@article {MATHEDUC.06206587,
author = {Schumann, Heinz},
title = {Interactive geometric constructions in the virtual space.},
year = {2010},
journal = {Bolet\'{\i}n. Sociedad ``Puig Adam" de Profesores de Matem\'aticas},
number = {86},
issn = {1135-0261},
pages = {12-54},
publisher = {Sociedad ``Puig Adam" de Profesores de Matem\'aticas, Madrid},
abstract = {Summary: Skills in the generation of geometric constructions using analogue and/or digital tools are just as important as skills in the common arithmetic, numeric and algebraic algorithms as part of the methodological competence taught in general mathematical instruction. Geometric constructions are both a mathematical subject in their own right and a precondition for problem solving in the geometry classroom. The introduction of dynamic geometry systems brought about an enhancement of the method of construction in synthetic geometry of the plane. Adequate three-dimensional constructions, on the other hand, were impracticable except as mental constructions; for visualization, they had to be reduced to practicable constructions in the plane using the methods of descriptive geometry. Now, however, the intuitive prototypic tool {\tt Cabri 3D}, which was developed primarily for school geometry, opens up the possibility of performing three-dimensional constructions in the virtual space, which gives us a completely new access to synthetic spatial geometry. This contribution will therefore develop elements of a didactics of interactive geometric construction in a virtual space: definition of the concept of spatial geometric construction", discussion of basic spatial geometric constructions, an outline of the available options for spatial geometric construction in {\tt Cabri 3D} many exemplary applications, and an attempted preliminary didactic assessment.},
msc2010 = {G40xx (U70xx G70xx G90xx)},
identifier = {2013e.00485},
}