Geometric Thinking

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Students’ Geometric Thinking 8



In the last 20 years, the perception of learning as internalization of knowledge is criticized and problemized in mathematics education society (Lave & Wenger, 1991; Sfard, 2000; Forman & Ansell, 2001). Lave and Wenger (1991) describe learning as a process of “increasing participation in communities of practices” (p.49). Sfard (2000) also emphasized the new understanding of learning as “Today, rather than speaking about “acquisition of knowledge,” many people prefer to view learning as becoming a participant in a certain discourse” (p.160).

This new perspective in the understanding of learning brings different views to mathematics teaching practice. While the structure of mathematics lessons is organized in the sequence of Initiation- Response-Evaluation (IRE) in the traditional mathematics classrooms, with the reform movement, participation of the students become the centre of the mathematics classrooms (O’ Connor, 1993; Steele, 2001). Initiating topic or problems, starting or enhancing discussions, providing explanations are the role of the teacher in the traditional classrooms but these roles become a part of students’ responsibilities in the reform mathematics classrooms (Forman, 1996).

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Turkey also tries to organize their mathematics curriculum according to these reform movements. With the new elementary mathematics curriculum, in addition to developing mathematical concepts, the goal of mathematics education is defined as enhancing students’ problem solving, communication and reasoning abilities. Doing mathematics is no more defined only as remembering basic mathematical facts and rules and following procedures, it also described as solving problems, discussing the ideas and solution strategies, explaining and defending own views, and relating mathematical concepts with other mathematical concepts and disciplines (MEB, 2006).

Parallel to new understanding of learning, reform movements in mathematics education, and new Turkish elementary mathematics curriculum, students’ roles such as developing alternative solution strategies and sharing and discussing these strategies gain great importance in mathematics education. Mathematics teachers are advised to create classroom discourse in which students will be encouraged to use different approaches for solving problems and to justify their thinking. This means that some researches and new mathematics curriculum give so much importance to encourage students to develop alternative problem solving strategies and share them with others. (MEB, 2006; Carpenter, Fennema, Franke, Levi & Empson, 1999; Reid, 1995).

One of the aims of the new mathematics curriculum is that the students stated their mathematical thinking and their implications during the mathematical problem solving process (MEB, 2006). According to new curriculum, the students should have opportunity to solve the problems using different strategies and to explain their thinking related to problem solving to their friends and teacher. Moreover, the students’ should state their own mathematical thinking and implications during the problem solving process and they should develop problem solving strategies in mathematics classrooms (MEB, 2006). Fraivillig, Murphy and Fuson (1999) reported that creating this kind of classrooms requires that teacher has knowledge about students’

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