Articulação entre Sequências Recursivas e teoria dos Grupos Finitos
o caso da Sequência de Padovan
DOI:
https://doi.org/10.33871/rpem.2024.13.31.9228Abstract
This article aims to present an approach to explore the Padovan sequence in conjunction with finite group theory in the context of mathematics education. To this end, we adopt the Didactic Engineering as research methodology, in its first two phases - preliminary analyses and conception and a priori analysis -, combined with the Theory of Didactic Situations, to compose a teaching model. We used the GeoGebra software as support, where we relate the Padovan sequence, which is an infinite sequence, to finite groups through modular congruence, rewriting it as a finite sequence. From the construction and its analysis, it was possible to visualize the behavior of the Padovan sequence modulo m, revealing cyclical patterns in the sequence that can be interpreted as elements of finite groups. We discuss how these results can be applied in the classroom in an approach to teaching concepts of finite groups and numerical sequences, in an associated and meaningful way.Downloads
References
ALMOULOUD, S. A.; COUTINHO, C. Q. S. Engenharia Didática: características e seus usos em trabalhos apresentados no GT-19 / ANPEd. REVEMAT - Revista Eletrônica de Educação Matemática, v. 3, n. 1, p. 62-77, 2008. https://doi.org/10.5007/1981-1322.2008v3n1p62.
XXXXX
XXXXX
ARTIGUE, M. Perspectives on design research: the case of didactical engineering. In: BIKNERAHSBAHS, A.; KNIPPING, C.; PRESMEG, N. Approaches to qualitative research in mathematics education, Springer, 2014. (p. 467–496).
ARTIGUE, M. Méthodologies de recherche en didactique des mathématiques : Où en sommes-nous? Educação Matemática Pesquisa, v. 22, n. 3, p. 25-64, 2020. https://doi.org/10.23925/1983-3156.2020v22i3p025-064
BAIRRAL, M. A.; BARREIRA, J. C. F. Algumas particularidades de ambientes de geometria dinâmica na educação geométrica. Revista do Instituto GeoGebra Internacional de São Paulo, v. 6, n. 2, p. 46–64, 2017.
BROUSSEAU, G. Theory of Didactical Situations in Mathematics: Didactique des mathématiques 1970-1990. Kluwer Academic Publishers, 2002.
BROUSSEAU, G. Introdução ao estudo das situações didáticas: conteúdos e métodos de ensino. São Paulo: Ática, 2008.
FERREIRA, R. C. Números Mórficos. 94 f. Dissertação, (Mestrado em Matemática) - Universidade Federal da Paraíba, João Pessoa, 2015. https://repositorio.ufpb.br/jspui/handle/tede/8040?locale=pt_BR
GARCIA, A.; LEQUAIN, Y. Elementos de Álgebra. Projeto Euclides. Rio de Janeiro: IMPA, 2015.
HEFEZ, A. Aritmética. Coleção PROFMAT. Rio de Janeiro: SBM, 2014.
MATHIAS, C. V.; SILVA, H. A.; LEIVAS, J. C. P. Provas sem palavras, visualização, animação e GeoGebra. Revista do Instituto GeoGebra Internacional de São Paulo, v. 8, n. 2, p. 62-77, 2019. http://dx.doi.org/10.23925/2237-9657.2019.v8i2p062-077
XXXXX
XXXXX
XXXXX
XXXXX
SPINADEL, V.; BUITRAGO, A. R. Towards Van Der Laan’s plastic number in the plane. Journal for Geometry and Graphics, v. 13, n. 2, p. 163-175, 2009. https://www.heldermann-verlag.de/jgg/jgg13/j13h2spin.pdf.
TAS, S.; KARADUMAN, E. The Padovan sequences in finite groups. Chiang Mai Journal of Science, v. 41, p. 456-462, 2014.
WEYL, H. Symmetry. New Jersey: Princeton University Press, 1983.
ZAHIROVIĆ, S.; BOŠNJAK, I.; MADARÁSZ, R. A study of enhanced power graphs of finite groups. Journal of Algebra and its Applications, v. 19, n. 4, 2019. https://doi.org/10.1142/S0219498820500620
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Revista Paranaense de Educação Matemática
![Creative Commons License](http://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.