Predications of the Limit Concept: An Application of Repertory Grids

This study uses repertory grid methodology together with a predicational view of human thinking to describe the informal models of the limit concept held by two college calculus students. It describes how their models, based on iteratively choosing points that get closer to the limiting value, are affected by experimental sessions designed to alter them. The informal models are based on the notion of actual infinity, which poses a severe cognitive obstacle to the learning of the formal definition of limit. The study also suggests that the predicational view of cognition, together with analysis of repertory grid data based on fuzzy set theory, can be useful in studying students' concept images of advanced mathematical concepts.