Symmetry also known as transformational geometry is an important concept in the learning area of geometry in primary and secondary school mathematics curriculum. Conceptual understanding about transformation geometry helps students not only to understand nature and its beauty, but also to enhance aesthetics opinion (Aksoy & Bayazit, 2010). Technology in mathematics facilitates conceptual development, exploration, reasoning, and problem solving (Drier, Dawson, & Garofalo, 1999). According to NCTM (1989), students should use computer software based on dynamic view of transformations which represent physical motion (slides, flips, and turns) to explore properties of transformations. As a new technology, Dynamic Geometry Environments (DGEs) help students to interact with geometrical objects and their relations by manipulating (Healy & Hoyles, 2001). Geogebra which is one of the DGEs enables students to explore, create, and analyze a wide range of mathematics concepts in the field of algebra, geometry, trigonometry, and other areas. It is believed that Geogebra  “permits activities that need high level thinking, entails pupils engaging with the potential that ICT brings, such as users learning from feedback, seeing patterns, making actions, working with dynamic images, etc.” (Edwards & Jones, 2006, p. 30). The purpose of the study is to investigate conceptions of reflective symmetry of 6^th grade students who interacted with computer tasks in a DGE with Geogebra.  In line with this purpose, the research question of the study is ‘What is the nature of 6^th grade students’ conceptualizations of reflective symmetry when engaging in computer tasks on the technological tool, Geogebra?’

Theoretical perspective of this study is based on the SOLO taxonomy and conceptual/procedural knowledge. The SOLO taxonomy which is an acronym for "Structure of the Observed Learning Outcome” was developed by Biggs and Collis (1982). This taxonomy, a neo-Piagetian model, helps to analyze the complexity of students’ responses to tasks (Shaugnessy, 2007). The SOLO taxonomy consists of five levels of response which are evaluated to the nature and strength of connections: prestructural, unistructural, multistructural, relational, and extended abstract.  These five levels seem to form a hierarchy of structural organization of the knowledge from incompetence to expertise. At the prestructural level, responses of students are incomplete or irrelevant to area. Students focus on a single aspect of the task at the unistructural level, whereas at the multistructural level students pick up several aspects of the task serially (but they are not interrelated). Several aspects of knowledge are integrated into a structure at the relational level. At the last level (extended abstract) students can generalize the knowledge to a new domain.

Procedural knowledge, which means “‘know to how to do it’ knowledge”, relates it to “terms such as process, problem solving, and strategic thinking and requires distinguishing in different levels of procedure” (McCormick, 1997, p. 143). On the other hand, conceptual knowledge is interested in interrelationships among items of knowledge (Rittle-Johnson, Siegler & Alibali, 2001). In addition to, there are bidirectional relations between conceptual and procedural knowledge (Rittle-Johnson and Siegler, 1998).

Aksoy, Y., & Bayazit, İ. (2010). Simetri kavramının öğrenim ve öğretiminde karşılaşılan zorlukların analitik bir yaklaşımla incelenmesi. In E. Bingölballi & M. F. Özmantar (Ed.), İlköğretimde karşılaşılan matematiksel zorluklar ve çözüm önerileri (pp. 187-215). Ankara: PegemA. Biggs, J. and Collis, K. F. (1982) Evaluating the quality of learning: the SOLO taxonomy. New York: Academic Press. Drier, H., Dawson, K. M., & Garofalo, J. (1999) Not your typical math class. Educational Leadership, 56(5), 21-25. Washington, D.C.: Department of Supervision and Curriculum Development. Edwards, L. D. (1991). Children’s learning in a computer microworld for transformational geometry. Journal for Research in Mathematics Education , 22(2), 122-137. Edwards, J. A., & Jones, K. (2006). Linking geometry and algebra with GeoGebra. Mathematics Teaching, 194, 28-30. Healy, L., & Hoyles, C. (2001). Software tools for geometrical problem solving: potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235-56. Hoyles, C., & Healy, L. (1991). Unfolding meanings for reflective symmetry. International Journal of Computers for Mathematical Learning, 2, 27-59. McCormick, R. (1997) Conceptual and procedural knowledge. International Journal of Technology and Design Education, 7, 141-159. National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and evaluation standards for school mathematics. Reston, Va: NCTM. Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical skills (pp. 75-328). Hove, UK: Psychology Press. Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346-362. Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957-1009). Greenwich, CT: Information Age Publishing, Inc. and NCTM.