PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
What comes to mind? A case study of concept images in topology
Page: 210
Prior research has shown that students tend to reason in terms of the informal components of their concept images rather than rely on formal concept definitions when working with topics in mathematics. However, students’ concept images may be incomplete or inaccurate, or students’ evoked concept images may exclude important features of concepts or classes of examples. This report describes two students’ evoked concept images of concepts in general topology as revealed through their completion of proof tasks as well as some of the effects those images had on their success in proving. We also discuss the impact of the students’ exploration of their example spaces on their concept images and on their proof writing.