Visualizing geometrical counterexamples using digital tools

In my study about pre-service secondary mathematics teachers’ (PSMTs) understanding about the nature of theorems in geometry, I noticed that it was challenging for the PSMTs to visualize and draw counterexamples to disprove the given mathematical statements. The use of the dragging feature of some digital tools, such as The Geometer’s Sketchpad (GSP), in teaching and learning proof and reasoning has been widely discussed and become an ongoing research trend. In this conference session presentation, I will introduce the background of the use of dragging feature in dynamic geometry environment and present two examples showing how this feature could be useful in helping the learners find counterexamples for the two geometrical statements, and thus enhance their understanding about the meaning and usage of counterexamples in geometrical reasoning. The session is potentially beneficial to pre-service/in-service secondary math teachers and teacher educators