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The Power of One: The Importance of Flexible Understanding of an Identity Element

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Title: The Power of One: The Importance of Flexible Understanding of an Identity Element
Language: English
Authors: Schiller, Lauren K., Fan, Ao, Siegler, Robert S.
Source: Journal of Numerical Cognition. 2022 8(3):430-442.
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: 13
Publication Date: 2022
Sponsoring Agency: National Science Foundation (NSF)
Contract Number: R305A180514
1844140
Document Type: Journal Articles
Reports - Research
Education Level: Junior High Schools
Middle Schools
Secondary Education
Descriptors: Numbers, Mathematics Instruction, Multiplication, Division, Middle School Students, Fractions, Mathematical Concepts, Concept Formation, Arithmetic, Problem Solving, Accuracy, Textbooks, Teaching Methods, Content Analysis, Task Analysis, Knowledge Level, Suburban Schools, Prediction
ISSN: 2363-8761
Abstract: The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of students indicated that 36/36 = 1), most students did not recognize and apply knowledge of fraction forms of one to estimate numerical magnitudes, solve arithmetic problems, and evaluate arithmetic operations. Specifically, students were less accurate in locating fraction forms of one on number lines than integer forms of the same number; they also were slower and less accurate on fraction arithmetic problems that included one as a fraction (e.g., 6/6 + 1/3) than one as an integer (e.g., 1 + 1/3); and they were less accurate evaluating statements involving fraction forms of one than the integer one (e.g., lower accuracy on true or false statements such as 5/6 × 2/2 = 5/6 than 4/9 × 1 = 4/9). Analyses of three widely used textbook series revealed almost no text linking fractions in the form n/n to the integer one. Greater emphasis on flexible understanding of fractions equivalent to one in textbooks and instruction might promote greater understanding of rational number mathematics more generally
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1375263
Database: ERIC
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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: The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of students indicated that 36/36 = 1), most students did not recognize and apply knowledge of fraction forms of one to estimate numerical magnitudes, solve arithmetic problems, and evaluate arithmetic operations. Specifically, students were less accurate in locating fraction forms of one on number lines than integer forms of the same number; they also were slower and less accurate on fraction arithmetic problems that included one as a fraction (e.g., 6/6 + 1/3) than one as an integer (e.g., 1 + 1/3); and they were less accurate evaluating statements involving fraction forms of one than the integer one (e.g., lower accuracy on true or false statements such as 5/6 × 2/2 = 5/6 than 4/9 × 1 = 4/9). Analyses of three widely used textbook series revealed almost no text linking fractions in the form n/n to the integer one. Greater emphasis on flexible understanding of fractions equivalent to one in textbooks and instruction might promote greater understanding of rational number mathematics more generally
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      – Text: English
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        PageCount: 13
        StartPage: 430
    Subjects:
      – SubjectFull: Numbers
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: Multiplication
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      – SubjectFull: Division
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      – SubjectFull: Fractions
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      – SubjectFull: Mathematical Concepts
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      – SubjectFull: Concept Formation
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      – SubjectFull: Arithmetic
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      – SubjectFull: Prediction
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      – TitleFull: The Power of One: The Importance of Flexible Understanding of an Identity Element
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