Supporting children’s development of cardinality understanding

Bermejo, Vicente J.; Morales, S.E. Guzman; deOsuna, Jenny Garcia

doi:10.1016/j.learninstruc.2004.06.010

Cited by 33 publications

(28 citation statements)

References 22 publications

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“…Thus it was cardinality understanding, rather than simply count list knowledge, that appeared to play an important Running head: PRESCHOOL MAGNITUDE REPRESENTATIONS 27 role in children's broader mathematical development. This adds to the weight of evidence that assessing count list knowledge provides only a limited picture of children's understanding of counting (e.g., Condry & Spelke, 2008;Wynn, 1995) and that cardinality understanding is distinct from counting skill (Bermejo, Morales, & deOsuna, 2004). In keeping with some previous research, our count elicitation task involved a set of objects for children to count (e.g., Le Corre & Carey, 2007;Slaughter et al, 2006), while other studies have asked children to count without a set of objects (e.g., Barth et al, 2009;.…”

Section: Methodological Implicationsmentioning

confidence: 97%

“…Therefore, alongside activities to promote the connection between numbers and quantities, children should be given the opportunity to develop their understanding of the symbolic counting system itself. Simple activities that involve challenging children to reflect upon the number of items in a set have been found to successfully enhance children's understanding of cardinality (Bermejo et al, 2004). Engaging with a wide variety of activities involving counting may thus help children along the path to a rich understanding of numbers and all their meanings.…”

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confidence: 99%

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Magnitude Representations and Counting Skills in Preschool Children

Batchelor

Keeble

Gilmore

2015

Mathematical Thinking and Learning

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When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this mapping only occurs once children have cardinality understanding. One difficulty with the current literature is that studies have employed tasks that only indirectly assess children's nonsymbolic-symbolic mappings. We introduce a task in which preschoolers made magnitude comparisons across representation formats (e.g., dot arrays vs. verbal number), allowing a direct assessment of mapping. We gave this task to 60 children aged 2;7 -4;10, together with counting and Give-a-Number tasks. We found that some children could map between nonsymbolic quantities and the number words they understood the cardinal meaning of, even if they had yet to grasp the general cardinality principle of counting.Keywords: counting, magnitude comparison, cardinality, preschool children, number Running head: PRESCHOOL MAGNITUDE REPRESENTATIONS 3 Magnitude Representations and Counting Skills in Preschool ChildrenWe know from more than a decade's worth of research that infants, children and adults can represent and manipulate numerical information nonsymbolically, without number words or digits. These nonsymbolic representations are robust across multiple modalities and set sizes. Children and adults can compare, add and subtract small and large quantities in visual arrays (Barth, Kanwisher, & Spelke, 2003;McCrink & Wynn, 2004), auditory sequences (Barth et al., 2003;Barth, La Mont, Lipton, & Spelke, 2005) and moving displays of actions (e.g., puppet jumps) (Wood & Spelke, 2005;Wynn, 1996;Wynn, Bloom, & Chiang, 2002).The nonsymbolic representations employed in these tasks are approximate and in an analogue format. They are inherently noisy and the variance associated with them increases with the absolute size of the magnitudes represented. As a result, success on these tasks depends on the ratio (or numerical distance) between the numerosities to be compared 1 . As the quantities get closer together, discrimination becomes more effortful and less precise.Importantly, the precision of these representations varies across individuals and increases over development. Infants can discriminate numerosities with ratios as small as 2:3, whilst preschool children show a ratio-limit of 3:4, and adults, 7:8 (Barth et al., 2003;Feigenson, Dehaene, & Spelke, 2004).When children begin to count they learn to use external symbols to represent number.These symbolic representations enable exact number comparison and manipulation. There is evidence that when children acquire this symbolic system, the preexisting nonsymbolic system is not overridden; rather, nonsymbolic representations become mapped onto the newly acquired symbolic representations. The evidence for this is at least threefold. Firstly, children...

