RUME 28
2026
Alexandria, Virginia
Quantitative Meanings for Graphs: States, Transformations, and Covariation
Page: 826
Research on students’ and teachers’ quantitative reasoning continues to underscore its importance for their learning and development. This importance requires that researchers continue to make strides in identifying salient and important ways of reasoning quantitatively. In this paper, we delineate four forms of quantitative reasoning to characterize both students’ images of situations and their graphing meanings related to those images. Specifically, we differentiate between students conceiving quantities’ changes via states reasoning, transformational reasoning, and gross or quantified covariational reasoning. We connect these forms of reasoning to their meanings for graphs when attempting to represent those quantities.