RUME 26
2024
Omaha, Nebraska
U-Substitution Through Quantitative Reasoning: A Conceptual Analysis
Page: 913
Research has shown how crucial quantities-based meanings are for calculus concepts. While past work has developed important quantitative approaches to integration, the major topic of u- substitution typically has not been fully detailed in these paradigms. This theoretical paper extends this past work to clearly define and elaborate u-substitution through a quantitative perspective. We use conceptual analysis based on quantities, starting with a concrete example of a solar panel producing energy. We abstract from this example to define u-substitution as a transformation from one quantitative relationship, via nested multivariation, to another quantitative relationship. We also detail a three-part structure within this transformation.