Learning Limits of Functions: Students' Conceptual Development

Students at a Swedish university were subjects in a study about learning limits of functions. The students were enrolled in their first university course in mathematics. They studied algebra and calculus. Students solve problems and work with theory to learn mathematics. There are many possible problems for the students to handle including the notion of function, the formal definition and limits as unattainable values for functions. The students' perceptions were investigated in terms of traces of concept images through interviews and problem solving. The results imply that most students' foundations were not sufficiently strong for them to understand the concept of limit well enough to be able to form coherent concept images. Many students did not possess enough knowledge about limits to solve and explain solutions to non-standard problems. Some students arrived at correct answers through erroneous reasoning.