PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Shape thinking and students’ graphing activity
Page: 782
We describe a construct called shape thinking that characterizes individuals’ ways of thinking about graphs. We introduce shape thinking in two forms–static and emergent–that have materialized in our work with students and teachers over the past two decades. Static shape thinking entails thinking of a graph as an object in and of itself, and as having properties that the student associates with learned facts. Emergent shape thinking entails envisioning a graph in terms of what is made (a trace) and how it is made (covarying quantities). We provide illustrations of the shape thinking forms using examples from data that we have gathered with secondary students, teachers, and undergraduate students. We close with future research and teaching directions with respect to students’ shape thinking.