Secondary students' 'dynamic reinvention of geometric proof' through the utilization of linking visual active representations

In this paper we describe a twofold teaching experiment carried out in a year 10 mathematics class in Greece which sought to investigate a) how the building and testing of LVAR (Linking Visual Active Representations) modes by the students supported by the Geometer's Sketchpad dynamic geometry software, impacts on students way of thinking with regard to the conjecturing and proving processes; and b) if transformations through different semi-predesigned LVAR modes lead students to structure mental transformations relative to the development of their van Hiele level. It was found that students formulated conjectures by, initially using an inductive way of thinking; they implemented logical connections in the form of articulated logical concatenations, developed thinking processes and applied skills, while formulating a mathematical model to interpret the real-world problem