The distance between students’ concept image and quadrilateral object definition based on students’ mathematical ability

Students learn mathematics through practical applications without applying it. Consequently, the concept images and definitions that students offer do not match. This study examines the gap in mathematical ability between the concept images of professionals in mathematics education and students' concept images of content, including quadrilaterals. This study employed a qualitative approach with a hermeneutic phenomenology method. Sixty-two seventh-grade students were involved in conducting this study. Some instruments, such as quadrilateral-related tests and semi-structured interview questions, were used to collect the data. The results of quadrilateral-related tests and interviews revealed that most students with high mathematical ability, some with medium mathematical ability, and a small number with low mathematical ability have a concept image that matches the definition but cannot produce proof of the properties of a quadrilateral. In addition, a small number of students with high mathematical talents, some with medium mathematical abilities, and a large number of students with low mathematical abilities were unable to completely explain each rectangle's formal definition and properties. This indicates that there are some students whose concept image is low. So, several alternatives and effective mathematics learning should be implemented to facilitate students in enhancing students concept image.