PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Painter’s paradox: Epistemological and didactical obstacle
Page: 1054
In mathematics education research paradoxes of infinity have been used in the investigation of students’ conceptions of infinity. We analyze one such paradox – the Painter’s Paradox – and examine the struggles of a group of Calculus students in an attempt to resolve it. This study shows that contextual considerations hinder students’ ability to resolve the paradox mathematically. We suggest that the conventional approach to introducing area and volume concepts in Calculus presents a didactical obstacle. A possible alternative is considered.