However, if students want to find the angle bisector via using compass and straightedge, they have to find create strategies, use basic construction rules, and think geometrically to find the appropriate steps for the construction.Īccording to Axler and Ribet (2005), to understand Euclidean geometry, it is necessary to know about the nature and scope of compass and straightedge constructions. If students want to find the bisector of a given angle in Geometer’s Sketchpad, they can select the angle and the tool angel bisector in the construction menu and then they automatically get the angle bisector. For example, Geometer’s Sketchpad which is a dynamic geometry program involves tools in the construction menu such as ‘midpoint’, ‘intersection’, and ‘angle bisector’. Thus, using different tools such as compass, straightedge, and dynamic geometry programs might cause some differences in students’ reasoning process in geometric constructions.
How students construct geometric figures is directly connected to the development of their geometric reasoning (Köse, Tanışlı, Erdoğan, & Ada, 2012). Some researchers described geometrical constructions by mentioning the use of compass and straightedge (e.g., Axler & Ribet, 2005 Djorić & Janičić, 2004). According to Lim (1997), geometric construction involves carrying out procedural steps to construct geometric entities such as perpendicular line, parallel line, and angle bisectors using geometrical instruments. Geometric construction was described as “a problem situation in which it is required that a desired figure be drawn with the aid of specified instruments (such as the straightedge and compasses) and using specific given data” (Albrecht, 1952, p.5). Throughout the development of geometry, it was stated that geometric constructions have an important role (Stupel, Oxman, & Sigler, 2014) and it is one of the earliest concepts of mathematics (Kuzle, 2013). To comprehend these processes and the connections among them is necessary for being proficient in geometry (Duval, 1998).
Geometry which is considered as one of the major concepts in mathematics and mathematics education (Clements & Battista, 1992 NCTM, 2000) involves three cognitive processes construction, reasoning, and visualization (Duval, 1998).
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