Robust and soft constructions: two sides of the use of dynamic geometry environments.
Colette Laborde Colette.Laborde@imag.fr
Université Joseph Fourier Institut Univ. Formation des maitres
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.
