Non-routine problem solving processes of Turkish mathematically gifted students

This study aimed to investigate the problem solving processes of Turkish mathematically gifted students when they engaged in solving non-routine mathematical problems. In accordance with the nature of the study, case study were chosen as research design. The sample of the study was five mathematically gifted students who were members of Mathematics Olympiads Group organized by National Ministry of Education, and at the top ten degree of in National Mathematic Olympiad regulated by TUBITAK, the National Science Foundation (NSF) in Turkey. Data was collected by two-hour long paper and pencil test containing eight non-routine problems and one-hour long structured task-based interviews. Data was analyzed by within and cross case data analysis techniques. Results of the study showed that Polya's four-phase problem solving processes were attainable by all these mathematically gifted students. Particular to especially the looking back and the carry out the plan stages, results showed that for mathematically gifted students problem solving processes include justification within the looking back stage. In addition, carry out the plan phase of the problem solving process of mathematically gifted students involve three common characteristics: focusing on the quantities, associating numerical and symbolic results with the givens in the problem context, being aware of all parts/steps of the solution processes. These results in-juxtaposition to each other implied that while solving non-routine problems mathematically gifted students engage in quantitative reasoning. Implications for teaching suggests extricating the mathematically gifted students' reasoning processes during classroom discussions to foster average students' reasoning quantitatively and to learn from each other.