Zero – an Uncommon Number: Preschoolers‘ Conceptual Understanding of Zero
Keywords:
Numerical cognition, zero, ordinal representation, early numeracy, conceptual developmentAbstract
The conceptual development of natural number in preschoolers is well-researched. However, less is known about the conceptual development of zero. Recent studies suggested that children develop an understanding of zero after learning to count. It remains unclear, when a conceptual understanding of “zero” as number word for an empty set emerges. This paper integrates numerical and language theories about how, where and when the concept of zero forms and integrates in the class of natural number. The counting skills of N=107 preschoolers was assessed in the number range between zero and eight as well as their ordinal understanding of zero. The results show that compared to the natural numbers, zero was substantially more difficult. Further, children were more likely to locate zero within the number word sequence than to give zero items, which contradicts findings regarding natural numbers. Regarding zero, ordinal comparison and ordering were easier then addition and subtraction by counting. The results suggest that the conceptual development of zero differs qualitatively from the natural numbers. Based on the results, the ordinal understanding of zero as a predecessor of one plus its matching linguistic concepts is proposed to be the driver of the conceptual development of zero.
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References
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Wynn, K. (1992). Addition and subtraction by human infants. Nature, 27, 749–750
Bottazzini, U. (2021). Wie die Null aus dem Nichts entstand. München: dtv.
Bialystok, E., & Codd, J. (2000). Representing quantity beyond whole numbers: Some, none, and part. Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale, 54(2), 117-128.
Carey, S. (1999). Sources of conceptual change. In l. K. Scholnick, K. Nelson, S. A. Gelman, & P. H. Miller (Eds.), Conceptual development: Piaget’s legacy (pp. 293-326. Routledge.
Carey, S. (2009). The Origin of Concepts. Oxford University Press.
Sarnecka, B. W., & Carey, S. (2006). The development of human conceptual representations. UC Irvine.
Clements, D. H., & Sarama, J. H. (2014). Learning Trajectories: Foundations for effective, research-based education. In A. P. Maloney, J. Confrey & K. H. Nguyen (Eds.), Learning Over Time (pp.1–30). Information Age.
Clements, D. H., Sarama, J. H., & Liu, X. H. (2008). Development of a measure of early mathematics achievement using the Rasch model: the Research-Based Early Maths Assessment. Educational Psychology, 28(4), 457–482.
Dehaene, S. (1999). The Number Sense. Oxford University Press.
Feigenson, L., Carey, S., & Hauser, M. (2002). The representations underlying infants' choice of more: Object files versus analog magnitudes. Psychological science, 13(2), 150-156.
Fritz, A., Ehlert, A. & Leutner, D. (2018). Arithmetische Konzepte aus kognitiv-psychologischer Sicht. Journal für Mathematik-Didaktik, 39, 7–41.
Gelman, R., and Gallistel, C. R. (1978). The Child’s Understanding of Number. Harvard University Press.
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the" Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults. Developmental psychology, 44(5), 1457-1465.
Hartmann, J., Fritz, A., 2021. Language and mathematics: How children learn arithmetic through specifying their lexical concepts of natural numbers. In A. Fritz, E. Gürsoy, & M. Herzog (Eds.). Diversity Dimensions in Mathematics and Language Learning (pp.21-39). De Gruyter.
Herzog, M., Ehlert, A., & Fritz, A. (2019). Development of resilient place value concepts. In A. Fritz, V. Haase & P. Räsänen (Eds.), The International Handbook of Mathematical Learning Difficulties (pp.561–580). Springer.
Ifrah, G. (1998). The Universal History of Numbers. From Prehistory to the Invention of the Computer. Harville Press.
Krajsci, A., Kojouharova, P. & Lengyel, G. (2021). Development of Preschoolers´ Understanding of Zero. Frontiers in Psychology, 12, 583734.
Le Corre, M., van de Walle, G., Brannon, E. & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52, 130 – 169.
Le Corre, M. & Carey, S. (2007). One, two, three, four, nothing more: An investigationof the conceptual sources of the verbal counting principles. Cognition, 105(2), 395–438.
Le Corre, M. (2014). Children acquire the later-greater principle after the cardinal principle. British Journal of Developmental Psychology, 32(2), 163-177.
Le Corre, M., van de Walle, G., Brannon, E.M., & Carey, S. (2006). Re-visiting the competence /performance debate in the acquisition of the counting principles. Cognitive Psychology, 52, 130–169.
Merritt, D. J., & Brannon, E. M. (2013). Nothing to it: precursors to a zero concept in preschoolers. Behavioural Processes, 93, 91–97.
Negen, J., & Sarnecka, B. (2012). Number-concept acquisition and general vocabulary development. Child Development, 83(6), 2019–2027.
Pixner, S., Dresen, V. & Moeller, K. (2018). Differential Development of Children’s Understanding of the Cardinality of Small Numbers and Zero. Frontiers in Psychology, 9, 01636
R Core Team. (2018). R [Computer software]. Vienna. https://www.R-project.org [Accessed July 22, 2021].
Ricken, A., Fritz, A. & Balzer, L. (2013). MARKO – D: Mathematik und Rechenkonzepte im Vorschulalter - Diagnose. Göttingen: Hogrefe.
Robitzsch A, Kiefer T, Wu M (2021). TAM: Test Analysis Modules. R package version 3.7-16
Sarnecka, B.W. & Lee, M.D. (2009). Levels of number knowledge during early childhood. Journal of Experimental Child Psychology, 103(3), 325 – 337.
Schulz, A., Leuders, T., & Rangel, U. (2020). The use of a diagnostic competence model about children’s operation sense for criterion-referenced individual feedback in a large-scale formative assessment. Journal for Psychoeducational Assessment, 8(4), 426 –444.
Siegler, R. S., & Alibali, M. W. (2005). Children’s thinking. Prentice Hall.
Sigler, L. E. (trans.) (2002), Fibonacci's Liber Abaci. Springer.
Wellman, H. M., & Miller, K. F. (1986). Thinking about nothing: Development of concepts of zero. British Journal of Developmental Psychology, 4(1), 31-42.
Wiese, H. (2007). The co-evolution of number concepts and counting words. Lingua, 117,758–772
Wright, B. D. & Linacre, J. M. (1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8, 370.
Wynn, K. (1992). Addition and subtraction by human infants. Nature, 27, 749–750
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Published
2022-03-16
How to Cite
Hartmann, J., Herzog, M., & Fritz, A. (2022). Zero – an Uncommon Number: Preschoolers‘ Conceptual Understanding of Zero. International Electronic Journal of Elementary Education, 14(3), 353–361. Retrieved from https://www.iejee.com/index.php/IEJEE/article/view/1740
