An examination of seventh grade students' competencies in problem posing and solving in the context of measurement

Problem posing and problem solving are considered critical skills in enhancing students' mathematical understanding. The aim of this study is to examine seventh grade students' competencies in problem posing and problem solving in the context of measurement. In the study, the case study model was adopted, which is one of the qualitative research methods. As the sampling method, criterion sampling was used, which is one of the purposive sampling methods. The sample of the study consists of 10 seventh grade students studying in a middle school located in the city center of Tokat during the second semester of the 2023–2024 academic year. During the data collection process, three different tools were used: "problem posing form," "problem solving form," and "semi-structured interview form." The data collected in the study were analyzed using content analysis. The data obtained from the students were analyzed under two headings: findings related to problem posing competencies and findings related to problem solving competencies. The findings obtained from the problem posing form revealed that students most frequently made linguistic errors or deficiencies. When the problems created by the students were examined, different types of errors such as impossible/impractical situations, fictional errors, mathematical errors, unnecessary information, and lack of information were also encountered. It was determined that the number of completely correctly structured problems was lower compared to the partially correctly structured problems. In the problems in the problem solving form, while the step in which students were most competent was the implementation step, the step in which they were least competent was the reviewing step. In general, it was concluded that students' problem solving competencies were more developed than their problem posing competencies. At the end of the study, recommendations were made for mathematics teachers, researchers, and authors of mathematics textbooks or resource books. It was observed that students were particularly insufficient in the "reviewing" step of the problem solving process, and it was recommended that activities aimed at developing this step should be included more frequently in lessons. For the development of problem posing skills, it was recommended that mathematics textbooks include more problem-posing questions related to geometry topics. It is recommended that teachers include problem-posing activities for students during classroom practices in order to develop their problem-posing competencies. In this context, it is emphasized that mathematics textbooks should include more problem-posing questions on geometry topics particularly, and focusing more on the steps of problem solving. In addition, several suggestions have been offered to researchers who will conduct studies on this subject in order to contribute to the literature. Keywords: Problem Posing, Problem Solving, Measurement, Mathematics Education, Middle School Students