Examination of problem-posing processes by considering mathematical thinking skills of the gifted students

To rise to the level of contemporary civilizations of our country, educated generations who can solve the problem, can develop their selves, are qualified, don't to hesitate to show their differences. It can be said that one of the human resources to be educated for this aim is highly gifted individuals. For this reason, it can be said that there is a need for teaching programs with enriched content to improve the performance of these individuals. In these programs, it may be necessary to pay particular attention to thinking processes. Because, analytical thinkers and reasoners are known to be successful not only in mathematics but also in practical life and in other fields. Individuals who are thinking of this type can claim a mathematical argument and investigate and express it in mathematical ways. No matter what field and subject, thinking is, in its most obvious form, an issue or a problem solving activity. Among these kinds of thinking, when mathematical thinking is expressed in two stages; it can be expressed that in the first stage, as problem defining, and finding or creating the solution, and in the second stage as checking on the accuracy of the solution. When we think of mathematical thinking as a problem solving, it can be said that problem posing is one of the differences which increase the problem solving skill of the individual.In this context, considering that problem posing in highly gifted individuals is a highlevel product of mathematical thinking; The general problem of the research is determined as "What is the level of mathematical thinking skills by considering problem posing process of gifted students?". The sample of the study using mixed method consists of 103 students (Nfemale = 59, Nmale = 44) who study at elementary school and 9th grade level and were enrolled in Yusuf Demir Science and Arts Center during 2018-2019 academic year. As a data collection tool, Demographic Information Form, Mathematical Thinking Scale developed by Ersoy (2012) and interviews were used. In addition, according to the data obtained from the analysis results of the 'Mathematical vi Thinking Scale' which was applied as a measurement tool, problem posing studies were conducted with 15 students selected by criterion sampling method. In the analysis of the quantitative data, parametric tests were used depending on the normality via SPSS 22 package program and descriptive analysis was used for qualitative data. As a result of the study, when the posing problems of the students who scored lower, middle and higher from Mathematical Thinking Scale were compared according to their grade levels; it was determined that the quality of posing problems of the students who scored low and medium scores from the Mathematical Thinking Scale were lower than those of those who received high scores, in terms of objectives and explanations in the curriculum. On the other hand, when the effects of the grade level on the mathematical thinking of the students were examined, it was found that the students in the 5th grade had high mathematical thinking in comparison with 9th grade students. As a result of the research, the problem posing studies, which are determined to be among the activities increasing the mathematical thinking, should not only be limited to primary education in the curriculum, but also it should be included in the secondary education program. Key Words: Mathematical Thinking, Problem Posing, Gifted Student