Children's mappings of large number words to numerosities

doi:10.1016/j.cogdev.2009.04.001

Cognitive Development

Volume 24, Issue 3, July–September 2009, Pages 248-264

https://doi.org/10.1016/j.cogdev.2009.04.001 Get rights and content

Abstract

Previous studies have suggested that children's learning of the relation between number words and approximate numerosities depends on their verbal counting ability, and that children exhibit no knowledge of mappings between number words and approximate numerical magnitudes for number words outside their productive verbal counting range. In the present study we used a numerical estimation task to explore children's knowledge of these mappings. We classified children as Level 1 counters (those unable to produce a verbal count list up to 35), Level 2 counters (those who were able to count to 35 but not 60) and Level 3 counters (those who counted to 60 or above) and asked children to estimate the number of items on a card. Although the accuracy of children's estimates depended on counting ability, children at all counting skill levels produced estimates that increased linearly in proportion to the target number, for numerosities both within and beyond their counting range. This result was obtained at the group level (Experiment 1) and at the level of individual children (Experiment 2). These findings provide evidence that even the least skilled counters do exhibit some knowledge of the form of the mapping between large number words and approximate numerosities.

Section snippets

Experiment 1

All participants completed an estimation task, and child participants completed a verbal counting assessment, in order to determine their understanding of the relation between large number words and numerical meanings both within and beyond their productive verbal counting ranges. The estimation task assessed abilities to produce verbal estimates of the number of objects in a visually presented array. Previous research has shown that adults’ estimates and children's estimates for numerosities

Experiment 2

The results of Experiment 1 suggest that even children who cannot reliably produce a verbal count sequence up to 35 can produce increasing estimates for larger numbers beyond their productive counting range. Because relatively few data points were collected for each individual child, the analyses of Experiment 1 were carried out on group data as in previous work (Lipton & Spelke, 2005). But when relatively unskilled counters are presented with tasks of this sort, there may be a great deal of

General discussion

We investigated the relationship between children's productive verbal counting skill and their understanding of mappings between number words and numerical magnitudes in the large number range. Five-year-old children were asked to estimate the number of items on a card and were sorted into three groups based on counting skill (Level 1, Level 2, and Level 3 counters). The main finding, supported by two experiments, was the novel result that even children who have mastered very little of the

Acknowledgments

The authors thank AnjaLi Carrasco, Rachel Jacobson, Jessica Tsai, Annie Paladino, Julie Neuspiel, and Elise Herrig for help with data collection; Elizabeth Spelke, Susan Carey, and anonymous reviewers for comments on previous versions of the manuscript; and the parents, children, and preschool coordinators who made this work possible. This project was supported by Hughes Summer Research Fellowships to A.S. and J.S. and a Wesleyan University Project Grant to H.B.

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Citation Excerpt :
In particular, we developed and pre-registered several measures that sought to differentiate between children with a fully memorized list versus those who count using rules. The first was a commonly used measure of children’s counting mastery which involves testing how high they can count without error - what we call their “Initial Highest Count” (Almoammer et al., 2013; Barth, Starr, & Sullivan, 2009; Cheung et al., 2017; Davidson et al., 2012; Marušič et al., 2016; Fuson et al., 1982; Siegler & Robinson, 1982; Wagner, Chu, & Barner, 2019). However, a problem with this measure is that for some children it has the potential to underestimate knowledge of productive counting rules: Whereas some children — especially those who make errors on decade transitions like 29 — can count higher when prompted, other children who make errors nearby in the count list (e.g., 32) are unable to continue counting, suggesting that their list is likely memorized, and not generated by rules (Siegler & Robinson, 1982).
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Numerous studies from developmental psychology have suggested that human symbolic representation of numbers is built upon the evolutionally old capacity for representing quantities that is shared with other species. Substantial research from mathematics education also supports the idea that mathematical concepts are best learned through their corresponding physical representations. We argue for an independent pathway to learning “big” multi-digit symbolic numbers that focuses on the symbol system itself. Across five experiments using both between- and within-subject designs, we asked preschoolers to identify written multi-digit numbers with their spoken names in a two-alternative-choice-test or to indicate the larger quantity between two written numbers. Results showed that preschoolers could reliably map spoken number names to written forms and compare the magnitudes of two written multi-digit numbers. Importantly, these abilities were not related to their non-symbolic representation of quantities. These findings have important implications for numerical cognition, symbolic development, teaching, and education.

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Children's mappings of large number words to numerosities

Abstract

Section snippets

Experiment 1

Experiment 2

General discussion

Acknowledgments

Cognition

Journal of Experimental Child Psychology

Trends in Cognitive Sciences

Cognition

Cognition

Cognition

Trends in Cognitive Sciences

Cognition

Cognition

Cognition

Cognition

Cognitive Psychology

Learning and Motivation

Cognition

Cognition

Cognition

Cognitive Psychology

Trends in Cognitive Sciences

Cognition

Cognition

Abstract number and arithmetic in preschool children

Proceedings of the National Academy of Sciences

Developmental and individual differences in pure numerical estimation

Developmental Psychology