Uma seqüência de ensino para o estudo de progressões geométricas via fractais

• Autor(a) principal: Gonçalves, Andrea Gomes Nazuto
• Data de Publicação: 2007
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/11504
• topic: Progressões geométricas; Geometria dinâmica; Geometria -- Estudo e ensino; Fractais; Educacao matematica; Matematica -- Estudo e ensino; Fractals; Geometric progressions; Dynamic geometry; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The objective of this research is to investigate the learning of Geometric Progressions by fractals and their influences on the construction of the knowledge of this subject. Starting from this objective our research questions emerge: How the use of the fractals motivate can be in the perception of the solemnity-similarity? How can the solemnity-similarity contribute in the process of generalization of the formulas of the geometric progression to High School students? So, we developed a teaching sequence, using some elements of the methodology of research denominated engineering didacticism. The conceived sequence is constituted by three blocks, and in the first, we worked the fractals construction; in the second we used the Dynamic Geometry to represent them; and in the third party we focused the generalizations. We used in our research the theoretical presuppositions of Parzysz for the geometry teaching, in what it concerns at their four levels of development of the geometric thought; Machado's ideas that suggest in the construction of a geometric object an articulation among four processes: perception, physical construction, representation and conceptual organization; the situations of resolutions of problems for development of significant concepts proposed by Vergnaud; and also the Dynamic Geometry to motivate the student to investigate. The analysis of the results obtained in the application of the didactic sequence showed that the construction, the manipulation and the observation take to the perception of the solemnity-similarity this, has the aim to facilitate the process of generalization of the mathematical elements that compound the study of Geometric Progressions. In spite of, the number of students used in the sequence (22 couples) brought us great difficulties in the application of the activities, however, it reflected an atmosphere similar to the found at classroom