Uma abordagem para a prova com construções geométricas e Cabri-géomètre - Araújo, Ivanildo Basílio de (2007)
This study, inserted in the theme of the use of digital teachnologies within Mathematics Education, discusses the teaching and learning of proof. It aims to investigate an approach to proof in geometry with its basis in geometrical constructions using the software Cabri-Géomètre. With this aim in mind, a teaching experiment involving students from the 7th grade of school from the public school system of the state of São Paulo was conducted. The experiment was carried out in two phases: the design phase and the analysis phase. In the design phase, three sets of activities were created and tested, two involved use of the dynamic geometry software, will the thirds was paper and pencil based. The dynamic geometry activities were inspired by Mascheroni´s geometry of the compass. During the analysis phase, Balacheff´s notions related to types of proof produced by students (pragmatic and conceptual) were employed (BALACHEFF, 1987, 1988). Through the medium of the dynamic geometry activities, the study sought to explore not only the impact of the dynamism but also how the availability of different tools for the solution of the same problem influenced students´ strategies and thinking. The activities drew from the possibilities associated with geometrical constructions, in terms of aspects inductive and deductive proofs as well as movements between these two poles. Results points to how the use of Cabri encouraged students to at least give attention to empirical verifications of geometrical proprieties within the constructed figures, but may also have contributed to the tendency to focus more on constructions and descriptions than on justifications. Another notable result relates to students´ difficulties with the notion of robust construction, indicating that the screen of Cabri is frequently confused with the paper and pencil environment