Middle school students' and mathematicians' judgments of mathematical typicality
Author(s) / Creator(s)
Walkington, Candace
Cooper, Jennifer
Leonard, Olubukola
Williams-Pierce, Caroline
Kalish, Chuck
Abstract / Description
K-12 students often rely on testing examples to explore and determine the truth of mathematical conjectures. However, little is known about how K-12 students choose examples and what elements are important when considering example choice. In other domains, experts give explicit consideration to the typicality of examples – how representative a given item is of a general class. In a pilot study, we interviewed 20 middle school students who classified examples as typical or unusual and justified their classification. We then gave middle school students and mathematicians a survey where they rated the typicality of mathematical objects in two contexts – an everyday context (commonness in everyday life) and a mathematical context (how likely conjectures that hold for the object are to hold for other objects). Mathematicians had distinct notions of everyday and mathematical typicality – they recognized that the objects often seen in everyday life can have mathematical properties that can limit inductive generalization. Middle school students largely did not differentiate between everyday and mathematical typicality – they did not view special mathematical properties as limiting generalization, and rated items similarly regardless of context. These results suggest directions for learning mathematical argumentation and represent an important step towards understanding the nature of typicality in math.
Keyword(s)
typicality proof inductive generalizationPersistent Identifier
Date of first publication
2018-06-07
Journal title
Journal of Numerical Cognition
Volume
4
Issue
1
Page numbers
243–270
Publisher
PsychOpen GOLD
Publication status
publishedVersion
Review status
peerReviewed
Is version of
Citation
Walkington, C., Cooper, J., Leonard, O., Williams-Pierce, C., & Kalish, C. (2018). Middle school students' and mathematicians' judgments of mathematical typicality. Journal of Numerical Cognition, 4(1), 243–270. https://doi.org/10.5964/jnc.v4i1.70
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jnc.v4i1.70.pdfAdobe PDF - 997.02KBMD5: 37f67a57130a36ec35edee6193eb22e9
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Author(s) / Creator(s)Walkington, Candace
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Author(s) / Creator(s)Cooper, Jennifer
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Author(s) / Creator(s)Leonard, Olubukola
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Author(s) / Creator(s)Williams-Pierce, Caroline
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Author(s) / Creator(s)Kalish, Chuck
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PsychArchives acquisition timestamp2018-11-21T11:42:53Z
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Made available on2018-11-21T11:42:53Z
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Date of first publication2018-06-07
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Abstract / DescriptionK-12 students often rely on testing examples to explore and determine the truth of mathematical conjectures. However, little is known about how K-12 students choose examples and what elements are important when considering example choice. In other domains, experts give explicit consideration to the typicality of examples – how representative a given item is of a general class. In a pilot study, we interviewed 20 middle school students who classified examples as typical or unusual and justified their classification. We then gave middle school students and mathematicians a survey where they rated the typicality of mathematical objects in two contexts – an everyday context (commonness in everyday life) and a mathematical context (how likely conjectures that hold for the object are to hold for other objects). Mathematicians had distinct notions of everyday and mathematical typicality – they recognized that the objects often seen in everyday life can have mathematical properties that can limit inductive generalization. Middle school students largely did not differentiate between everyday and mathematical typicality – they did not view special mathematical properties as limiting generalization, and rated items similarly regardless of context. These results suggest directions for learning mathematical argumentation and represent an important step towards understanding the nature of typicality in math.en_US
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Publication statuspublishedVersion
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Review statuspeerReviewed
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CitationWalkington, C., Cooper, J., Leonard, O., Williams-Pierce, C., & Kalish, C. (2018). Middle school students' and mathematicians' judgments of mathematical typicality. Journal of Numerical Cognition, 4(1), 243–270. https://doi.org/10.5964/jnc.v4i1.70en_US
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ISSN2363-8761
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Persistent Identifierhttps://hdl.handle.net/20.500.12034/1283
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Persistent Identifierhttps://doi.org/10.23668/psycharchives.1475
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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.v4i1.70
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Keyword(s)typicalityen_US
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Keyword(s)proofen_US
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Keyword(s)inductive generalizationen_US
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Dewey Decimal Classification number(s)150
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TitleMiddle school students' and mathematicians' judgments of mathematical typicalityen_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 numbers243–270
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Volume4
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Visible tag(s)Version of Record