The Euler line: Students' Exploration in a Dynamic Geometry Environment.

This study investigates the impact of a dynamic geometry environment, GeoGebra, in enabling grade 9 students to explore a geometrical task related to the Euler's line. The research subjects were grade 9 students in India and Sweden who had no prior experience of using dynamic geometry. Their approach to geometrical reasoning, argumentation and conjecture making has been analysed using Marton's theory of variation, Pea's theory of technology as amplifier and reorganizer and with Marrades and Gutiérrez categorization of proofs. Results indicate that when students of both countries worked on geometrical tasks in GeoGebra, they arrived at similar conclusions. For both groups of students, GeoGebra played the role of amplifier and reorganiser in enabling their explorations. Further, in some of the construction and dragging episodes it was observed that the four functions of variation, namely, contrast, generalisation, separation and fusion played a significant role in developing students' geometrical thinking. Results further indicate that the dynamic geometry environment (DGE) facilitated the making of conjectures and developing empirical proof. However, when it came to developing a deductive proof, students required adequate scaffolding. In general, it concluded that students perform adequately when given investigatory problems in such an environment. They learn new mathematics and learn to handle the DGE at the same time. [ABSTRACT FROM AUTHOR]