Geometrical Constructions in Dynamic and Interactive Mathematics Learning Environment

This paper concerns teaching Euclidean geometry at the university level. It is based on the authors’ personal experience. It describes a sequence of learning activities that combine geometrical constructions with explorations, observations, and explanations of facts related to the geometry of triangle. Within this approach, a discussion of the Euler and Nigel lines receives a unified treatment via employment of a plane transformation that maps a triangle into its medial triangle. I conclude
that during this course delivery, the role of constructions in dynamic and interactive environment was significant for students’ genuine understanding of the subject. In particular, it helped them to work with concrete figures and develop their own preformal approaches before learning general theorems and proofs. At the same time it was essential to follow such strategies as gradually lead students from basic to advanced
constructions, from making simple analogies to generalizations based on critical ideas and unified principles, and emphasize structural
interconnectedness of the problems each of which adds a new element into a bigger picture.