A study that documents 10 students' understanding of the limit concept. Common informal models of limit were identified. The dynamic aspect of these models was extremely resistant to change. This resistence was influenced by (among others) the value they put on conceptually simple and practically useful models (the everyday demands of calculus), and their tendency to view anomalous (afwijkende) problems as minor exceptions to rules. These factors make it difficult for students to appreciate the need for a more formal definition.
The current curriculum provides little motivation for a formal definition. Just as students' informal limit models tend to parallel those of the mathematical community prior to Cauchy, it is possible that only by appreciating the sorts of problems that motivated Cauchy's work will motivate students to understand its implications.