The development of students geometrical thinking through transformational processes and interaction techniques in a dynamic geometry environment

The paper draws on a didactic experiment conducted in a secondary school mathematics class-room in Greece which aimed to explore a) ways in which students develop problem representa-tions, reasoning and problem-solving, making decisions and receiving feedback about their ideas and strategies in a DGS-supported environment b) ways in which students develop rigourous proof through building linking visual active representations and c) ways to develop students ’ van Hiele level. The mathematical problem the students engaged with – either in the Geometer’s Sketchpad dynamic geometry enviroment (Jackiw, 1988) or in the static environment- generated potentially insightful data on the issues focused on the comparison between the experimental and control groups. Initially, three pairs from the experimental group explored the treasure problem within a dynamic geometry environment. The discussions and results of the discussion were videotaped. The problem was then reformulated by the researcher taking into account the research group’s retroaction, and re-explored by both the control and experimental groups in a paper– pencil test. The researcher then (semi) pre-designed multiple-page sketches detailing the sequen-tial phases of the solution to the problem using rigorous proof, and in so doing transferring he