Exploring 5th and 6th grade students' understanding of basic geometrical concepts based on the theory of figural concept

In this study, it was aimed to explore how fifth and sixth grade students understand basic geometrical concepts considering the theory of figural concept. For this purpose, the researcher reviewed the related literature and prepared a comprehensive instrument including basic geometric concepts and figures. The study is a correlation and comparison type relational survey model from quantitative research methods. The data were collected with 450 fifth and sixth grade students during the fall semester of 2017-2018 academic year. The study was conducted in three phases. The students were asked to define ten basic geometric concepts and then completed a test with seven figural questions related to these concepts. Finally, interviews were held with the students who were selected on the basis of the data obtained from both tests. At the end of the study, it was found that there is a significant relationship between both tests. There was no significant difference in both tests according to the class level, but as the mathematics achievement levels increased, students were found to be more successful in both tests. It was found that the most difficult concepts for students were angle and perpendicular lines and determined that they were difficult to define for many students. It was also determined that when students made a decision in figural questions, the meaning of the figure was controlled by figural constraints rather than formal constraints. In addition, they were confused about the concepts and were usually influenced by prototype forms when making decisions.