Developmental and individual differences in pure numerical estimation.

Booth, Julie L.; Siegler, Robert S.

doi:10.1037/0012-1649.41.6.189

Cited by 615 publications

(892 citation statements)

References 17 publications

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“…(It should be noted that the linearity and slope indexes from our young preschoolers were somewhat lower than those reported by Muldoon et al, 2011, on their sample of Chinese preschoolers, which can be explained by the fact that their sample was older [M age = 4.5 years] than our young preschoolers.) Similarly, for the 0-100 number line, we found that the linearity indexes seemed much higher than those reported by Siegler and his colleagues for American kindergarteners (see Table 7) and, in fact, were similar to those for first and second graders in Siegler's American samples (Booth & Siegler, 2006;Laski & Siegler, 2007;Siegler & Booth, 2004;Siegler & Mu, 2008). Finally, for the 0-1000 number line, the linearity indexes were higher than those obtained for American second graders (Booth & Siegler, 2006;Opfer & Siegler, 2007;Siegler & Opfer, 2003).…”

Section: Discussionsupporting

confidence: 69%

“…This hypothesis appeared to be supported. When comparing our results with those from previous studies of Western children, it appears that the estimates of Chinese preschoolers were more accurate and linear on the 0-10, 0-100, and 0-1000 number lines than their Western age mates (Booth & Siegler, 2006;Muldoon et al, 2011;Siegler & Booth, 2004;Siegler & Mu, 2008;. Table 7 shows a summary of previous studies based on Western samples.…”

Section: Discussionsupporting

confidence: 56%

“…To index accuracy of estimation, we calculated percentage absolute error (PAE) using the formula of (Estimate -Estimate Quantity)/Scale of Estimates (see Booth & Siegler, 2006Muldoon et al, 2011;Slusser et al, 2013). As shown in Table 1, the mean PAE decreased systematically with age on all three 0-10 number line tasks.…”

Section: Accuracy Of Estimationmentioning

confidence: 99%

“…Another way to examine age differences is to use individual children's linearity index (adjusted R 2 ), which would vary to a greater extent than the median estimate of the group (e.g., Booth & Siegler, 2006;Siegler & Booth, 2004;Siegler & Mu, 2008). Table 3 shows the mean linearity index by task and age group.…”

Section: Fit Of Logarithmic and Linear Modelsmentioning

confidence: 99%

“…The strongest support for the logarithmic-to-linear shift hypothesis came from a large number of developmental studies carried out by Siegler and his colleagues (Booth & Siegler, 2006Laski & Siegler, 2007;Opfer & Siegler, 2007;Opfer & Thompson, 2008;Opfer et al, 2011;Siegler & Booth, 2004;Siegler & Mu, 2008;Siegler & Opfer, 2003;. They identified different ages at which American children move away from logarithmic representations and develop linear representations of different ranges of numbers.…”

Section: Introductionmentioning

confidence: 99%

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Development of numerical estimation in Chinese preschool children

Chen

Pan

et al. 2013

Journal of Experimental Child Psychology

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a b s t r a c tAlthough much is known about the development of mental representations of numbers, it is not clear how early children begin to represent numbers on a linear scale. The current study aimed to examine the development of numerical estimation of Chinese preschoolers. In total, 160 children of three age groups (51 3-and 4-year-olds, 50 5-year-olds, and 59 6-year-olds) were administered the numerical estimation task on three types of number lines (Arabic numbers, dots, and objects). All three age groups took the test on the 0-10 number lines, and the oldest group also took it on the 0-100 and 0-1000 Arabic number lines. Results showed that (a) linear representation of numbers increased with age, (b) representation of numbers was consistent across the three types of tasks, (c) Chinese participants generally showed earlier onset of various landmarks of attaining linear representations (e.g., linearity of various number ranges, accuracy, intercepts) than did their Western counterparts, as reported in previous studies, and (d) the estimates of older Chinese preschoolers on the 0-100 and 0-1000 symbolic number lines fitted the two-linear and linear models better than alternative models such as the one-cycle, two-cycle, and logarithmic models. These results extend the small but accumulating literature on the earlier development of number cognition among Chinese preschoolers compared with their Western counterparts, suggesting the importance of cultural factors in the development of early number cognition.

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Section: Discussionsupporting

confidence: 69%

Section: Discussionsupporting

confidence: 56%

Section: Accuracy Of Estimationmentioning

confidence: 99%

Section: Fit Of Logarithmic and Linear Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development of numerical estimation in Chinese preschool children

Chen

Pan

et al. 2013

Journal of Experimental Child Psychology

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The Development of Mathematical Reasoning

Nuñes

Bryant

2015

Handbook of Child Psychology and Developmental Science

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Psychological research on the development of children's mathematical reasoning has focused either on their understanding of quantities or on their knowledge of number. A synthesis between these two different kinds of theory can be achieved by acknowledging that numbers have two meanings: a representational meaning, defined by their use as signs for quantities or relations between quantities, and an analytical meaning, defined by the conventions in the number system. In the introduction, this chapter introduces these two meanings of numbers and explores the vital connections between them. The subsequent sections analyze how children's mathematical knowledge develops by their increasing ability to use different numerical representations (e.g., from the use of fingers to represent quantities to the use of conventional signs), by their growing understanding of invariant relations between quantities (e.g., realizing that, given a fixed number of cookies, the more people sharing the cookies, the less each one receives) and by their increasing awareness of the relevance of specific concepts to different situations (e.g., understanding the relevance of division to the solution of situations more readily connected to multiplication). Throughout the chapter, the connection between the nature of quantities and their numerical representations is explored. The final substantive section focuses on the use of numbers to quantify space and relations between spatial dimensions, and argues that understanding relations between different dimensions in space (e.g., length, width, and area) is crucial to quantifying space. The chapter ends with a brief discussion of directions for future research.

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The Neurocognitive Bases of Numerical Cognition

Sella

Hartwright

Kadosh

2018

Stevens' Handbook of Experimental Psychology and Cognitive Neuroscience

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Numerical Cognition describes the processes that one uses to assimilate, ascribe and manipulate numerical information. This chapter is organised into two sections. The first draws heavily on data from Developmental and Experimental Psychology. We use this to outline core findings related to processing numerical information in humans. In particular, we describe the trajectory of the acquisition of basic numerical skills. Starting in early infancy, we outline the processes that are believed to underlie non-symbolic representation. Next, we summarise core studies that examine the representation of symbolic quantities (Arabic system). Lastly, we briefly report the relationship between basic numerical processing and mathematical achievement. The second part of the chapter explores evidence from Neuropsychology and Neuroscience. The core methodological approaches used are briefly outlined with sign-posting to relevant literature. Next, we examine data from early lesion studies, followed by a short review of one of the most influential models in the study of Numerical Cognition, the Triple Code Model. Lastly, we look at the neurocognitive features of number, such as different modes of representation and the processing of quantity. Throughout, the core literature plus recent advances are summarised, giving the reader a thorough grounding in the Neurocognitive Bases of Numerical Cognition.

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Developmental and individual differences in pure numerical estimation.

Cited by 615 publications

References 17 publications

Development of numerical estimation in Chinese preschool children

Development of numerical estimation in Chinese preschool children

The Development of Mathematical Reasoning

The Neurocognitive Bases of Numerical Cognition

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