Drawing performance of middle school students related to the concepts of perpendicularity and height in triangles

This study aimed to examine the drawing performance of 7th and 8th grade students regarding the concepts of "perpendicularity" and "altitudes of a triangle." The study was conducted using a cross-sectional survey design. Data was data obtained from a total of 612 students attending five middle schools affiliated with the Ministry of National Education in the Western Black Sea Region in Turkey. Of the participants, 321 were in the 7th grade and 291 were in the 8th grade. Drawing tests were used as the data collection tool; students were administered a pre-test, a perpendicularity drawing test, and a height in a triangle drawing test in that order. The findings show that the position of the point, the direction of the line, and whether or not the extension of the line is needed are the determining variables in students' performance on drawings of perpendicular lines. The need for the extension of the line emerged as the most effective factor in students' mistakes. Differences in students' achievement levels were observed depending on the type of triangle, its orientation, and the position of the altitude. The success rate was higher in acute triangles, while students had more difficulty in right and obtuse triangles. In addition, it was observed that students made conceptual errors such as drawing the median, perpendicular bisector, or perpendicular to the wrong side instead of the altitude. It was found that eighth-grade students were more successful in both concepts than seventh-grade students. The inadequacies observed in non-prototype drawings indicate that students' understanding of perpendicularity and height in triangles needs to be developed in a more systematic way.