EXPLORING THE EVOLUTION OF GEOMETRICAL THINKING
This proposal briefly describes a research identifying the experience of a group of pre-service teachers while improving their geometrical thinking in an exploratory project. As the participant researcher, I documented all the process, as will be described in detail in the final paper, and analysed their artefacts, such as pictures and dynamic worksheets, they had created, by employing comparative content analysis and their online discussions by employing discourse analysis to explore how they improved their geometrical thinking.
The project itself was a learning trajectory, encouraging pre-service teachers to explore ornaments situated nearby. The participant pre-service teachers taking a method course to teach mathematics at elementary classroom were encouraged to explore the ornaments and take their pictures, to identify transformations used in the ornaments they found, and to create dynamic worksheets by using GeoGebra, a software from Dynamic and Interactive Mathematics Learning Environments (DIMLE) , .
Geometry situated in ornaments has been interest of many mathematicians and mathematics educators as well as graphical artists, such as Huseyin Kilickan  and Miroslaw Majewski . The project had been situated in the Realistic Mathematics Education  framework such that the participants were supposed to connect their real life experience with the artefacts, GeoGebra dynamic worksheets, they created. The data suggested the ways not only how they improved their understanding of transformation but also how they had developed a learning strategy to teach their prospective students.
The final paper will illustrate findings on how their geometrical thinking evolved during the project. In addition, I will include one specific example illustrating all the stages of the project for one participant. Finally, I will discuss possible implications of the project both in teacher training and student educating perspectives as well as further research opportunities on the topic.
At the conference, I suggest presenting orally such that I can share some of my data with the audience and discuss the ways how I interpreted participants’ evolving geometrical thinking.
 Karadag, Z., Martinovic, D., & Freiman, V. (2011). Dynamic and Interactive Mathematics Learning Environments (DIMLE). In L. R. Wiest, & T. Lamberg (Eds.), The Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Reno, Nevada.
 Martinovic, D., & Karadag, Z. (2012). Dynamic and interactive mathematics learning environments: the case of teaching limit concept. Teaching mathematics and its applications, doi:10.1093/teamat/hrr029
 Kilickan, H. (2004). Turk bezeme sanati [The art of Turkish ornaments]. Inkilap kitabevi.
 Majewski, M. (2012). Szkice O Geometrii I Sztuce: miedzy Wschodem i Zachodem.Wydawnictwo Aksjomat.
 Freudenthal, H. (1991). Revisiting Mathematics Education. China Lectures. Dordrecht: Kluwer Academic Publishers.