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Comments Regarding 'Numerical Estimation Strategies Are Correlated with Math Ability in School-Age Children'

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Title: Comments Regarding 'Numerical Estimation Strategies Are Correlated with Math Ability in School-Age Children'
Language: English
Authors: Clarissa A. Thompson, Pooja G. Sidney, Charles J. Fitzsimmons, Marta Mielicki, Lauren Schiller, Daniel A. Scheibe, John E. Opfer, Robert S. Siegler
Source: Grantee Submission. 2022.
Peer Reviewed: Y
Page Count: 32
Publication Date: 2022
Sponsoring Agency: Institute of Education Sciences (ED)
National Science Foundation (NSF)
Contract Number: R305U200004
R305A180514
1941132
Document Type: Reports - Evaluative
Descriptors: Mathematics Skills, Young Children, Number Concepts, Accuracy, Scores, Mathematics Tests, Achievement Tests, Computation, Mathematics Achievement, Academic Ability, Fractions, Preschool Children
DOI: 10.1016/j.cogdev.2022.101188
Abstract: In the target article, Xing and colleagues (2021) claimed that 6- to 8-year-olds who spontaneously referenced the midpoint of 0-100 number lines made more accurate magnitude estimates and scored higher on a standardized math achievement test than other children. Unlike previous studies, however, the authors found no relation between accuracy on the number line estimation task and a dot discrimination task used to assess the Approximate Number System (ANS). These findings, the authors claim, constitute evidence against the idea that children's numerical magnitude understanding entails representational change. We disagree. In the literature on the development of numerical magnitude understanding, the "gold standard" assessment is the number-line estimation task (Schneider et al., 2018, Siegler and Opfer, 2003, Siegler et al., 2009). Unlike numerical comparisons ("Which is larger--N1 or N2?") or numerical orderings ("Can you put N1, N2, and N3 in order from smallest to largest?"), number-line estimates tell us how much larger the person understands the numbers to be. For example, when placing 15 on a 0-100 number line, the child's estimate tells us how large they think 15 is in comparison to 0 and 100. Proponents of the representational change approach (e.g., Opfer et al., 2011, Siegler and Opfer, 2003) argue that number-line estimation reflects understanding of how numerical magnitudes relate to one another. In contrast, proponents of the proportion judgment approach (e.g., Barth & Paladino, 2011; Slusser, Santiago, & Barth, 2013) argue that number-line estimation performance reflects children's ability to place estimates on a number line relative to the 0 endpoint (i.e., unbounded model)1, the 0 and right-most endpoint (i.e., 1-cycle model), or the endpoints and the midpoint of the number line (i.e., 2-cycle model). Proponents of both approaches agree that estimates improve over the course of development, becoming less variable and more accurate. However, they disagree on how best to interpret patterns of data arising from number-line estimation. Are young children's estimates best fit by a mixed log-linear model (representational change approach; Opfer, Thompson, & Kim, 2016; Kim and Opfer, 2017, Kim and Opfer, 2020) or one of several cyclical power functions (proportion judgment approach; Barth & Paladino, 2011; Slusser et al., 2013) when model complexity (e.g., number of free parameters) is taken into consideration? In this rebuttal to Xing et al.'s target article, Numerical estimation strategies are correlated with math ability in school-age children, we argue that: 1. Number-line estimates reflect numerical magnitude representations, some task-specific features, and strategic behavior. 2. Proportional reasoning and representational change accounts must be compared head-to-head. 3. Whole numbers are ratios, too. Therefore, research on fractions can clarify mechanisms of developmental change in number-line estimation. [This paper was published in "Cognitive Development" v62 2022.]
