The effects of operator position and superfluous brackets on student performance in simple arithmetic
Author(s) / Creator(s)
Ngo, Vy
Perez Lacera, Luisa
Closser, Avery Harrison
Ottmar, Erin
Abstract / Description
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.
Keyword(s)
perceptual learning mathematical cognition structure sense simple arithmetic superfluous bracketsPersistent Identifier
Date of first publication
2023-03-31
Journal title
Journal of Numerical Cognition
Volume
9
Issue
1
Page numbers
107–128
Publisher
PsychOpen GOLD
Publication status
publishedVersion
Review status
peerReviewed
Is version of
Citation
Ngo, V., Perez Lacera, L., Closser, A. H., & Ottmar, E. (2023). The effects of operator position and superfluous brackets on student performance in simple arithmetic. Journal of Numerical Cognition, 9(1), 107-128. https://doi.org/10.5964/jnc.9535
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Author(s) / Creator(s)Ngo, Vy
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Author(s) / Creator(s)Perez Lacera, Luisa
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Author(s) / Creator(s)Closser, Avery Harrison
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Author(s) / Creator(s)Ottmar, Erin
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PsychArchives acquisition timestamp2023-04-28T10:04:25Z
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Made available on2023-04-28T10:04:25Z
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Date of first publication2023-03-31
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Abstract / DescriptionFor 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.en_US
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Publication statuspublishedVersion
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Review statuspeerReviewed
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CitationNgo, V., Perez Lacera, L., Closser, A. H., & Ottmar, E. (2023). The effects of operator position and superfluous brackets on student performance in simple arithmetic. Journal of Numerical Cognition, 9(1), 107-128. https://doi.org/10.5964/jnc.9535en_US
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ISSN2363-8761
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Persistent Identifierhttps://hdl.handle.net/20.500.12034/8349
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Persistent Identifierhttps://doi.org/10.23668/psycharchives.12826
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Language of contenteng
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PublisherPsychOpen GOLD
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Is version ofhttps://doi.org/10.5964/jnc.9535
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Is version ofhttps://doi.org/10.23668/psycharchives.12208
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Is version ofhttps://doi.org/10.23668/psycharchives.12206
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Is related tohttps://doi.org/10.23668/psycharchives.12205
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Is related tohttps://doi.org/10.23668/psycharchives.12204
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Is related tohttps://doi.org/10.23668/psycharchives.12208
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Is related tohttps://doi.org/10.23668/psycharchives.12206
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Is related tohttps://osf.io/xnps6/
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Keyword(s)perceptual learningen_US
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Keyword(s)mathematical cognitionen_US
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Keyword(s)structure senseen_US
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Keyword(s)simple arithmeticen_US
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Keyword(s)superfluous bracketsen_US
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Dewey Decimal Classification number(s)150
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TitleThe effects of operator position and superfluous brackets on student performance in simple arithmeticen_US
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DRO typearticle
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Issue1
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Journal titleJournal of Numerical Cognition
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Page numbers107–128
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Volume9
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Visible tag(s)Version of Recorden_US