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How Much as Compared to What: Relative Magnitude as a Key Idea in Mathematics Cognition

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Visualizing Mathematics

Part of the book series: Research in Mathematics Education ((RME))

Abstract

Most topics beyond basic arithmetic require relative magnitude reasoning. This chapter describes the link between relative magnitude reasoning and spatial scaling, a specific type of spatial thinking. We discuss use of the number line, proportional reasoning, and fractions. Consideration of the relational reasoning involved in mathematics can advance our understanding of its relation to spatial skills, and has implications for mathematics instruction, such as using spatial reasoning interventions in developing effective methods for supporting relative magnitude understanding. We review evidence that interventions can be successful in promoting better relative magnitude understanding and associated spatial-relational reasoning, and suggest that education considers ways of including relative magnitude learning, along with more traditional whole-number operations, in early educational efforts.

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Authors and Affiliations

  1. Curry School of Education, University of Virginia, Charlottesville, VA, USA

    Jamie Jirout

  2. Department of Psychology, Temple University, Philadelphia, PA, USA

    Nora S. Newcombe

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  1. Jamie Jirout
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  2. Nora S. Newcombe
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Correspondence to Jamie Jirout .

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Editors and Affiliations

  1. Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD, USA

    Kelly S. Mix

  2. Department of Teaching and Learning, The Ohio State University, Columbus, OH, USA

    Michael T. Battista

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Jirout, J., Newcombe, N.S. (2018). How Much as Compared to What: Relative Magnitude as a Key Idea in Mathematics Cognition. In: Mix, K., Battista, M. (eds) Visualizing Mathematics. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-98767-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-98767-5_1

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