Investigation of middle school students' mathematical reasoning skills in problems with different cognitive demand levels

The aim of this study is to examine the mathematical reasoning skills of 8th grade middle school students in problems at different cognitive demand levels. In this study, a case study, one of the qualitative research designs, was used. In determining the participants in the study, the easily accessible sampling method, one of the purposeful sampling methods, was used and the sample was formed from 8th grade students studying at a middle school in the Zonguldak/Alaplı region in the 2024-2025 academic year. In order to reveal the mathematical reasoning processes of the students in problems at different cognitive demand levels, various mathematical problem situations, which were determined based on the literature and finalized by conducting pilot interviews, were used. Data were collected through individual interviews with each participant and these interviews were recorded with a video camera. The collected data were analyzed using the descriptive analysis method, considering the relevant literature. According to the findings obtained from the data, it is seen that the participants exhibited all of the analysis, generalization and verification cognitive demand levels in mathematical problems in the reasoning steps. It was concluded that the students were in low-level reasoning actions at low levels and high-level reasoning actions at high levels in problem situations prepared in accordance with cognitive levels. In addition, the mathematical reasoning indicators revealed by some problems showed that reasoning in students was limited when their cognitive level was low, whereas in cases where their cognitive level was high, there was a variety in reasoning actions. It was thought that in order to increase the intensity of reasoning actions in the solution process of mathematical problem situations, problems with high cognitive levels and transferable to daily life should be preferred. In the study, while evaluating the problem situations prepared according to the cognitive demand levels according to the reasoning actions, it was seen that they were included in the analysis, generalization and verification steps in the reasoning levels. Based on this, it was concluded that the students exhibited reasoning skills at different levels according to these cognitive demand levels.