Creating a context for learning: Activating children’s whole number knowledge prepares them to understand fraction division
Author(s) / Creator(s)
Sidney, Pooja Gupta
Alibali, Martha Wagner
Abstract / Description
When children learn about fractions, their prior knowledge of whole numbers often interferes, resulting in a whole number bias. However, many fraction concepts are generalizations of analogous whole number concepts; for example, fraction division and whole number division share a similar conceptual structure. Drawing on past studies of analogical transfer, we hypothesize that children’s whole number division knowledge will support their understanding of fraction division when their relevant prior knowledge is activated immediately before engaging with fraction division. Children in 5th and 6th grade modeled fraction division with physical objects after modeling a series of addition, subtraction, multiplication, and division problems with whole number operands and fraction operands. In one condition, problems were blocked by operation, such that children modeled fraction problems immediately after analogous whole number problems (e.g., fraction division problems followed whole number division problems). In another condition, problems were blocked by number type, such that children modeled all four arithmetic operations with whole numbers in the first block, and then operations with fractions in the second block. Children who solved whole number division problems immediately before fraction division problems were significantly better at modeling the conceptual structure of fraction division than those who solved all of the fraction problems together. Thus, implicit analogies across shared concepts can affect children’s mathematical thinking. Moreover, specific analogies between whole number and fraction concepts can yield a positive, rather than a negative, whole number bias.
Keyword(s)
analogical transfer analogical priming mathematics learning fraction division whole number biasPersistent Identifier
Date of first publication
2017-07-21
Journal title
Journal of Numerical Cognition
Volume
3
Issue
1
Page numbers
31–57
Publisher
PsychOpen GOLD
Publication status
publishedVersion
Review status
peerReviewed
Is version of
Citation
Sidney, P. G., & Alibali, M. W. (2017). Creating a context for learning: Activating children’s whole number knowledge prepares them to understand fraction division. Journal of Numerical Cognition, 3(1), 31–57. https://doi.org/10.5964/jnc.v3i1.71
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Author(s) / Creator(s)Sidney, Pooja Gupta
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Author(s) / Creator(s)Alibali, Martha Wagner
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PsychArchives acquisition timestamp2018-11-21T11:42:43Z
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Made available on2018-11-21T11:42:43Z
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Date of first publication2017-07-21
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Abstract / DescriptionWhen children learn about fractions, their prior knowledge of whole numbers often interferes, resulting in a whole number bias. However, many fraction concepts are generalizations of analogous whole number concepts; for example, fraction division and whole number division share a similar conceptual structure. Drawing on past studies of analogical transfer, we hypothesize that children’s whole number division knowledge will support their understanding of fraction division when their relevant prior knowledge is activated immediately before engaging with fraction division. Children in 5th and 6th grade modeled fraction division with physical objects after modeling a series of addition, subtraction, multiplication, and division problems with whole number operands and fraction operands. In one condition, problems were blocked by operation, such that children modeled fraction problems immediately after analogous whole number problems (e.g., fraction division problems followed whole number division problems). In another condition, problems were blocked by number type, such that children modeled all four arithmetic operations with whole numbers in the first block, and then operations with fractions in the second block. Children who solved whole number division problems immediately before fraction division problems were significantly better at modeling the conceptual structure of fraction division than those who solved all of the fraction problems together. Thus, implicit analogies across shared concepts can affect children’s mathematical thinking. Moreover, specific analogies between whole number and fraction concepts can yield a positive, rather than a negative, whole number bias.en_US
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Publication statuspublishedVersion
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Review statuspeerReviewed
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CitationSidney, P. G., & Alibali, M. W. (2017). Creating a context for learning: Activating children’s whole number knowledge prepares them to understand fraction division. Journal of Numerical Cognition, 3(1), 31–57. https://doi.org/10.5964/jnc.v3i1.71en_US
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ISSN2363-8761
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Persistent Identifierhttps://hdl.handle.net/20.500.12034/1249
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Persistent Identifierhttps://doi.org/10.23668/psycharchives.1441
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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.v3i1.71
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Keyword(s)analogical transferen_US
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Keyword(s)analogical primingen_US
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Keyword(s)mathematics learningen_US
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Keyword(s)fraction divisionen_US
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Keyword(s)whole number biasen_US
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Dewey Decimal Classification number(s)150
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TitleCreating a context for learning: Activating children’s whole number knowledge prepares them to understand fraction divisionen_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 numbers31–57
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Volume3
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Visible tag(s)Version of Record