Investigation of the development of problem positioning and solving skills of seventh grade students with problem-basing activities for illustrations on rational numbers

The research aims to investigate the problem-posing skills of seventh-grade students using illustration on rational numbers, and to reveal their views on this subject. In addition, it is also aimed to investigate whether there is a significant relationship between students' problem-solving skills and illustration-based problem-posing skills on rational numbers. In the research, teaching experiment method was used. The study group consists of 31 seventh-grade students, studying at a public school in the Eastern Black Sea region, Turkey, who were selected by an easily accessible case sample and voluntarily participated in the study. The data were collected using the Problem-Posing Data Scale, Problem-Solving Skill Scale, worksheets prepared with illustrations, and semi-structured interview form. The data obtained in the study were analyzed using qualitative and quantitative data analysis methods. According to the results of the study, the problem-posing activities using illustration were found to positively improve the problem-posing skills of seventh-grade students, the majority of the students was found to be able to pose a problem on rational numbers in the desired manner, and it was also found that the students select which they can establish a correct relationship between a whole and its parts in order to pose the correct type of problems, and that they were found to express exactly what's required and given in the problem, and create the problem clearly. However, as applications with illustrations progressed, students who did not make any effort were started to make an effort. It was revealed that students' problem-posing activities with illustrations contribute to understanding the subject of rational numbers, strengthening the subject, improvement in problem-posing and solving skills, and embodying abstract subjects by visualizing the courses. Furthermore, the problem-posing studies with illustrations have revealed that lessons can become more fun, students are willing to engage, and that the method can be useful in all subjects of the mathematics course and in other courses. Based on the results obtained within the scope of the study, it is recommended to use problem-posing activities with illustrations more in the educational process.