Configured-groups hypothesis: fast comparison of exact large quantities without counting
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.
KeywordsNumber sense Configured groups External representation Numerical cognition Educational psychology
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.
- Clements DH (1999) Subitizing: what is it? Why teach it? Teach Child Math 5:400–405Google Scholar
- Dehaene S (2011) The number sense: how the mind creates mathematics, revised and updated edition. Oxford University Press, OxfordGoogle Scholar
- Hyde DC (2011) Two systems of non-symbolic numerical cognition. Front Hum Neurosci 5, Article 150. doi: 10.3389/fnhum.2011.00150
- Ifrah G (2000) The Universal History of Numbers: from prehistory to the invention of the computer. Wiley, HobokenGoogle Scholar
- Link T, Huber S, Nuerk HC, Moeller K (2014) Unbounding the mental number line-new evidence on children’s spatial representation of numbers. Front Psychol 4, Article 1021. doi: 10.3389/fpsyg.2012.00315
- Sayers J, Andrews P, Björklund Boistrup L (2016) The role of conceptual subitising in the development of foundational number sense. In: Meaney T, Helenius O, Johansson ML, Lange T, Wernberg A (eds) Mathematics education in the early years. Results from the POEM2 Conference, 2014. Springer, New York, pp 371–394. doi: 10.1007/978-3-319-23935-4