent large numbers. Previous studies suggest that these external representations make it easier to use symbolic strategies such as counting ten by ten, enabling humans to differentiate exactly two large numbers. The main hypothesis of this work is that configured groups also allow for a differentiation of large exact numbers, even when symbolic strategies become ineffective. In experiment 1, the children from grade 3 were asked to compare two large collections of objects for 5 s. When the objects were organized in configured groups, the success rate was over .90. Without this configured grouping, the children were unable to make a successful comparison. Experiments 2 and 3 controlled for a strategy based on non-numerical parameters (areas delimited by dots or the sum areas of dots, etc.) or use symbolic strategies. These results suggest that configured grouping enables humans to distinguish between two large exact numbers of objects, even when innate number sense and symbolic strategies are ineffective. These results are consistent with what we call “the configured group hypothesis”: configured groups play a fundamental role in the acquisition of exact numerical abilities.

Keywords

Number sense Configured groups External representation Numerical cognition Educational psychology 

Notes

Acknowledgements

Jean-Luc Parmentelot, Sylvain Begue, Josette Suspène, Sylvaine Mailho, Nathalis Burgues-Gensel, Pierre Villenave, Anne Terrière, Véronique Perrier, Céline Burgues, Gaëlle Imbert, Laurent Icher, Mrs Ortis, Mrs Peyrou, Denis Caillard, Nathalie Le Goffic, Nathalie Precigout, Nathalie Corpet, Julie Rozières, Mrs Barral, Mrs Cornic, Valérie Buosi, Marie-Pierre Caldeira, Olivier Carmouze, Stéphanie Sauvage, Aurélie Cazottes, Muriel Abeille, Catalina Martin Joga, parents and their children.

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Copyright information

© Marta Olivetti Belardinelli and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Sébastien Miravete
    • 1
  • André Tricot
    • 1
  • Slava Kalyuga
    • 2
  • Franck Amadieu
    • 1
  1. 1.CLLE InstituteUniversity of Toulouse 2ToulouseFrance
  2. 2.School of EducationUniversity of New South WalesSydneyAustralia

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