Models of Limit Held by College Calculus Students

Abstract

This study documents 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Common informal models of limit were identified among the 10 students, who were then presented with alternative models of limit and with anomalous limit problems. The problems were designed to encourage students to make changes in their own models to reflect a more formal conception. Individual models of limit varied widely even among students who initially described limits in similar ways. The dynamic aspect of these models was extremely resistant to change. This resistance was influenced by students' belief in the a priori existence of graphs, their prior experiences with graphs of simple functions, the value they put on conceptually simple and practically useful models, and their tendency to view anomalous problems as minor exceptions to rules. These factors combined to inhibit students' motivation to adopt a formal view of limit.