Investigation of secondary school students' mathematical problem posing skills for different representation situations

In this study, it was aimed to examine the problem posing skills of sixth, seventh and eighth grade students for different representation situations. It was examined how the problems posed by the students participating in the research changed according to their class and academic achievement levels. The study was carried out in the fall semester of the 2021-2022 academic year with 87 secondary school students in a secondary school in the Eyüpsultan district of Istanbul. In the study, which was designed as a case study, one of the qualitative research methods, the data were obtained with the "Problem Posing Test" and "Interview Form" developed by the researcher. Silver and Cai (1996)'s problem posing evaluation scheme was used in the analysis of the data obtained from the problem posing paper. According to the data obtained from the study, it was seen that 57% of the answers given by the students were solvable problems suitable for the given ones. In terms of class level, seventh grade students were more successful in problem posing in accordance with the given ones, and students with high academic achievement were more successful in terms of academic level. Most of the problems that were set up in accordance with the given ones were in the 'low' category in terms of mathematical complexity and in the category of 'homework' in terms of linguistic complexity. However, as the grade level and achievement level of the students increased, the mathematical and linguistic complexity of the problems also increased. When the answers given by the secondary school students to different representations are examined, it has been determined that the most successful representation type at all grade and academic levels is the table representation type. The table representation was followed by verbal, pictorial and symbolic representations, respectively. Similarly, it has been determined that the mathematical and linguistic complexity of the problems posed for table and picture representation is higher than other representations.