Cardinality development and counting.

Abstract

Cardinality means that the last number word used in counting refers to the entire set of items and is thought to be crucial to correct counting. This research focuses on the cardinality acquisition and on the relation between cardinality and counting. Three groups of 24 children {3 years, 5 months to 5 years, 0 months) each received 4 kinds of tasks. First, they counted forward; then were shown sets that were counted for them backward sequentially, jumping forward in the sequence, or forward and backward; and asked to say how many items were in the set. Empirical evidence is gathered regarding the 6 understanding levels of cardinality proposed by V. Bermejo and M. O. Lago (1990). Likewise, these data provide no empirical support for considering counting as a single prerequisite to cardinality. Finally, a new approach to the relation between counting and cardinality is suggested.Counting is a complex ability that requires the integration of some principles to be performed correctly. In fact, children need 2 years or more to count correctly and probably even more time to use counting efficiently (see Bermejo & Lago, 1994). According to the model of Gelman and Gallistel (1978), several principles are required to perform counting correctly, such as one-to-one correspondence, stable order, and cardinality. Cardinality means that children use the last number word of counting to refer to the number of items in the set counted. It is a way of quantifying the items of a set.Currently, there is much research regarding the acquisition of early arithmetical concepts, but many unresolved issues still remain. Such is the case, for instance, with cardinality acquisition and its relation to counting. The goal of this research is to analyze these two topics: cardinality acquisition and the relation between counting and cardinality on a counting task.Concerning cardinality acquisition, Schaeffer, Eggleston, and Scott (1974) proposed that cardinality resulted from the integration of two prior processes: counting and subitizing (i.e., immediate apprehension of small numerosities). Gelman and coworkers (

How Spencer made number: First uses of the number words

“…Most researchers also agree that children learn the meanings of one, two, and three before they understand how counting is used to determine cardinality (e.g., that a set counted ''1-2-3-4" has four items) (Bermejo, 1996;Chi & Klahr, 1975;Descoeudres, 1921;Fuson, 1988;Klahr & Wallace, 1973;LeCorre & Carey, 2007;Schaeffer, Eggleston, & Scott, 1974;Wagner & Walters, 1982;Wynn, 1990Wynn, , 1992. These studies have shown that when young children are asked to name or produce very small sets, they do so without counting.…”

“…They can match equivalent sets, label small numerosities, and use counting to determine cardinality (e.g., Bermejo, 1996;Bermejo & Lago, 1990;Fuson, 1988;Gelman & Gallistel, 1978;Huttenlocher, Jordan, & Levine, 1994;LeCorre & Carey, 2007;Mix, 1999;Mix, Sandhofer, & Baroody, 2005;Wynn, 1990). There have been different ideas about the origins of these skills-ideas that have generated abundant research on infancy and early childhood while largely ignoring toddlerhood (see Mix, Huttenlocher, & Levine, 2002, for a review).…”

Development of Mathematical Understanding

“…Although an implicit understanding of cardinality and ordinality appears to emerge before children learn the sequence of number words (Bermejo, 1996;Brainerd, 1979;Brannon & Van de Walle, 2001;R. Cooper, 1984;Huntley-Fenner & Cannon, 2000;Ta'ir, Brezner, & Ariel, 1997;Wynn, 1990Wynn, , 1992b, the mapping of these concepts onto the counting sequence is an essential step in the development of arithmetical competencies.…”

“…Their performance is inconsistent and often influenced by factors other than cardinality. For small set sizes (e.g., less then 10), most children have a good grasp of cardinal value by 5 years (Bermejo, 1996;Freeman, Antonucci, & Lewis, 2000), but generalization to larger sets and a consistent focus on cardinality information over other information (e.g., perceptual cues) may not emerge for several more years (Piaget, 1965).…”

Examine Counting Procedure among Students with Mild Intellectual Disability: A Case of Penang Malaysia

“…Sarnecka and Lee (2009) maintained that children with disability may appear as if they have mastered counting of numbers because they seem confident in reciting the counting sequence and repeating the last number word used in the count to answer the question "how many", but what this appearance might reflect is just an observational learning (Clements & Sarama, 2009). Bermejo, 1996;see Sadler and Faith (2009) confirmed that some young children had master cardinality principle; they go through phases of subset knowing. This might be due to less counting experience these children have due to their deficiency.…”