Counting and cardinality in English nursery pupils

Abstract

This study examines the development of counting and cardinality in a structured sample of 60 English 3 1/2-4 1/2 year-olds attending local education authority nursery classes in socially mixed areas of Portsmouth. Children were given two types of task: counting sets of animals, and giving specified numbers of items from a pile. Three measures of cardinal understanding were used: spontaneous repetition of the last word on completion of a counting trial, repetition of the last word in reply to a question, and use of counting vs. grabbing when asked to give a specific number of items from a heap. In line with research on other populations the results indicate a pronounced developmental discrepancy between procedural and conceptual knowledge of counting, but cardinality appears to develop six months later in this population than in other populations studied. There were marked individual differences, however. Proficiency with object counting was found to be necessary, but not sufficient, for cardinal understanding. Children rarely repeated final count words spontaneously. Last word repetition in response to a verbal prompt depended on the nature of the prompt. Contrary to previous research, the present results indicate that last word repetition elicited by the prompt 'how many?' is not merely a conventional reply but generally implies an understanding of cardinality. The findings also indicate that an understanding of cardinality emerges relatively suddenly, consistent with the discovery or construction of a principle. Whether nursery pupils treat counting simply as a conventional routine without cardinal significance appears to depend on the situation as well as on their understanding of cardinality. The findings are discussed in relation to Karmiloff-Smith's Representational Redescription model.

Counting and cardinal understanding in children with Down syndrome and typically developing children

“…Research with typically developing children shows understanding that the last count word indicates the numerosity of the whole set emerges 6 to 12 months after procedural counting skills have become established (Frye, Braisby, Lowe, Maroudas, & Nicholls, 1989;Wynn, 1990Wynn, , 1992; in a UK population, cardinality was found to emerge a few months either side of the fourth birthday (Fluck & Henderson, 1996).…”

“…It was predicted that no counters would be seen in this phase, again based on the fi nding that most children do not demonstrate understanding of cardinality before four years of age (Fluck & Henderson, 1996). Table 8 shows the number of counters and grabbers observed in each group.…”

“…In previous studies (Wynn, 1990;Fluck & Henderson, 1996) children have been found either to grab handfuls of items to give ('grab') or to attempt to count out the requested amount ('count'). A 'count' response implies that the child appreciates the cardinal signifi cance of counting, even if that response itself is inaccurate.…”

“…Only two of the typically developing children were aged four years, which is the age at which Fluck and Henderson (1996) found children to demonstrate understanding of cardinality. Of the children with Down syndrome, 20 out of 23 had a chronological age of 47 months or above, but only three had a non-verbal mental age above this level.…”

Learning to represent exact numbers

“…That is, any time from a couple of months before their third birthday to a couple of months after their fourth birthday (Negen & Sarnecka, 2012;Sarnecka & Carey, 2008;Sarnecka & Gelman, 2004;Sarnecka et al, 2007;Sarnecka & Lee, 2009;Slusser et al, 2013;Slusser & Sarnecka, 2011). Children from lowerincome backgrounds come to understand cardinality significantly later, at age 4 or older (Fluck & Henderson, 1996;Jordan & Levine, 2009). …”