Natural alternatives to natural number: The case of ratio
Author(s) / Creator(s)
Matthews, Percival G.
Ellis, Amy B.
Abstract / Description
The overwhelming majority of efforts to cultivate early mathematical thinking rely primarily on counting and associated natural number concepts. Unfortunately, natural numbers and discretized thinking do not align well with a large swath of the mathematical concepts we wish for children to learn. This misalignment presents an important impediment to teaching and learning. We suggest that one way to circumvent these pitfalls is to leverage students’ non-numerical experiences that can provide intuitive access to foundational mathematical concepts. Specifically, we advocate for explicitly leveraging a) students’ perceptually based intuitions about quantity and b) students’ reasoning about change and variation, and we address the affordances offered by this approach. We argue that it can support ways of thinking that may at times align better with to-be-learned mathematical ideas, and thus may serve as a productive alternative for particular mathematical concepts when compared to number. We illustrate this argument using the domain of ratio, and we do so from the distinct disciplinary lenses we employ respectively as a cognitive psychologist and as a mathematics education researcher. Finally, we discuss the potential for productive synthesis given the substantial differences in our preferred methods and general epistemologies.
Keyword(s)
number perception ratio rational numberPersistent Identifier
Date of first publication
2018-06-07
Journal title
Journal of Numerical Cognition
Volume
4
Issue
1
Page numbers
19–58
Publisher
PsychOpen GOLD
Publication status
publishedVersion
Review status
peerReviewed
Is version of
Citation
Matthews, P. G., & Ellis, A. B. (2018). Natural alternatives to natural number: The case of ratio. Journal of Numerical Cognition, 4(1), 19–58. https://doi.org/10.5964/jnc.v4i1.97
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Author(s) / Creator(s)Matthews, Percival G.
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Author(s) / Creator(s)Ellis, Amy B.
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PsychArchives acquisition timestamp2018-11-21T11:42:55Z
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Made available on2018-11-21T11:42:55Z
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Date of first publication2018-06-07
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Abstract / DescriptionThe overwhelming majority of efforts to cultivate early mathematical thinking rely primarily on counting and associated natural number concepts. Unfortunately, natural numbers and discretized thinking do not align well with a large swath of the mathematical concepts we wish for children to learn. This misalignment presents an important impediment to teaching and learning. We suggest that one way to circumvent these pitfalls is to leverage students’ non-numerical experiences that can provide intuitive access to foundational mathematical concepts. Specifically, we advocate for explicitly leveraging a) students’ perceptually based intuitions about quantity and b) students’ reasoning about change and variation, and we address the affordances offered by this approach. We argue that it can support ways of thinking that may at times align better with to-be-learned mathematical ideas, and thus may serve as a productive alternative for particular mathematical concepts when compared to number. We illustrate this argument using the domain of ratio, and we do so from the distinct disciplinary lenses we employ respectively as a cognitive psychologist and as a mathematics education researcher. Finally, we discuss the potential for productive synthesis given the substantial differences in our preferred methods and general epistemologies.en_US
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Publication statuspublishedVersion
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Review statuspeerReviewed
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CitationMatthews, P. G., & Ellis, A. B. (2018). Natural alternatives to natural number: The case of ratio. Journal of Numerical Cognition, 4(1), 19–58. https://doi.org/10.5964/jnc.v4i1.97en_US
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ISSN2363-8761
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Persistent Identifierhttps://hdl.handle.net/20.500.12034/1291
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Persistent Identifierhttps://doi.org/10.23668/psycharchives.1483
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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.v4i1.97
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Keyword(s)numberen_US
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Keyword(s)perceptionen_US
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Keyword(s)ratioen_US
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Keyword(s)rational numberen_US
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Dewey Decimal Classification number(s)150
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TitleNatural alternatives to natural number: The case of ratioen_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 numbers19–58
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Volume4
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Visible tag(s)Version of Record