Middle School Students’ Interpretation of Definitions of the Parallelogram Family: Which Definition for Which Parallelogram?

Abstract

The aim of this study was to investigate how students interpret the verbal definitions given for quadrilaterals in parallelogram family and reasoning in this interpretation process. It was also aimed to reveal the easiest definitions for students to understand, and to determine which mathematical terms they do not understand in given definitions. The study sample consisted of 16 volunteer eighth grade students. Data were collected with the clinical interview method and analyzed with thematic analysis method. The results revealed that the exclusive definition and inclusive definition (based on sides) of a parallelogram, the exclusive definitions of a rectangle and a rhombus, and the definition of a square based on diagonals were identified more accurately by the students. Analysis of the students’ reasoning process showed that the vast majority of the students made their decisions by comparing a given definition with other quadrilaterals and that few students explained their reasons to choose a definition directly. It was also determined that prototype quadrilateral images were effective in thinking process of the students who inaccurately interpreted definitions in this process. Finally, the students mostly had difficulty in understanding expressions such as rotational symmetry, bisecting, bisecting perpendicularly, having at least one angle of 90°, having one right angle, perpendicular bisector and symmetrical across the perpendicular bisector.