RUME 28
2026
Alexandria, Virginia
Exploring Covariational Reasoning Pathways in Undergraduate Mathematical Modeling
Page: 1331
Modeling plays an important role in helping students make sense of and analyze complex biological systems, which is essential for those in life sciences or health professions. This study investigates undergraduate students’ covariational reasoning (CR) when engaging in tasks requiring movement across multiple representations, such as developing a trajectory from a time series and, conversely, developing a time series from a trajectory. A trajectory illustrates how two variables change in a space formed by those variables, while a time series demonstrates how a variable changes as a function of time. Covariational reasoning refers to an understanding of how two quantities interact with one another, and is foundational to reasoning with multiple quantities, comprehending the concept of function, and modeling dynamic events. Building on our previous work, we focus on how students reason through multiple representational shifts and how their CR manifests across tasks. Ten task-based think-aloud interviews were conducted with students who had completed a life science modeling course at a research-intensive university in the southwestern region of the United States. Interview data were deductively coded using Thompson and Carlson’s (2017) six levels of CR, followed by reflexive thematic analysis (Braun & Clarke, 2006). Preliminary findings elucidate the dynamic and flexible nature of CR, as students shifted between reasoning levels depending on task demands. We present three empirical cases to illustrate the various CR pathways and show how classroom norms and teacher expectations may shape students’ conceptions of what counts as “correct.”