Abstractor: As Provided
IES Funded: Yes
Entry Date: 2024
Accession Number: ED639265
Database: ERIC
FullText Text:
  Availability: 0
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  Data: Comments Regarding 'Numerical Estimation Strategies Are Correlated with Math Ability in School-Age Children'
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  Data: <searchLink fieldCode="AR" term="%22Clarissa+A%2E+Thompson%22">Clarissa A. Thompson</searchLink><br /><searchLink fieldCode="AR" term="%22Pooja+G%2E+Sidney%22">Pooja G. Sidney</searchLink><br /><searchLink fieldCode="AR" term="%22Charles+J%2E+Fitzsimmons%22">Charles J. Fitzsimmons</searchLink><br /><searchLink fieldCode="AR" term="%22Marta+Mielicki%22">Marta Mielicki</searchLink><br /><searchLink fieldCode="AR" term="%22Lauren+Schiller%22">Lauren Schiller</searchLink><br /><searchLink fieldCode="AR" term="%22Daniel+A%2E+Scheibe%22">Daniel A. Scheibe</searchLink><br /><searchLink fieldCode="AR" term="%22John+E%2E+Opfer%22">John E. Opfer</searchLink><br /><searchLink fieldCode="AR" term="%22Robert+S%2E+Siegler%22">Robert S. Siegler</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Grantee+Submission%22"><i>Grantee Submission</i></searchLink>. 2022.
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  Data: 32
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  Data: 2022
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  Data: R305U200004<br />R305A180514<br />1941132
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  Data: 10.1016/j.cogdev.2022.101188
– Name: Abstract
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  Data: In the target article, Xing and colleagues (2021) claimed that 6- to 8-year-olds who spontaneously referenced the midpoint of 0-100 number lines made more accurate magnitude estimates and scored higher on a standardized math achievement test than other children. Unlike previous studies, however, the authors found no relation between accuracy on the number line estimation task and a dot discrimination task used to assess the Approximate Number System (ANS). These findings, the authors claim, constitute evidence against the idea that children's numerical magnitude understanding entails representational change. We disagree. In the literature on the development of numerical magnitude understanding, the "gold standard" assessment is the number-line estimation task (Schneider et al., 2018, Siegler and Opfer, 2003, Siegler et al., 2009). Unlike numerical comparisons ("Which is larger--N1 or N2?") or numerical orderings ("Can you put N1, N2, and N3 in order from smallest to largest?"), number-line estimates tell us how much larger the person understands the numbers to be. For example, when placing 15 on a 0-100 number line, the child's estimate tells us how large they think 15 is in comparison to 0 and 100. Proponents of the representational change approach (e.g., Opfer et al., 2011, Siegler and Opfer, 2003) argue that number-line estimation reflects understanding of how numerical magnitudes relate to one another. In contrast, proponents of the proportion judgment approach (e.g., Barth & Paladino, 2011; Slusser, Santiago, & Barth, 2013) argue that number-line estimation performance reflects children's ability to place estimates on a number line relative to the 0 endpoint (i.e., unbounded model)1, the 0 and right-most endpoint (i.e., 1-cycle model), or the endpoints and the midpoint of the number line (i.e., 2-cycle model). Proponents of both approaches agree that estimates improve over the course of development, becoming less variable and more accurate. However, they disagree on how best to interpret patterns of data arising from number-line estimation. Are young children's estimates best fit by a mixed log-linear model (representational change approach; Opfer, Thompson, & Kim, 2016; Kim and Opfer, 2017, Kim and Opfer, 2020) or one of several cyclical power functions (proportion judgment approach; Barth & Paladino, 2011; Slusser et al., 2013) when model complexity (e.g., number of free parameters) is taken into consideration? In this rebuttal to Xing et al.'s target article, Numerical estimation strategies are correlated with math ability in school-age children, we argue that: 1. Number-line estimates reflect numerical magnitude representations, some task-specific features, and strategic behavior. 2. Proportional reasoning and representational change accounts must be compared head-to-head. 3. Whole numbers are ratios, too. Therefore, research on fractions can clarify mechanisms of developmental change in number-line estimation. [This paper was published in "Cognitive Development" v62 2022.]
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PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=ED639265
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      – Type: doi
        Value: 10.1016/j.cogdev.2022.101188
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 32
    Subjects:
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Young Children
        Type: general
      – SubjectFull: Number Concepts
        Type: general
      – SubjectFull: Accuracy
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      – SubjectFull: Scores
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      – SubjectFull: Mathematics Tests
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      – SubjectFull: Achievement Tests
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      – SubjectFull: Computation
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      – SubjectFull: Mathematics Achievement
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      – SubjectFull: Academic Ability
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      – SubjectFull: Fractions
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      – SubjectFull: Preschool Children
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      – TitleFull: Comments Regarding 'Numerical Estimation Strategies Are Correlated with Math Ability in School-Age Children'
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