International Journal for Mathematics Teaching and Learning [Online] http://www.ex.ac.uk/cimt/ijmtl/ijmenu.htm Geometric Explorations with Dynamic Geometry Applications based on van Hiele Levels Sinan OLKUN * N. Beylem SINOPLU Deniz DERYAKULU Ankara University, Faculty of Educational Sciences, Turkey ABSTRACT: The purpose of this paper is to present classroom-tested geometry activities based on the van Hiele geometric thinking levels using dynamic geometry applications. The other ideas behind the activities include teacher questioning, active student participation, and student- centered decision-making. During the lessons student teachers engaged in self-exploration and reinvention of geometric relations. It was evident from the episodes that students raised their level of geometric thinking by building on their current geometric understanding. Key Words: dynamic geometry, van Hiele levels, teacher questioning INTRODUCTION Traditional elementary and middle school geometry curricula focus on having students learn list of definitions and properties of shapes. This focus is misguided. Instead of memorizing properties and definitions, students should develop personally meaningful geometric concepts and ways of reasoning that enable them to carefully analyze spatial problems and situations (Battista 2001). Instruction should also aim at raising the level of students’ thinking. Currently, the best description of students’ thinking about two-dimensional shapes is the van Hiele theory of geometric thinking (Battista, 2002). Improving students’ geometric thinking levels is one of the major aims of mathematics education since geometric thinking is very important in many scientific, technical and occupational areas as well as in mathematics. For example, in Turkey one third of the mathematics questions in the university entrance examination contain geometric content (Olkun, Toluk, Durmus, 2002). However, geometry is often neglected in the school mathematics especially in the elementary period. Some possible reasons for this negligence would be the lack of resources such as concrete materials, computer software, and the lack of knowledge and expertise about how to use computers and other materials for instructional purposes. National Council of Teachers of Mathematics (NCTM) suggests, in Principals and Standards for School Mathematics, that interactive geometry software can be used to enhance student learning (NCTM, 2000). The purpose of the present article is to present geometry activities for elementary school students based on the van Hiele geometric thinking levels (van Hiele, 1986) using a dynamic geometry application, Geometers’ Sketchpad. The instructional activities were designed to emphasize students learning through explorations instead of teaching a specific mathematical content. Therefore, the other ideas behind the activities include teacher questioning, active student participation, and student centered decision-making (Hannafin; Burruss & Little, 2001). First, we will give a glance of theoretical frameworks that are useful in understanding and leading students’ geometric thinking and learning. Then, we are going to cite several classroom episodes in which students made some progress and raised their level of geometric thinking. * Correspondent author: olkun@ education.ankara.edu.tr