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

• Jamie Jirout
• Nora S. Newcombe
Chapter
Part of the Research in Mathematics Education book series (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.

## Keywords

Spatial scaling Spatial learning Spatial development Spatial visualization Scale Spatial representations Representations Diagrams Spatial-relational Relative magnitude Absolute magnitude Magnitude reasoning Number line estimation Proportional reasoning Fractions Symbolic understanding Benchmark strategy Manipulatives Interventions Spatial play

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## Authors and Affiliations

1. 1.Curry School of EducationUniversity of VirginiaCharlottesvilleUSA