### Identification and Construction of Axial Symmetry: [article]

Kyriaki Natsou, Democritus University Of Thrace
2020
Axial symmetry belongs to the field of Geometric Transformations. However, it appears in many geometric formations that are encountered everyday in artworks, especially in painting and in architecture. Furthermore, it constitutes a characteristic of many structures in nature, such as the human body. Consequently, the person receives stimuli regarding axial symmetry from a young age and forms perceptions about it. During his attendance at school, axial symmetry is taught to the students
more » ... ted into a more strict and formal mathematical structure. Frequently, the person recalls the knowledge which has been acquired through his everyday experience, in order to cope with the symmetrical geometric situations that he encounters. Based on this reality, the present study aims to investigate the strategies that are used by the students in order to identify and construct symmetrical geometric figures. In addition, it is investigated how these strategies are related with the formal and informal students' mathematical knowledge. A qualitative approach was followed for the research to be conducted, based on task interviews of 15 students of the 6 th grade of elementary school. The results indicate two basic strategies used to identify axial symmetry: the Visual Ascertainment of the symmetry and Folding, which are included in the category of Holistic strategies. On the contrary, in order to construct symmetrical geometric figures, students resort to strategy combination patterns, based on Analytic strategies, with the Orthogonal Procedure to be the predominant one. Afterwards, they alter the Analytic strategies to Holistic, aiming at the completion of the construction. These different kinds of approaches indicate the utilization of the informal mathematical knowledge for the identification of axial symmetry and of the formal for the construction of symmetrical figures. Therefore, it becomes apparent that constructions encourage students' analytical-synthetical thinking and urge them to proceed from Holistic to Analytic approach regarding axial symmetry.