Concepção de uma seqüência de ensino para o estudo da semelhança: do empírico ao dedutivo

• Main Author: Luis, Silviane Rigolon
• Publication Date: 2006
• Format: Master thesis
• Language: por
• Source: Repositório Institucional da PUC_SP
• Download full: https://tede2.pucsp.br/handle/handle/11094
• topic: Semelhança; homotetia; transformações; congruência; provas; Educacao matematica; Matematica -- Estudo e ensino; Similarity; homothetic; transformations; congruence; proofs; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The aim of this research is to investigate how the concept of similar figures can be presented in a significant and motivate way to the students attending the first grade of Brazilian high school system, so that the proof can be an integrant part of this process. We tried to answer the research questions: How is the transition from concrete geometry to space-graphic geometry within the context of similar figures? How does the passing of empirical validations to the deductive occurs in this context? For this, using the Didactic Engineering methodology, we developed a didactic sequence composed by three blocks, in the first and second ones; we worked with empirical validations, using concrete materials in a computerized environment and in the third one with deductive validations using paper and pencil. In our research we used the theoretical presuppositions of Parsysz to the Geometry teaching, where he emphasizes four stages of the development of geometric thought; The Balacheff s ideas about proofs validations processes, are distinguished the pragmatic proofs and the intellectual proof and with the ideas from Freudenthal that proposes for the teaching of the demonstration a local organization. The results of the experimentation aim to evidences of the concrete geometry with the manipulation of many objects stimulated the students in the investigation process and discover regularities that lead them to the idea of similarity concept as well, contributing to the acknowledgement of implicit properties in the figures presented by the dynamism of the Cabri-Géomètre software. Besides, the work done with the empiric validations was important for the students learn the concept of similarity, awakening them to the importance of justify their results and preparing them to the process of deducting validations, given that in this process we can observe an evolution in the structures of the presented proofs