An action research on developing mathemetical creativity of gifted students through problem posing activities

This research aims to develop problem posing ability and mathematical creativity of seventh grade gifted students through problem-posing activities. The research is based on Stoyanova's (1997) problem posing model and investigates problem posing situations under three categories: structured, semi-structured, and free. The research utilizes action research which is one of the qualitative research methods. It was conducted in two phases, namely pilot and main study. The participants of the study were determined via purposive sampling method and the gifted students with problem posing difficulty formed the participant group. The participants of the pilot study were seventh grade students attending to Düzce and Sakarya Science and Art Center while the participants of the main study were seventh grade students attending to Bolu Science and Art Center. The study was performed in the second semester of 2018-2019 academic year and spanned in total of a 17 week period. Data collection tools of the study were Problem Posing Test developed by the researcher, semi-structured interview questions, problem posing activities, study papers, student diaries and notes taken by the researcher and the observer during the main study. Data analysis was performed in three progressive steps of pre-application, application, and post-application. In pre- and post-application steps, problems posed regarding the problem situations in Problem Posing Test were assessed using a researcher developed rubric and the adequacy level of the students regarding the problem posing ability was determined. In the second step, posed problems were analyzed based on two components of divergent thinking of fluency and flexibility, and creativity quotation score was used to determine mathematical creativity levels of the students. Finally, semi-structured interviews conducted before and after the main study were analyzed. The data collected during the main study was analyzed regarding to investigation of three main topics: problems posed during main study, regulations regarding these problems, and students' views on the course. The validity and reliability of collected data were assessed through expert analysis, variation, long time interaction, detailed description, and control of researcher bias. Inter-coder reliability coefficient was calculated and utilized for unbiased analysis of the posed problems and interview answers. Students who were identified to be unsuccessful in problem posing were observed to have difficulties with language and expression, mathematical rules and concepts and solvable problem posing. They were also observed to pose few problems mostly being in similar categories and thus determined to be unsuccessful in mathematical creativity. These students had difficulties with self-expression and understanding mathematical concepts and formulas, and had mostly posed simple verbal problems at the beginning of the study. However, they showed improvements during the study in their abilities of flexible and complex problem posing. Compared to problems posed before the study, the number of problems posed increased and these problems showed diversity in terms of flexibility. Moreover, it was also found that approximately half of the problems were related to real-life situations. Wilcoxon Signed Rank Test was performed to test the significance of obtained findings and the test results indicated the significance of the study in improvement of the students in their problem posing ability and mathematical creativity. Additionally, in interviews, the students showed improvements in their capacities of idea generation, flexible thinking and diverse problem posing supporting the test results. They showed improvements in their problem solving capability, understanding of mathematical concepts, academic success and views towards mathematics. Moreover, the students stated that problem posing studies shouls be included in their coursework.