Young children’s notations for representing ordinal position and quantity: a longitudinal study of cross-task and within-task qualitative variations

Abstract

To support children’s transition to school mathematics, it is important to maintain sensitivity to notations that children produce in the domain of number and support connections between their informal number knowledge and written symbols. This paper presents an exploratory longitudinal study of the notations that 3-5-year-old children produced within two tasks that prompted them to communicate the ordinal position of an object in a sequence and quantity. Thirty-three children participated in three individual, task-based interviews, over one year. The frequency of numeral use in the quantity task was almost double the frequency of numerals used in the ordinal position task. A considerable cross-task difference in children’s numeral use was maintained for all data collection cycles. Notational behaviour was characterised by qualitative variability within and across the two tasks. Longitudinal individual pathways of notation production revealed that, in contrast to the quantity task, children’s move towards use of numerals for indicating ordinal position was often direct, from using other notations to using exclusively numerals, rather than characterised by a gradual emergence of some numerals amongst other notations. We discuss the observed behaviours in relation to different parameters, as illustrated by qualitative data. We propose that children’s notational choices can be an indication of intentional intertextual engagement that enables them to draw from across their literacies, to complete a task. The original evidence from this study provides the basis for further theorisation of the role that intertextual engagement may play in the development of symbolic function.

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ORCID for Chronoula Voutsina: orcid.org/0000-0003-2196-5816

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