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

AUTOR(ES)

Andrea Gomes Nazuto Gonçalves

DATA DE PUBLICAÇÃO

2007

RESUMO

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

ASSUNTO(S)

matematica educacao matematica fractais geometric progressions dynamic geometry progressões geométricas geometria -- estudo e ensino fractals geometria dinâmica matematica -- estudo e ensino

Documentos Relacionados

• Uma seqüência de ensino para o estudo das propriedades dos polígonos via pavimentação
• A RESOLUÇÃO DE PROBLEMAS COMO FERRAMENTA PARA A APRENDIZAGEM DE PROGRESSÕES ARITMÉTICAS E GEOMÉTRICAS NO ENSINO MÉDIO
• Concepção de uma seqüência de ensino para o estudo da semelhança: do empírico ao dedutivo
• Concepção de uma sequência didática para o ensino/aprendizagem da congruência
• Fractais, Congruências e Primos: Uma Estratificação Visual dos Números Inteiros via Fractais de Sierpinski