The Constructs of PhD Students about Infinity: An Application of Repertory Grids

Infinity has been one of the more difficult concepts for humanity to grasp. A major component of the research on mathematics education related to infinity has been the study of student’s conceptions and reasoning about calculus subjects, particularly limits and series. Some related studies are about Cantor’s ordinal and cardinal infinity. However since most students at the high school and college level are unfamiliar with symbolic representations and terminology, such as a set theoretic approach, a context (generally geometric) is used for investigating notions of infinity indirectly. In this paper we report on a study on the constructs of PhD Students about the notion of infinity. The aim of our study was to gain insight into the constructs about infinity held by PhD students and to investigate the effects of a graduate level set theory course on their informal models. We also propose repertory grid methodology as a way of capturing the constructs of students and argue that this methodology can help us to learn further details about the understanding of infinity