Secondary school 8th grade students' concept images for bisector, median and height in triangle

The aim of the research is to determine the concept images of middle school eighth grade students regarding the concepts of height, median and bisector. The participants of this study are 8th grade students from 6 different secondary schools in the central district of Balıkesir in the 2021-2022 academic year. In this study, in which multi-case research, one of the qualitative research models, was used, the students were first asked to answer the concept image determination form, and then a clinical interview was conducted with the students selected from among those who answered the form. The data collection tools of the research are the form of determining the concept images for the concepts of height in triangle, median and bisector, clinical interview form and individual interviews developed by the researcher. It was concluded that in the non-height image of the students, it is not perpendicular, in the non-medium side image, the edge is not divided into two equal parts, and in the non-intermediate image, the situations where the angle is not divided into two equal parts are dominant, and the majority of the students drew all 3 auxiliary elements correctly. It was seen that the students' concept images of these 3 auxiliary elements of the triangle were insufficient. Students have problems with their triangle drawings, regardless of the concept, students' drawings are made of prototypes, height and median are mentioned more together than the combinations of other auxiliary elements, researched concepts evoke expressions in the minds of students to define those concepts most, some students use the expressions "right center" for the median, "lower the perpendicular", "draw perpendicularly", some students draw a triangle or an isosceles extension that does not form an opposite side to the side, except for the height, and some of the students draw an isosceles or right-angle extension other than the height. It has been observed that they are aware that the median, bisector and height are the same line segments in triangles. Suggestions were made, such as examining students' concept images of the auxiliary elements of the triangle from the perspective of Van Hiele's geometric thinking levels and Skemp's instrumental and relational understanding theory.