Investigating of infinity concepts constructed in different age groups of students

The present research is composed of two main studies conducted with PhD students and young children. In these studies, repertory grid methodology and grounded theory were used to bring up the informal models and cognitive levels of students about infinity concepts. Researcher made a triangulation by using different data gathering and analysing techniques. By the following, data was collected systematically by interviewing, watching, coding etc.In the first study, 4 mathematicians were experienced in their understanding of the infinity notion. These mathematicians were PhD students in a university who were enrolled in a set theory course in the first semester of academic year 2006/2007. Constructs about infinity were elicited held by PhD students and the effects of the set theory course were investigated. In the second study, 6 young children?s (aged from 10 to 13 years old) infinity concepts were investigated by using grounded theory techniques. Several interviews were made with young children. Cartoon films and flash animations were used in the interviews and children were asked some questions about infinity. A task based interviews were also conducted which involved a variety of non-routine mathematical questions related with infinity concepts and participant interviews were conducted until the point of theoretical saturation.It was observed that PhD students generally had an understanding of potential infinity at the beginning of the set theory course and they also had shown some clues of the non-standart infinity. After the lectures the researcher observed some evidences of actual infinity hence the set theory course directed the students to the understanding of actual infinity. The researcher observed that young children have different understandings of infinity but mainly potential. It can also be mentioned about the clues of non-standart infinity. The young children?s and PhD students? understandings about potential ınfinity are not exactly the same. The phenomen of ?indefiniteness of infinity? is very important for young children. The researcher found smilarities between understandings of PhD students and young children. It is claimed that in spite of a long period of math education it can be mentioned about clear intuitive similarities between PhD students and young children. The results of the study revealed that even if the repertory grid methodology and grounded theory are successful on bringing up the informal models and cognitive levels of students, they are also consistent with each other. They have many common points and their structures are not very different.