An investigation of 7th grade students' meaning-making processes of quadrilaterals and their relationships according to the Pirie–Kieren model

The aim of this study is to examine how students with high and low academic achievement levels make sense of quadrilaterals and the relationships among them based on the Pirie–Kieren model. The research was conducted using a case study design, one of the qualitative research approaches, with six seventh-grade students. Activities were designed in line with the purpose of the study to help students explore angle, side, and area concepts in quadrilaterals, as well as the relationships among these concepts. To obtain more in-depth information regarding these activities, clinical interviews were conducted with the students. The data obtained from the interviews were analyzed through descriptive analysis according to the layers of the Pirie–Kieren model. The analysis results reveal notable differences between high- and low-achieving students in their meaning-making processes. It was found that students with low academic achievement could not reach the abstraction layer, whereas high-achieving students were able to reach this layer and even experience it multiple times. Additionally, differences were observed in students' processes of making sense of quadrilaterals and their hierarchical relationships depending on their academic achievement levels. Students with similar academic achievement levels tended to remain within similar layers throughout the process.