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The Effects of Operator Position and Superfluous Brackets on Student Performance in Simple Arithmetic

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Title: The Effects of Operator Position and Superfluous Brackets on Student Performance in Simple Arithmetic
Language: English
Authors: Ngo, Vy, Perez Lacera, Luisa, Closser, Avery Harrison, Ottmar, Erin
Source: Journal of Numerical Cognition. 2023 9(1):107-128.
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: 22
Publication Date: 2023
Sponsoring Agency: National Science Foundation (NSF)
Contract Number: 1724889
1931523
1645629
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Grade 5
Intermediate Grades
Middle Schools
Descriptors: Mathematics Skills, Arithmetic, Symbols (Mathematics), Computation, Cognitive Processes, Problem Solving, Accuracy, Homework, Educational Technology, Assignments, Mastery Learning, Reaction Time, Elementary School Students, Grade 5, Algebra, Perceptual Development
ISSN: 2363-8761
Abstract: For students to advance beyond arithmetic, they must learn how to attend to the structure of math notation. This process can be challenging due to students' left-to-right computing tendencies. Brackets are used in mathematics to indicate precedence but can also be used as superfluous cues and perceptual grouping mechanisms in instructional materials to direct students' attention and facilitate accurate and efficient problem solving. This online study examines the impact of operator position and superfluous brackets on students' performance solving arithmetic problems. A total of 528 students completed a baseline assessment of math knowledge, then were randomly assigned to one of six conditions that varied in the placement of higher-order operator and the presence or absence of superfluous brackets: [a] brackets-left (e.g., (5 * 4) + 2 + 3), [b] no brackets-left (e.g., 5 * 4 + 2 + 3), [c] brackets-center (e.g., 2 + (5 * 4) + 3), [d] no brackets-center (e.g., 2 + 5 * 4 + 3), [e] brackets-right (e.g., 2 + 3 + (5 * 4)), and [f] no brackets-right (e.g., 2 + 3 + 5 * 4). Participants simplified expressions in an online learning platform with the goal to "master" the content by answering three questions correctly in a row. Results showed that, on average, students were more accurate in problem solving when the higher-order operator was on the left side and less accurate when it was on the right compared to in the center. There was also a main effect of the presence of brackets on mastery speed. However, interaction effects showed that these main effects were driven by the center position: superfluous brackets only improved accuracy when students solved expressions with brackets with the operator in the center. This study advances research on perceptual learning in math by revealing how operator position and presence of superfluous brackets impact students' performance. Additionally, this research provides implications for instructors who can use perceptual cues to support students during problem solving.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1386923
Database: ERIC
FullText Text:
  Availability: 0
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  Data: The Effects of Operator Position and Superfluous Brackets on Student Performance in Simple Arithmetic
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  Data: <searchLink fieldCode="SO" term="%22Journal+of+Numerical+Cognition%22"><i>Journal of Numerical Cognition</i></searchLink>. 2023 9(1):107-128.
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  Data: Leibniz Institute for Psychology. Universitatsring 15, Trier, 54296, Germany. e-mail: support@psychopen.eu; Web site: https://jnc.psychopen.eu
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  Data: For students to advance beyond arithmetic, they must learn how to attend to the structure of math notation. This process can be challenging due to students' left-to-right computing tendencies. Brackets are used in mathematics to indicate precedence but can also be used as superfluous cues and perceptual grouping mechanisms in instructional materials to direct students' attention and facilitate accurate and efficient problem solving. This online study examines the impact of operator position and superfluous brackets on students' performance solving arithmetic problems. A total of 528 students completed a baseline assessment of math knowledge, then were randomly assigned to one of six conditions that varied in the placement of higher-order operator and the presence or absence of superfluous brackets: [a] brackets-left (e.g., (5 * 4) + 2 + 3), [b] no brackets-left (e.g., 5 * 4 + 2 + 3), [c] brackets-center (e.g., 2 + (5 * 4) + 3), [d] no brackets-center (e.g., 2 + 5 * 4 + 3), [e] brackets-right (e.g., 2 + 3 + (5 * 4)), and [f] no brackets-right (e.g., 2 + 3 + 5 * 4). Participants simplified expressions in an online learning platform with the goal to "master" the content by answering three questions correctly in a row. Results showed that, on average, students were more accurate in problem solving when the higher-order operator was on the left side and less accurate when it was on the right compared to in the center. There was also a main effect of the presence of brackets on mastery speed. However, interaction effects showed that these main effects were driven by the center position: superfluous brackets only improved accuracy when students solved expressions with brackets with the operator in the center. This study advances research on perceptual learning in math by revealing how operator position and presence of superfluous brackets impact students' performance. Additionally, this research provides implications for instructors who can use perceptual cues to support students during problem solving.
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  Data: EJ1386923
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 22
        StartPage: 107
    Subjects:
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Arithmetic
        Type: general
      – SubjectFull: Symbols (Mathematics)
        Type: general
      – SubjectFull: Computation
        Type: general
      – SubjectFull: Cognitive Processes
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Accuracy
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      – SubjectFull: Homework
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      – SubjectFull: Educational Technology
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      – SubjectFull: Assignments
        Type: general
      – SubjectFull: Mastery Learning
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      – SubjectFull: Reaction Time
        Type: general
      – SubjectFull: Elementary School Students
        Type: general
      – SubjectFull: Grade 5
        Type: general
      – SubjectFull: Algebra
        Type: general
      – SubjectFull: Perceptual Development
        Type: general
    Titles:
      – TitleFull: The Effects of Operator Position and Superfluous Brackets on Student Performance in Simple Arithmetic
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            NameFull: Ottmar, Erin
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