THEOREM OF PITAGORS AND THE FRACTAL PITAGORIC TREE: AN EXPERIMENT IN FUNDAMENTAL TEACHING

José Carlos Pinto Leivas, Anne Desconsi Hasselmann Bettin

Abstract


This article approaches a qualitative research that had as objective to use some notions of euclidean geometry of students of a nineth year of Elementary School to realize the need to know some aspects of fractal geometry to understand the world in which they live. As a teaching methodology was used Van Hiele Theory for the development of reasoning in geometry with the software Geogebra in the construction of the fractal Pythagorean Tree. The students realized activities of classification of geometric figures and elements of nature, that allowed them to group them in properties or characteristics in two geometries and, with exploration of the photography resource, it was possible, for example, to identify the self-similarity characteristic of the fractal objects. The results of the research showed the efficiency of the Van Hiele Theory and Geogebra in the understanding of properties of the two geometries, in particular, on the Pythagorean theorem.

References


BRUNET, A. R. G.; LEIVAS, J. C. P.; LEYSER, M. Semelhança de triângulos: o desafio de (re)construir práticas em sala de aula. In: Educação Matemática em Revista/ Sociedade Brasileira de Educação Matemática do Rio Grande do Sul (SBEM-RS). v.1, n.1(1999). Canoas: Ed. ULBRA, 2007.

JANOS, M.. Geometria Fractal. Rio de Janeiro: Editora Ciência Moderna Ltda., 2008.

JELINEK, K. R.; KAMPFF, A.J.C. A geometria que existe além do olhar: levando a geometria da natureza para dentro da escola. Educação matemática em revista/ Sociedade Brasileira de Educação Matemática do Rio Grande do Sul (SBEM-RS). v.1, n.10 (2009) – Canoas: Ed. ULBRA, 2009.

NASSER, L.; SANT’ANNA, N. P. Geometria segundo a Teoria de Van Hiele. Rio de Janeiro: Projeto Fundão, IM/UFRJ, 1998.

NASSER, L., et al. Geometria segundo a Teoria de Van Hiele – 3. ed. Instituto de Matemática/ UFRJ - Projeto fundão, 2000.

PADILHA, T. APARECIDA F. Conhecimentos Geométricos e Algébricos a partir da construção de fractais com uso do software GeoGebra. Dissertação de Mestrado. Lajeado/RS. UNIVATES, 2012.

TOMEI, C. Euclides - A conquista do espaço. São Paulo: Odysseus Editora, 2003.

VILLIERS, M. de. Algumas reflexões sobre a Teoria de Van Hiele. In: Educ. Matem. Pesq., São Paulo, v.12, n.3, pp.400-431, 2010. Disponível em: . Acesso em: 21 set. 2016.




DOI: https://doi.org/10.14571/brajets.v11.n3.444-457



Licensed under :

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 Unported License.

----------------------------------------------------------------------

Indexing, Scientific Societies and Directories

Logo CAPES Logo periodicos.CAPES Logo Google Scholar

Logo GIF Logo Latindex Logo BASE Logo PKP

Logo DIADORIM Logo IBICT Logo SIS

Logo Gaudeamus Logo ROAD Logo DOAJ