Visualization in mathematical abstraction and generalization processes and its role

The purpose of this study was to investigate visualizations and their roles in mathematical abstraction and generalization processes. Therefore, this study examines which kinds of visualizations were utilized, what were the formats of these visualizations and what were the ways of using these visualizations, what types of visual images were presented by participants and finally, what were the effects of used visalizations on these processes along with the changes in the visual images.The study employed case study technique which was a quantitative research method. Classroom observations and semi-structured interviews were data collection methods. The study was performed in two steps consisting of a pilot and main research. The pilot study was carried out with 13 participants selected from 24 undergraduate students during the Fall term in 2008-2009. The main research was conducted with 5 participants selected at the end of the pilot study.Four interviews were conducted with each participant. In the first round, 9 cases were presented in four stages during the abstraction process and in the second round, 4 cases were presented in 3 stages during the generalization process to investigate which visualizations and visual images were employed. In the third round, visualizations were presented to determine the effects of visualizations and variations in the visual images in the abstraction process and the fourth round investigated the effects of visualizations and variations of visual images in the generalization process. Geometers? Sketch Pad and Maple software were used for the visualizations. The collected data were coded and content analysis was performed.The results of this study showed that the visualization was widely employed but in different styles and different visual images were presented in these processes. Visualizations had an important role on the relations between concepts, had positive effects on the development of both processes and caused significant variations in visual images.In the light of the results, some suggestions were given about visualization and visual images to make clear these processes for mathematics learning and future academic researches.