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Section: Methodological Implicationsmentioning

confidence: 97%

mentioning

confidence: 99%

Magnitude Representations and Counting Skills in Preschool Children

Batchelor

Keeble

Gilmore

2015

Mathematical Thinking and Learning

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“…Condry and Spelke (2008) noted that students with disability have poor number words fluency compare to normal students (abstraction). Bermejo et al (2004) stated that children may simply count all five blocks instead of stopping at three, such not-stop" errors may be due to the fact that they do not remember the requested number or fail to monitor the counting-out process. Bermejo et al (2004) also observed that children may realized that remembering number count is important but may not realized the objects-counting process that can be summarized before stating the last number word used (cardinality principle).…”

Section: Counting Proceduresmentioning

confidence: 99%

“…Bermejo et al (2004) stated that children may simply count all five blocks instead of stopping at three, such not-stop" errors may be due to the fact that they do not remember the requested number or fail to monitor the counting-out process. Bermejo et al (2004) also observed that children may realized that remembering number count is important but may not realized the objects-counting process that can be summarized before stating the last number word used (cardinality principle). In fact, it has been found that these students demonstrate a poor understanding of some counting principles (Geary, et al, 2000) and/or poor or faulty conceptual knowledge (Baroody, 2003).…”

Section: Counting Proceduresmentioning

confidence: 99%

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

Taibat¹,

Ahmad²,

Ghazali³

2013

IES

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This study investigates counting procedure in number counting based on gender among students with mild intellectual disability. Quantitative approach was used for testing counting procedure in number counting among these students. The samples for the study comprise fifteen male and fifteen female students with intellectual disability. Descriptive statistics and T-test were used in analyzing the data. It was revealed from the result of the study that students with mild intellectual disability showed understanding of counting procedure in number counting. However, the results of the study showed that these students have difficulty in number counting using abstraction principle and order irrelevance principle. It was shown that there was no significant difference between males and females in number counting when applying counting procedure.

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“…According to Bermejo and colleagues (Bermejo, Morales, and Garcia de Osuna 2004;Bermejo 1996) cardinality develops through six stages:…”

Section: Counting Skills and Principlesmentioning

confidence: 99%

Number Sense: The Underpinning Understanding for Early Quantitative Literacy

Maclellan¹

2012

Numeracy

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The fundamental meaning of Quantitative Literacy (QL) as the application of quantitative knowledge or reasoning in new/unfamiliar contexts is problematic because how we acquire knowledge, and transfer it to new situations, is not straightforward. This article argues that in the early development of QL, there is a specific corpus of numerical knowledge which learners need to integrate into their thinking, and to which teachers should attend. The paper is a rebuttal to historically prevalent (and simplistic) views that the terrain of early numerical understanding is little more than simple counting devoid of cognitive complexity. Rather, the knowledge upon which early QL develops comprises interdependent dimensions: Number Knowledge, Counting Skills and Principles, Nonverbal Calculation, Number Combinations and Story Problems -summarised as Number Sense. In order to derive the findings for this manuscript, a realist synthesis of recent Education and Psychology literature was conducted. The findings are of use not only when teaching very young children, but also when teaching learners who are experiencing learning difficulties through the absence of prerequisite numerical knowledge. As well, distilling fundamental quantitative knowledge for teachers to integrate into practice, the review emphasises that improved pedagogy is less a function of literal applications of reported interventions, on the grounds of perceived efficacy elsewhere, but based in refinements of teachers' understandings. Because teachers need to adapt instructional sequences to the actual thinking and learning of learners in their charge, they need knowledge that allows them to develop their own theoretical understanding rather than didactic exhortations.

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Supporting children’s development of cardinality understanding

Cited by 33 publications

References 22 publications

Magnitude Representations and Counting Skills in Preschool Children

Magnitude Representations and Counting Skills in Preschool Children

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

Number Sense: The Underpinning Understanding for Early Quantitative Literacy

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