Article Version of Record

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 bias

Persistent 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
  • Author(s) / Creator(s)
    Sidney, Pooja Gupta
  • Author(s) / Creator(s)
    Alibali, Martha Wagner
  • PsychArchives acquisition timestamp
    2018-11-21T11:42:43Z
  • Made available on
    2018-11-21T11:42:43Z
  • Date of first publication
    2017-07-21
  • 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.
    en_US
  • Publication status
    publishedVersion
  • Review status
    peerReviewed
  • 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
    en_US
  • ISSN
    2363-8761
  • Persistent Identifier
    https://hdl.handle.net/20.500.12034/1249
  • Persistent Identifier
    https://doi.org/10.23668/psycharchives.1441
  • Language of content
    eng
  • Publisher
    PsychOpen GOLD
  • Is version of
    https://doi.org/10.5964/jnc.v3i1.71
  • Keyword(s)
    analogical transfer
    en_US
  • Keyword(s)
    analogical priming
    en_US
  • Keyword(s)
    mathematics learning
    en_US
  • Keyword(s)
    fraction division
    en_US
  • Keyword(s)
    whole number bias
    en_US
  • Dewey Decimal Classification number(s)
    150
  • Title
    Creating a context for learning: Activating children’s whole number knowledge prepares them to understand fraction division
    en_US
  • DRO type
    article
  • Issue
    1
  • Journal title
    Journal of Numerical Cognition
  • Page numbers
    31–57
  • Volume
    3
  • Visible tag(s)
    Version of Record