Dragging and Making Sense of Invariants in Dynamic Geometry

Various aspects of the potential of dynamic geometry systems (DGSs) have been widely documented, and DGSs are considered a form of technology that enhances the learning of mathematics. In particular, the dragging tool is effective in exploratory activities in which the goal is to produce conjectures: the movement of parts of the figure, which allows the identification of invariants, lies at the heart of such activities. Perceiving and interpreting invariants is a complex task for a nonexpert geometry student, as various studies have shown. Nevertheless, having students work through particular kinds of activities that involve perception and interpretation of invariants and engage in discussions with classmates, guided by the teacher, can help them learn mathematics. The activity presented here can be used in high school geometry and can help students develop the concepts of the premise and the conclusion of a conjecture. Students use their prior knowledge to enhance their learning while engaging in an interactive experience within a DGS.