RUME 28
2026
Alexandria, Virginia
The Persistence of Motion Graph Reasoning Amid Quantitative Conceptions of Coordinate Systems: The Case of Ava
Page: 340
We report on a qualitative case study of a college algebra student, Ava, who participated in a series of online task-based interviews involving graphs of different dynamic situations. Our analysis focused on the nature of Ava’s graph reasoning and coordinate system conceptions within and across these tasks. During Ava’s interviews, she primarily demonstrated Variation and Covariation graph reasoning while conceiving of the coordinate system quantitatively. Yet, she also had an expectation that her graphs would represent the motion of the objects in the dynamic situations or the motion of the traces in the graphs themselves. Ava’s Motion graph reasoning amid her quantitative conceptions of coordinate systems demonstrates overlap between quantitative and physical conceptions. Her case speaks to the richness of students’ conceptions of graphs; even when they conceive of quantitative coordinate systems, they can also expect a graph trace to resemble the motion of an object.