Preservice teachers' view on the concept of function a study including the utilization of concept maps

Abstract: The thesis consists of an overview of the subject, where in particular three papers are put into a frame. The overview part consists of: an introduction, a short description of some related research and theoretical framework, a summary of papers I-III and the concluding discussion. The thesis considers preservice teachers' view of the concept of function. It is primarily conducted during the concluding courses in mathematics of a teacher preparation program in mathematics and science, grades 4 to 9. Some of the findings show that a more developed conceptual knowledge of functions, as an object with a set of properties and an understanding of the function concept's network of relations and significance in mathematics, is not prominent in the preservice teachers' view upon functions as it appears in the study. This could mean that they as inservice teachers do not sufficiently promote the concept of function, or functional thinking, in their teaching. Furthermore, the concept maps give the impression that the preservice teachers' knowledge structures tend to be compartmentalized, including the knowledge structures representing the concept of function, thus preventing preservice teachers from building a conceptual framework rich of meaningful connections. A consequence could be that the preservice teachers become less flexible in their way of reasoning about concepts, and are only able to offer a more limited range of teaching strategies regarding different concepts and their relations to functions, as inservice teachers.