Creating a Context for Learning: Activating Children’s Whole Number Knowledge Prepares Them to Understand Fraction Division
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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PsychOpen GOLD/ Leibniz Insitute for Psychology
2017-07-01
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| Series: | Journal of Numerical Cognition |
| Subjects: | |
| Online Access: | http://jnc.psychopen.eu/article/view/71 |
| _version_ | 1797968302066106368 |
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| author | Pooja Gupta Sidney Martha Wagner Alibali |
| author_facet | Pooja Gupta Sidney Martha Wagner Alibali |
| author_sort | Pooja Gupta Sidney |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T02:43:39Z |
| format | Article |
| id | doaj.art-bad3e1e6a7e747278c0a2cb3ccc6947b |
| institution | Directory Open Access Journal |
| issn | 2363-8761 |
| language | English |
| last_indexed | 2024-04-11T02:43:39Z |
| publishDate | 2017-07-01 |
| publisher | PsychOpen GOLD/ Leibniz Insitute for Psychology |
| record_format | Article |
| series | Journal of Numerical Cognition |
| spelling | doaj.art-bad3e1e6a7e747278c0a2cb3ccc6947b2023-01-02T18:29:20ZengPsychOpen GOLD/ Leibniz Insitute for PsychologyJournal of Numerical Cognition2363-87612017-07-0131315710.5964/jnc.v3i1.71jnc.v3i1.71Creating a Context for Learning: Activating Children’s Whole Number Knowledge Prepares Them to Understand Fraction DivisionPooja Gupta Sidney0Martha Wagner Alibali1Department of Psychological Sciences, Kent State University, Kent, OH, USADepartment of Psychology, University of Wisconsin-Madison, Madison, WI, USAWhen 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.http://jnc.psychopen.eu/article/view/71analogical transferanalogical primingmathematics learningfraction divisionwhole number bias |
| spellingShingle | Pooja Gupta Sidney Martha Wagner Alibali Creating a Context for Learning: Activating Children’s Whole Number Knowledge Prepares Them to Understand Fraction Division Journal of Numerical Cognition analogical transfer analogical priming mathematics learning fraction division whole number bias |
| title | Creating a Context for Learning: Activating Children’s Whole Number Knowledge Prepares Them to Understand Fraction Division |
| title_full | Creating a Context for Learning: Activating Children’s Whole Number Knowledge Prepares Them to Understand Fraction Division |
| title_fullStr | Creating a Context for Learning: Activating Children’s Whole Number Knowledge Prepares Them to Understand Fraction Division |
| title_full_unstemmed | Creating a Context for Learning: Activating Children’s Whole Number Knowledge Prepares Them to Understand Fraction Division |
| title_short | Creating a Context for Learning: Activating Children’s Whole Number Knowledge Prepares Them to Understand Fraction Division |
| title_sort | creating a context for learning activating children s whole number knowledge prepares them to understand fraction division |
| topic | analogical transfer analogical priming mathematics learning fraction division whole number bias |
| url | http://jnc.psychopen.eu/article/view/71 |
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