Investigation of problem posing and problem solving processes of gifted and normally developing students on fractions

In this study, it was aimed to examine the problem posing and problem solving processes of gifted and normally developing 6th grade students about multiplication and division in fractions. In the research, multiple case study design, which is one of the qualitative research methods, was used in order to examine the problem posing and problem solving processes of the students in depth. The sample of the research, in which criterion sampling was used, consists of 25 6th grade students with normal development in a school in Serik district of Antalya province and 25 6th grade gifted students studying at a Science and Art Center in Antalya province Kepez district. In the research, "Problem Posing Test (PKT)", "Problem Solving Test (PCT)" prepared by the researcher in line with expert opinions, and "Semi Structured Interview Form" for the interview with 3 gifted and 3 normally developing students were used as data collection tools in the research. . Descriptive and content analysis were used in the analysis of the data. In the analysis of the data, the findings obtained from the Problem Posing Test were analyzed with the Problem Classification Scheme created by Baştürk, Ergin and Türnüklü (2013). The findings obtained in the Problem Solving Test were analyzed with the problem solving steps in the Progressive Scoring Scale created by Baki (2008). The mistakes made by the students in the problems they posed and the findings obtained from the interview were analyzed by content analysis. According to the results of the study, more than half of the problems posed by gifted students in both multiplication and division of fractions emerged as mathematical-sufficient problems, while this ratio was less than half in students with normal development in both fractions multiplication and division.When the errors in the mathematical problems posed by gifted and normally developing students are examined, problems such as problem posing that require other operations, attributing the meaning of natural numbers to fractions, mixing quantities with ratios, specifying units without units, posing problems by adding new numbers, inability to establish a part-whole relationship, and assigning a value to the whole are examined. 7 different error types were detected. In addition, in the mathematical problems posed by the students with normal development, the error of posing a problem independent of the numbers given in addition was encountered. According to the results obtained from the problem solving test of gifted and normally developing students, it was revealed that both gifted and normally developed students did not have a high level of problem solving related to multiplication and division operations in fractions.When a comparison is made between the two groups, gifted students showed higher performance, especially in the implementation phase of the plan, than the students who developed with the norm, except for the evaluation step. According to the results obtained from the interview questions, both gifted and normally developing students tried to reach problem solutions without using all the problem solving steps in the problem solving process. Keywords: Giftedness, Problem posing, Problem solving, Fractions