The golden number in basic education: a possible approach for the exploration of the constitutive axes of real numbers
DOI:
https://doi.org/10.15536/reducarmais.7.2023.3093Keywords:
Golden Number, Basic School, Constitutive Axles of Real Numbers, Irrational NumbersAbstract
A remarcable irrational number – the golden number – is little explored in Brazilian didactical textbooks and at the most recent national curriculum stanndarts. This text aimed to carry out an epistemological and didactical discussion involving a possible development and significance of the golden number in the segment of basic education. For this purpose, we made use of a theoretical contribution called constitutive axes of real numbers, pointed out in Machado (2009), which designates the discrete&continuous, exact&approximate and finite&infinite pairs as polarities that enables to situate and signify the knowledge of irrational numbers at basic education. The epistemological and didactical analysis revealed connections of the golden numer with the Fibonacci sequence and with simple continued fractions, which permeate a presentation articulating the constitutive axes of real numbers.
Downloads
References
BOYER, Carl Benjamin. História da Matemática. 9. ed. São Paulo: Editora Edgard Blücher, 1991.
BRASIL. Base Nacional Comum Curricular (2ª versão). Brasília: MEC, 2016.
_______. Parâmetros Curriculares Nacionais: Matemática. Brasília: SEMT/MEC, 1997.
CARAÇA, Bento de Jesus. Conceitos Fundamentais da Matemática. 5. ed. Portugal: Lisboa, 1970.
CERRI, Cristina. Desvendando os Números Reais. IME-USP, 2006.
CONDESSE, Viviana; MINNAARD Claudia. La familia de los números metálicos y su hijo pródigo: el número de oro. Revista Iberoamericana de Educación. n. 42, v.2. mar. 2007.
CRUMP, Thomas. La Antropología de los números. Editora: Alianza, 1993.
DOS SANTOS, Arlem Atanazio; ALVES, Francisco Régis Vieira. O estudo e o ensino da sequência de Fibonacci numa abordagem atualizada. Revista Thema, v. 13, n. 2, p. 42-53, 2016.
EUCLIDES. Os Elementos (Edição latina de Frederico Commandino). São Paulo: Edições Cultura. 1944.
HARIKI, Seiji. Sobre Frações Próprias, Impróprias e Aparentes. Revista do Professor de Matemática, IME-USP, São Paulo, 1993, n. 23, p. 19-22.
HILBERT, David. Sobre o Infinito. Tradução de Marcelo Papini. p. 1-11. In: Encontro de Matemáticos. Sociedade de Matemática de Westfalen: Münster, 1925, p. 161-190.
JERNAJCZYK, Jakub. Irrational images: the visualization of abstract mathematical terms. Mathematica Applicanda. v. 43, n.2, 2015, p. 269–279.
MACHADO, Nilson José. Matemática e Língua Materna. São Paulo: Editora Cortez, 1990.
_____________________. Matemática e Realidade. 3. ed. São Paulo: Editora Cortez, 1994.
_____________________. Sobre alguns desequilíbrios na apresentação da Matemática básica: discreto/contínuo, finito/infinito, exato/aproximado, determinístico/aleatório. São Paulo: IME-USP, 2009.
POMMER, Wagner Marcelo. A Construção de significados dos Números Irracionais no ensino básico: Uma proposta de abordagem envolvendo os eixos constituintes dos Números Reais. 2012. 235f. Tese (Faculdade de Educação). Universidade de São Paulo, São Paulo.
__________. Números irracionais na escolaridade básica: um olhar pelo viés dos eixos constitutivos dos números reais. Revista de Educação Matemática, v.15, p. 610-628, 2018.
REINA, Luis; WILHELMI, Miguel R.; LASA, Aitzol. Configuraciones epistémicas asociadas al número irracional. Sentidos y desafios en Educación Secundaria. Educación Matemática, v. 24, n. 3, dez. 2012. p. 67-97.
VOSKOGLOU, Michael Gr. An Application of the APOS/ACE Approach in Teaching the Irrational Numbers. Journal of Mathematical Sciences & Mathematics Education. v. 8, n.1, 2013. p. 30-47.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Wagner Marcelo Pommer
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
DECLARATION OF RESPONSIBILITY: I hereby certify that I partially or fully participated in the conception of the work, that I did not hide any links or financial agreements between the authors and companies that may be interested in this article publication. I certify that the text is original and that the work, partially or fully, or any other work with a substantially similar content written by me, was not sent to any other journal and it will not be send while my submission is being considered by Revista Educar Mais, whether in printed or electronic format.
The author responsible for the submission represents all the authors of the manuscript and, when sending the article to the journal, guarantees s/he has obtained the permission to do so, as well as s/he guarantees the article does not infringe upon anyone’s copyright nor violate any proprietary rights. The journal is not responsible for the opinions expressed.
Revista Educar Mais is Open Access, does not charge any fees, whether for submission or article processing. The journal adopts Budapest Open Access Initiative (BOAI)’s definition, i.e., any users are permitted to read, download, copy, distribute, print, search and link to the full texts of these articles.
All the articles are published under the Creative Commons Atribuição-NãoComercial 4.0 Internacional license. The authors keep the copyright of their production. That way, they must be contacted directly if there is any interest in commercial use of their work.
