Examination of the concept images of secondary school students for the concept of angles

This study aims to examine the concept images of middle school 7th and 8th grade students regarding angles within the framework of Fischbein's Figural Concept Theory. The participants of the study consist of 7th and 8th grade students studying at a public middle school in the central district of Balıkesir province during the 2023-2024 academic year. A nested mixed-method design, one of the mixed-method research designs, was employed in this study. As a data collection tool, a test consisting of 15 open-ended questions developed by the researcher was used. These questions were categorized into four subgroups: definition of angles, types of angles, angle relationships and properties, and parallel lines and angle relationships. The findings of the study indicate a statistically significant difference between students' figural and conceptual scores, with the difference favoring the figural scores. This result suggests that the figural component is dominant in students' understanding of the concept of angles. However, no statistically significant difference was found between the total concept image scores of students at different grade levels. A detailed analysis of student responses revealed that most students struggled with defining angles, although they generally performed well in defining and drawing acute, right, and obtuse angles. Nevertheless, they exhibited conceptual confusion regarding adjacent, complementary, and supplementary angles, particularly in distinguishing between complementary angles and adjacent complementary angles. Additionally, many students left questions related to alternate interior, alternate exterior, corresponding, and same-side interior angles unanswered. The majority of responses were provided in the form of drawings, yet these illustrations often failed to adequately convey the conceptual meaning. Based on the findings, it was concluded that the figural component is more dominant than the conceptual component in the learning process of angles. Various recommendations have been proposed to strengthen conceptual understanding and enhance students' deeper learning of the topic.