Vol. 34 No. 1 (2026): Online First
Articles

Expanding the Scope of Unit Transformation Graphs to Space and Measurement

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  • Joseph Antonides,
  • Anderson Norton
Joseph Antonides
Colorado State University
Anderson Norton
Virginia Tech

Published 2026-10-15

Keywords

  • unit coordination,
  • cognition,
  • radical constructivism,
  • multiplicative reasoning,
  • unit transformation graphs,
  • spatial reasoning
    • ...More
    Less

Copyright (c) 2026 Joseph Antonides, Anderson Norton

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Abstract

Building models of students’ mathematics allows researchers to understand, appreciate, and build on students’ reasoning. Grounded in Piagetian epistemology, unit transformation graphs provide a way to model students’ mathematics by explicating the mental actions that students use and coordinate in problem-solving. Prior research has focused on UTGs in numerical contexts, particularly fractions. The purpose of this theoretical article is to expand the scope of UTGs to model students’ spatial comparison, enumeration, and measurement, by modeling students’ coordinations of numerical and spatial mental actions. We illustrate this expansion with examples of one preservice elementary school teacher’s solutions to tasks involving 1D and 3D spatial quantities. We conclude with implications for both theory and practice.

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References

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