Relações entre os pólos do visto e do sabido no cabri 3D: Uma experiência com alunos do ensino médio - Rosalves, Márcia Yolanda (2006)
This research involves the teaching and learning of the geometry of space (three-dimensional geometry) in school mathematics. It considers, in particular, the relationships between geometrical objects and their representations in the plane. The works of Parzysz (1988; 1993), which served as the theoretical base for this study, point to the difficulties students that experience in interpreting representations of three-dimensional objects, in terms of construction (codification) and interpretation (decodification), as well as the conflict between the poles of seeing and knowing. The results presented by Parzysz concern experimentations carried out in the conventional paper-and-pencil environment. Considering the limitations of this environment and the difficulties associated with the identification of spatial relations given its static nature, the dynamic geometry environment of Cabri 3D was chosen as the context for this study. The aim was to investigate the role of the dynamic representation of this software in the study of space geometry. More precisely, the study seeks to analyse the possibilities related to the poles of seeing and knowing in the interactions of subjects with the tools and representations of Cabri 3D. The empirical part of the research involved the development of an experimental study strongly inspired by the methodology of Design Experiments, using the perspective of Steffe and Thompson (2000) and Cobb et al. (2003). High school students from a public-sector school in the city of São Paulo participated in this experiment. The results show that, in certain situation, the loss in information associated with Cabri 3D representation of spatial objects are less than in the paper-and-pencil environment. The evidence also suggested that both the dynamic aspect with the potential to manipulate and change the point of view onto the object represented and the treatment the enriching of representations made possible by the use of the construction tools aided in the process of decodification, amplifying the interpretation of the drawing on the part of the student and enabling a better use of perceptive inferences