Development and application of a geometric reflection module to conceptually teach eighth grade students about the symmetry axis

The purpose of this study is to develop and implement a geometric reflection module in accordance with the APOS theory framework, taking into account the reflection transformation gains in the eighth grade mathematics curriculum so that they can have a symmetry axis mapping view, to examine the perspectives and mental structures of eighth grade students on the axis of symmetry, which is the sub-concept of reflection transformation. The experimental group consisted of 8th grade, twelve students studying at a state school in the district of Eleşkirt in Ağrı. In the study, action research design, one of the qualitative research methods, was used.As a data collection tool, the developed reflection module, mathematics notebook (MND), audio recordings and observation notes were used. The obtained data were analyzed using content analysis and APOS (action, process, object and schema) theory. According to the research findings; it was concluded that five students had a process mentality and enabled the transition from the symmetry axis motion perspective to the mapping view that all students had action mentality and symmetry axis motion view at the beginning of the study while seven students had an action mentality and could not make the transition from the symmetry axis motion perspective to the mapping perspective at the end of the study. The transition process from the symmetry axis motion perspective to the mapping perspective, from simple to complex in the developed reflection module; it was expressed as the reflection image being "perpendicular" to the symmetry axis with the given figure and the given shape and plane consist of infinite points, the shape and the reflection image which are "equal distance" from the axis of symmetry and preservation of shape (size, shape). According to the findings of the study, the factors affecting the transition from the motion view to the mapping view are: Reflection module activities developed in accordance with the mental structures of the students, open-ended questions, paper folding method, use of geometry board, use of ruler-protractor, angles and the condition of the lines in relation to each other were determined as the subject. Keywords: APOS theory, Axis of symmetry, Mapping view, Motion view, Reflection module