Article Version of Record

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 number

Persistent 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
  • Author(s) / Creator(s)
    Matthews, Percival G.
  • Author(s) / Creator(s)
    Ellis, Amy B.
  • PsychArchives acquisition timestamp
    2018-11-21T11:42:55Z
  • Made available on
    2018-11-21T11:42:55Z
  • Date of first publication
    2018-06-07
  • 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.
    en_US
  • Publication status
    publishedVersion
  • Review status
    peerReviewed
  • 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
    en_US
  • ISSN
    2363-8761
  • Persistent Identifier
    https://hdl.handle.net/20.500.12034/1291
  • Persistent Identifier
    https://doi.org/10.23668/psycharchives.1483
  • Language of content
    eng
  • Publisher
    PsychOpen GOLD
  • Is version of
    https://doi.org/10.5964/jnc.v4i1.97
  • Keyword(s)
    number
    en_US
  • Keyword(s)
    perception
    en_US
  • Keyword(s)
    ratio
    en_US
  • Keyword(s)
    rational number
    en_US
  • Dewey Decimal Classification number(s)
    150
  • Title
    Natural alternatives to natural number: The case of ratio
    en_US
  • DRO type
    article
  • Issue
    1
  • Journal title
    Journal of Numerical Cognition
  • Page numbers
    19–58
  • Volume
    4
  • Visible tag(s)
    Version of Record