Students making connections through interactions with fractal geometry activities

Abstract

This thesis investigates grade nine students' engagement in interactive sessions in regard to fractal geometry. Students' experiences, perceptions and conceptual understandings of mathematics were studied. In addition, the thesis examines students making connections between mathematical topics, between mathematics and other disciplines and between mathematics and the real world. Twenty two grade nine students, aged 14 and 15 years, participated in six activity sessions. The manner in which they related their experiences, both verbal and written, was the main focus of this study. -- This case study is mainly descriptive and the collection of data was by observation, interviews, student journals and audio recording. The activities in fractal geometry were exploratory in nature but guiding questions were provided to assist students in the process of journal writing. The results of student interviews, discussions and observations are presented along with a compilation of student comments taken from their journals and written responses on activity worksheets. All of these were considered and included in the analysis and discussion. The final discussion includes comments from the teachers who were involved in the study and their impressions of what had occurred during the study. -- Of particular interest in this study were the students' perceptions of mathematics. Using an investigative approach to this study the students were observed making connections between fractal geometry and other areas of mathematics. There was an increase in students' confidence level, students' deepening understanding of mathematical concepts and students' recognition of emerging patterns. Many of the students' perceptions of mathematics were transformed through their participation in hands on, mathematical explorations of fractal geometry. Some students seemed to make connections between mathematical topics through their construction of the meaning of concepts such as self-similarity and processes such as iteration.