A Technological Environment for Promoting Mathematical Reasoning: A Dynamic Approach to Geometric Proof

Euclidean geometry and geometric proof have occupied a central place in mathematics education from classical Greek society through to twentieth century Western culture. It is proof which sets mathematics apart from the empirical sciences, and forms the foundation of our mathematical knowledge, yet the latter part of the twentieth century witnessed the demise of both Euclidean geometry and proof in school mathematics curricula in many countries. Research indicates that students often fail to understand the purpose of mathematical proof, and readily base their convictions on empirical evidence or the authority of a textbook or teacher. A major large-scale survey of above average Year 10 students in the UK (Healy and Hoyles 1999) has shown that many students, even those who have been taught proof, have little idea of the significance of mathematical proof, are unable to recognise a valid proof, and are unable to construct a proof in either familiar or unfamiliar contexts.