14
views
0
recommends
+1 Recommend
1 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Natural Alternatives to Natural Number: The Case of Ratio

      research-article
      * , a , , b
      ,
      Journal of Numerical Cognition
      PsychOpen
      number, perception, ratio, rational number

      Read this article at

      ScienceOpenPublisherPubMed
      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          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.

          Related collections

          Most cited references119

          • Record: found
          • Abstract: found
          • Article: not found

          Grounded cognition.

          Grounded cognition rejects traditional views that cognition is computation on amodal symbols in a modular system, independent of the brain's modal systems for perception, action, and introspection. Instead, grounded cognition proposes that modal simulations, bodily states, and situated action underlie cognition. Accumulating behavioral and neural evidence supporting this view is reviewed from research on perception, memory, knowledge, language, thought, social cognition, and development. Theories of grounded cognition are also reviewed, as are origins of the area and common misperceptions of it. Theoretical, empirical, and methodological issues are raised whose future treatment is likely to affect the growth and impact of grounded cognition.
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Mixed Methods Research: A Research Paradigm Whose Time Has Come

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              The mental representation of parity and number magnitude.

                Bookmark

                Author and article information

                Journal
                JNC
                J Numer Cogn
                Journal of Numerical Cognition
                J. Numer. Cogn.
                PsychOpen
                2363-8761
                2018
                07 June 2018
                : 4
                : 1
                : 19-58
                Affiliations
                [a ] University of Wisconsin-Madison , Madison, WI, USA
                [b ] University of Georgia , Athens, GA, USA
                [3]Department of Mathematics, Virginia Tech , Blacksburg, VA, USA
                [4]School of Teaching, Learning, and Curriculum Studies, Kent State University , Kent, OH, USA
                Author notes
                [* ]Department of Educational Psychology, University of Wisconsin – Madison, 1025 W. Johnson Street #884, Madison, Wisconsin 53706-1796, USA. Phone: (608) 263-3600, Fax: (608) 262-0843. pmatthews@ 123456wisc.edu
                Author information
                http://orcid.org/0000-0001-6265-813X
                http://orcid.org/0000-0002-1729-7694
                Article
                jnc.v4i1.97
                10.5964/jnc.v4i1.97
                31463363
                e2d00803-660c-4b61-b89b-4ecd3491f591
                Copyright @ 2018

                This is an open-access article distributed under the terms of the Creative Commons Attribution (CC BY) 4.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 01 November 2016
                : 03 June 2017
                Categories
                Theoretical Contributions

                Psychology
                rational number,number,perception,ratio
                Psychology
                rational number, number, perception, ratio

                Comments

                Comment on this article