Turtle's Navigation and Manipulation of Geometrical Figures Constructed by Variable Processes in a 3d Simulated Space

Issues related to 3d turtle’s navigation and geometrical figures’ manipulation in the simulated 3d space of a newly developed computational environment, MaLT, are reported and discussed here. The joint use of meaningful formalism and the dynamic manipulation of graphically represented 3d figures seem to offer new resources and to pose new challenges as far as geometrical activities and construction of meanings are concerned, which are strongly related to the representational infrastructure of MaLT. Abilities such as spatial orientation and spatial visualisation come into play and are interwoven with the software’s functionalities and semantics. Although the body-syntonic metaphor remains critical while navigating the turtle in the 3d simulated space, it seems that it has to be coordinated with other –often conflicting one anotherframes of reference. The strong link between spatial graphical and geometrical aspects, that was accentuated by the dragging functionalities of the software, helped students go beyond an immediate perceptual approach, relating geometrical figures with real 3d objects and the change of planes in 3d space with physical angle situations. In this framework the concept of angle as turn and measure with emphasis on directionality but also as a relationship between the planes defined by 2d figures has arisen as central. Figure 1. The interface of MaLT