RUME 28
2026
Alexandria, Virginia
Chunky or Smooth? Students’ Covariational Reasoning When Analyzing Phase Plane Trajectories
Page: 1363
Over the last few decades graphical and numerical methods have gained importance to study differential equations. One central skill when studying the long-term behaviors of models described by differential equations is the ability to navigate between time series and phase plane trajectories. Building on previous research that described how students mainly used smooth or chunky continuous reasoning when building these graphs, we investigated how students justify the use of either of these levels of reasoning. We gave students one (smooth) time series and two possible corresponding trajectories, one smooth and one chunky. While all students said that the smooth trajectory best corresponded to the given time series, the reasonings invoked varied greatly. We will present and discuss the different types of arguments invoked by the students as well as implications for practice.