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Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions

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Title: Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions
Language: English
Authors: Jeffrey Kramer Bye (ORCID 0000-0002-2636-3657), Jenny Yun-Chen Chan (ORCID 0000-0003-1479-5935), Avery H. Closser (ORCID 0000-0003-2712-8509), Ji-Eun Lee (ORCID 0000-0001-8521-8997), Stacy T. Shaw (ORCID 0000-0002-4326-9937), Erin R. Ottmar (ORCID 0000-0002-9487-7967)
Source: Journal of Numerical Cognition. Article e14103 2024 10.
Availability: Leibniz Institute for Psychology. Universitatsring 15, Trier, 54296, Germany. e-mail: support@psychopen.eu; Web site: https://jnc.psychopen.eu
Peer Reviewed: Y
Page Count: 23
Publication Date: 2024
Document Type: Journal Articles
Reports - Research
Education Level: Junior High Schools
Middle Schools
Secondary Education
Descriptors: Middle School Students, Middle School Mathematics, Arithmetic, Mathematics Skills, Problem Solving, Computation, Algebra, Mathematics Anxiety, Predictor Variables, Error Patterns, Individual Differences, Educational Games, Perceptual Development, Perceptual Motor Learning
ISSN: 2363-8761
Abstract: Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order of precedence (the order of operations). Research has shown that the syntactic structure of problems, and students' perceptual processes, are involved in mathematics performance and developing fluency with precedence. We examined 837 U.S. middle schoolers' propensity for precedence errors on six problems in an online mathematics game. We included an algebra knowledge assessment, math anxiety measure, and a perceptual math equivalence task measuring quick detection of equivalent expressions as predictors of students' precedence errors. We found that students made more precedence errors when the leftmost operation was invalid (addition followed by multiplication). Individual difference analyses revealed that students varied in propensity for precedence errors, which was better predicted by students' performance on the perceptual math equivalence task than by their algebra knowledge or math anxiety. Students' performance on the perceptual task and interactive game provide rich insights into their real-time understanding of precedence and the role of perceptual processes in equation solving.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1459951
Database: ERIC
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  Data: <searchLink fieldCode="AR" term="%22Jeffrey+Kramer+Bye%22">Jeffrey Kramer Bye</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-2636-3657">0000-0002-2636-3657</externalLink>)<br /><searchLink fieldCode="AR" term="%22Jenny+Yun-Chen+Chan%22">Jenny Yun-Chen Chan</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-1479-5935">0000-0003-1479-5935</externalLink>)<br /><searchLink fieldCode="AR" term="%22Avery+H%2E+Closser%22">Avery H. Closser</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-2712-8509">0000-0003-2712-8509</externalLink>)<br /><searchLink fieldCode="AR" term="%22Ji-Eun+Lee%22">Ji-Eun Lee</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-8521-8997">0000-0001-8521-8997</externalLink>)<br /><searchLink fieldCode="AR" term="%22Stacy+T%2E+Shaw%22">Stacy T. Shaw</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-4326-9937">0000-0002-4326-9937</externalLink>)<br /><searchLink fieldCode="AR" term="%22Erin+R%2E+Ottmar%22">Erin R. Ottmar</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-9487-7967">0000-0002-9487-7967</externalLink>)
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  Data: Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order of precedence (the order of operations). Research has shown that the syntactic structure of problems, and students' perceptual processes, are involved in mathematics performance and developing fluency with precedence. We examined 837 U.S. middle schoolers' propensity for precedence errors on six problems in an online mathematics game. We included an algebra knowledge assessment, math anxiety measure, and a perceptual math equivalence task measuring quick detection of equivalent expressions as predictors of students' precedence errors. We found that students made more precedence errors when the leftmost operation was invalid (addition followed by multiplication). Individual difference analyses revealed that students varied in propensity for precedence errors, which was better predicted by students' performance on the perceptual math equivalence task than by their algebra knowledge or math anxiety. Students' performance on the perceptual task and interactive game provide rich insights into their real-time understanding of precedence and the role of perceptual processes in equation solving.
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    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 23
    Subjects:
      – SubjectFull: Middle School Students
        Type: general
      – SubjectFull: Middle School Mathematics
        Type: general
      – SubjectFull: Arithmetic
        Type: general
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Problem Solving
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      – SubjectFull: Computation
        Type: general
      – SubjectFull: Algebra
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      – SubjectFull: Mathematics Anxiety
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      – SubjectFull: Predictor Variables
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      – SubjectFull: Error Patterns
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      – SubjectFull: Individual Differences
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      – SubjectFull: Educational Games
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      – SubjectFull: Perceptual Development
        Type: general
      – SubjectFull: Perceptual Motor Learning
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    Titles:
      – TitleFull: Perceiving Precedence: Order of Operations Errors Are Predicted by Perception of Equivalent Expressions
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