The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers’ Transformational Geometry Success

Abstract

Mathematics, having an important place in human life and playing a great role in developing many human cognitive capabilities, is divided into various subject areas. One of these subject areas is geometry (Kurak, 2009). Geometry consists of geometric objects, shapes, and their features and relationships to each other (Topta§, 2008) Geometry helps students become closely acquainted with the world they live in. For example, the shapes of rooms, their construction and trim work forms are geometrical (Baykul, 2002). According to Struchens, Harris, and Martin (2003), students start to understand the world around of them, can analyze problems, and in order to understand intangible symbols better, define them by shapes (as cited in Gulten & Gulten, 2004). On the other hand, the National Council of Teachers of Mathematics (NCTM, 2000) dwells on the importance of geometry for the principles and standards of school mathematics, and it focuses on the fact that geometry develops the reasoning and proof-finding abilities of students. Jones (2002), on the other hand, states that geometry includes interesting problems and surprising theorems, and this supports students in developing their abilities of visualization, critical thought, instinctive reasoning, perspective, estimation, logical inference, deductive reasoning, and proof-finding. For this reason, geometry is an important subject area which should be addressed from pre-school throughout higher education (Goos & Spencer, 2003). With the implementation of the mathematics program in 2005, some subject areas started to become more prominent. One of these subjects is transformational geometry (displacement, reflection, and rotational transformation) (Guven & Kaleli-Yilmaz, 2012).Transformational geometry, which improves students' geometric experimentation, imagination, reasoning, and three-dimensional perception skills, consists of reflection, displacement, and rotation (Fletcher, 1973; Gurbuz, 2008; Milli Egitim Bakanhgi [MEB], 2005; NCTM, 2000; Soon, 1989). According to Knuchel (2004), people need knowledge of transformational geometry in order to develop qualitative senses about the external world as well as to organize objects and events. Students can establish a connection between art and mathematics thanks to the information they receive on transformational geometry; they can realize the importance of mathematics in daily life. Additionally, seeing geometric figures rotated, translated, and repeated (as in carpet patterns) helps the student who has knowledge about this topic to view things differently (Duatepe & Ersoy, 2001). For this reason the topic of transformational geometry should be taught to students from childhood, and it should be emphasized that reflection, displacement, and rotation can be seen in many natural structures and events.It is very important for primary school students to learn basic knowledge about transformational geometry and continue their education successfully in the years that follow. As Carroll (1998) stated, students who gain effective experience with geometry in primary school are able to apply reasoning to situations which contain geometry in secondary school. For example, reflection transformation relative to a line is used to teach analytical geometry, the following years' topic, and rotational transformation is used to teach solid-body volume. Moreover, transformational geometry basically forms a basis for the concepts of functions, a concrete foundation for vectors, and the formulation of the similarity theorem, making the world mathematical (Schuester, 1973). Transformational geometry should be taught to students beginning at childhood in order to transform their knowledge into conceptual and concrete understandings; teachers should help students understand the topics of reflection, symmetry, and rotational transformation correctly.The topic of transformational geometry is not only in mathematics but is also included in other disciplines. …