PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
The role of lines and points in the construction of emergent shape thinking
Page: 571
In this study, we focus on a student’s meanings for lines and points in the context of graphing covarying quantities. Specifically, we illustrate a student conceiving a line as representing a direction of movement of a dot on a coordinate plane. Consequently, the student did not conceive a dot moving in the coordinate plane as leaving a trace of infinitely many points; similarly, points on a line did not exist until they were physically and visually plotted. We conclude that the student’s meanings for lines and points had a significant impact on his graphing activities, in particular, on his construction of emergent shape thinking.