Dragging maintaining symmetry: can it generate the concept of inclusivity as well as a family of shapes?

This article describes a project using Design Based Research methodology to ascertain whether a pedagogical task based on a dynamic figure designed in a Dynamic Geometry Software (DGS) program could be instrumental in developing students’ geometrical reasoning. A dragging strategy which I have named ‘Dragging Maintaining Symmetry’ (DMS) was shown to be important for the making of mathematical meanings in the context of Dynamic Geometry. In particular, it encouraged students’ development of the concept of inclusive relations between shapes generated from the dynamic figure, especially the rhombus as a special case of the kites. This development was not automatic and in addition to their work with the dynamic figure the students were shown an animation of the figure under DMS. Watching the animation allowed the students to attend to the continuous nature of the changing figure and proved to be the catalyst for moving their reasoning towards perceiving inclusive relations between the rhombus and kite.