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

An Alternative Quantitative Reasoning Approach to Integration by Substitution

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  • Kevin Moore,
  • Sohei Yasuda,
  • Webster Wong
Kevin Moore
University of Georgia
Sohei Yasuda
University of Georgia
Webster Wong
University of Georgia

Published 2026-05-21

Keywords

  • conceptual analysis,
  • integration by substitution,
  • accumulation,
  • quantitative reasoning

Copyright (c) 2026 Kevin Moore, Sohei Yasuda, Webster Wong

Creative Commons License

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

Abstract

In this paper, we present a conceptual analysis for integration for substitution that centers major ideas of quantitative reasoning, including accumulation rates, relationships between measures and unit magnitudes, and the multiplicative dependency of quantities. Our centering of these idea enables integration by substitution to occur through coordinating accumulation rates and intervals to reconstruct a desired integral structure. Our approach was inspired by the conceptual analysis provided by Jones and Fonbuena (2024), and thus we compare our approach with theirs throughout in order to highlight similarities and differences between the two. We close by acknowledging that a conceptual analysis is only as good as its use in working to support learning, and thus call for future work that transitions the analysis to work with students.

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