Robust and soft constructions: two sides of the use of dynamic geometry environments.

Abstract

Variation is the essence of dynamic geometry environments. This talk aims at discussing two paradigms of use of variation in dynamic geometry environments: robust and soft constructions. Robust constructions are those for which the drag mode preserves their properties. Such constructions should be constructed by using the geometrical objects and relationships characterizing the construction to obtain. In such constructions variation is used as a verification means. In soft constructions, variation is part of the construction itself and a property becomes visible only when another one is satisfied. By means of several examples based on Cabri Geometry II and Cabri 3D, it will be shown how the soft paradigm can contribute to the learning. On the one hand, soft constructions can be part of the « private » side of the work of the students and help them identify dependency relationships between properties, on the other hand they can be used in mathematics teaching to introduce students to better understand the functioning of fundamental notions such as those of implication, valid property, hypothesis and conclusion.