The process of solving skill-based problems about multipliers and multiples by advanced learners in math and gifted students

Globalization has also been reflected in mathematics education, and as a result, international exams, in which Turkey also participate, have become widespread since the 20th century. After participating in international exams in Turkey, it started to make changes in the questions in the exams it held throughout the country. The most striking of these changes is the preparation of skill-based questions that measure metacognitive skills in the High School Entrance System exam. In order to solve such questions effectively, as emphasized in the mathematics curriculum, the problem solving process must be managed well and correctly. In this research, it is aimed to examine the processes of solving skill-based questions about multipliers and multiples. The difficulties experienced by the students in the process of solving skill-based questions and the points they missed were determined. In this study, case study, one of the qualitative research methods, was used. The study group consists of 8 students, 4 of whom are highly successful in mathematics and 4 of whom are gifted, studying in the 8th grade. The Factors and Multiples Achievement Test consisting of 10 open-ended questions was developed in order to measure the students' skills on the subject of multipliers and multiples. While applying the Multipliers and Multiples Achievement Test, we conducted a clinical interview with each student and enabled the students to solve the questions by thinking aloud. We made the descriptive analysis of the obtained data according to the Polya’ problem solving steps. While presenting the findings, we made use of the tables and interpreted them according to each question and step. As a result of the research, we determined that the students who successfully realized the step of understanding the problem were able to perform the other steps and solve the questions correctly. We also found that students who are successful in mathematics try to apply Polya's problem solving steps more and are more successful than gifted students. According to these results, we recommend that students use Polya's problem-solving steps effectively while solving problems and that the research results should be investigated in more detail