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This study investigates middle school students’ reasoning about parallelism and perpendicularity of two line segments. Data were collected from 83 middle school students through an identification task consisting of various examples and non-examples of the parallelism and perpendicularity of two line segments. One-to-one interviews were also conducted with fifteen students to support students’ written reasons. The results indicated that middle school students identify parallel/perpendicular line segments by using three types of reasoning:  visual reasoning ,  attribute reasoning , and  language-based reasoning . With the influence of the concept images shaped by prototypical and intuitive examples and linguistic factors, some students either focused on non-critical attributes of the concepts as the critical ones or omitted critical attributes of the concepts. Hence, they either identified examples of parallel line segments and perpendicular line segments as non-examples or considered non-examples of the concepts as examples.

Middle school students’ reasoning with regards to parallelism and perpendicularity of line segments