The examination of mathematical thinking processes of students diagnosed as gifted and undiagnosed in different environments

The general aim of the education is to prepare individuals for life and to gain mental skills that will enable them to be successful in real life. In daily life, every situation that needs to be solved is actually a problem state. The most common and efficient use of thinking structures required for the solution of problems is mathematics. The mental processes necessary to solve problems are part of mathematical thinking. In this respect, it should be one of the most important skills students should have. The simplest definition of mathematical thinking can be the use of mathematical techniques to solve problems directly or indirectly. In this case, the extent to which the processes and sub-components of mathematical thinking exist in students and how they can be measured are issues to be investigated. On the other hand, there are studies on the success of dynamic mathematics software to reveal mathematical thinking processes. It is necessary to investigate whether students can be diagnosed gifted by revealing mathematical thinking processes in the process of gifted diagnosis and whether there will be differences in mathematical thinking processes. In this study, it was aimed to investigate whether the problem-solving processes of students who are diagnosed and undiagnosed gifted with paper-and-pencil and dynamic mathematics software differed in the sub-components of mathematical thinking. The study which was conducted in the qualitative research design, included 3 gifted students who were enrolled to BILSEM in Giresun and 3 non-gifted students who were studying in a public school. All students in the study are 7th grade students. The research process was designed to measure the mathematical thinking processes of the students and the 6 activities which were finalized after the expert opinions were solved by the students with paper-and-pencil. Then, the students received education process related to the use of customized dynamic mathematics software which lasted for 6 course hours. After the education process, the students solved 6 activities with paper-and-pencil with dynamic mathematics software. In-depth interviews were conducted without commenting on the accuracy or inaccuracy of the solutions in the solution processes of the activities. The data of the study were collected through student responses in the solution process of activities, solution processes on dynamic mathematics software and interviews conducted with semi-structured meetings. The researcher formed the codes that include the steps and sub-components of mathematical thinking taking into consideration the common statements in the studies on mathematical thinking. The data obtained for each activity were analyzed separately for each mathematical thinking process according to the codes generated based on the literature. As a result of the research, it was seen that the findings obtained from the activities solved with paper-and-pen were distinguished the gifted and non-gifted students in the process of solution of the mathematical thinking processes in the privatization and generalization section. However, in the process of privatization and generalization, there is no clear distinction between the dynamic mathematics software processes as the majority of students have correct and adequate behaviors. It was seen that distinguishability in assumption in mathematical thinking processes and in dynamic mathematics software in proof stages are more prominent. As a result of the study, it was observed that both groups were found to have non-different thinking processes in some components, while the processes that differentiated the diagnosed and undiagnosed students were observed in the field of mathematical thinking which is a field-specific thinking. This situation has revealed that the field-specific giftedness should not be underestimated while the diagnosis of giftedness is made and field-specific giftedness should be defined. In this context, the potential of different environments can be taken into account in revealing the difference between the mathematical thinking of diagnosed and undiagnosed gifted students. Considering that the process of selection of students and giftedness diagnosis to BILSEMs started in elementary school, it is recommended to disseminate dynamic mathematics software which will enable students' potential to be observed in high-level mathematical thinking processes at primary school level.