Mathematical proof and epistemological obstacles: Assumptions of the methodological teaching proposal of the Fedathi sequence

Carlos Henrique Delmiro Araújo; Daniel Brandão Menezes

doi:10.29333/iejme/12315

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Carlos Henrique Delmiro Araújo ¹ ^* , Daniel Brandão Menezes ²

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¹ Secretaria Municipal de Educação de Canindé, BRAZIL² Universidade Estadual Vale do Acaraú, BRAZIL^* Corresponding Author

Abstract

The Multimedia Research Laboratory, inserted in the Federal University of Ceará has the Multimedia Mathematics Education Group, in which they study the mathematics teaching with the methodological contribution of the Fedathi sequence (FS). In one of the study meetings, the members raised the issue of how a class in the light of the FS could be, which would address mathematical proof. To this end, the mathematical object used to illustrate the answer to this question was the ordering in the set of rational numbers, aiming at the didactic session in the mathematics undergraduate course. Thus, this research aimed to develop a model of mathematical proof approach based on the FS methodological proposal, attempting to solve the issue raised. To make this work possible, the FS research methodology was used, with a qualitative bias. Regarding the results, it was possible to develop the model with the purpose of performing mathematical proof using the FS as a teaching methodology, considering that this way of mediating knowledge is not a transmission of content, but rather, a way of providing learning.

Keywords

rational numbers
ordered field
teaching methodology

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 17, Issue 4, November 2022, Article No: em0707

https://doi.org/10.29333/iejme/12315

Publication date: 06 Aug 2022

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References

Alves, F. R. V. (2011). Aplicações da sequência Fedathi na promoção do raciocínio intuitivo no cálculo a várias variáveis [Applications of the Fedathi sequence in promoting intuitive reasoning in multi-variable calculation] [PhD thesis, Universidade Federal do Ceará].
Araújo, C. H. D., Menezes, D. B., & Borges Neto, H. (2020). Sequência Fedathi e o papiro de rhind: O caso do problema 79. Boletim Cearense de Educação e História da Matemática [Ceará Bulletin of Education and History of Mathematics], 7(19), 41-56. https://doi.org/10.30938/bocehm.v7i19.2757
Barbosa, J. C. (2020). Raízes: Concepções teóricas, pedagógicas e tecno-práticas de um objeto educacional digital (OED) baseado na sequência Fedathi [Roots: Theoretical, pedagogical and techno-practical conceptions of a digital educational object (DEO) based on the Fedathi sequence] [Master’s thesis, Universidade Federal do Ceará].
Barroso, N. M. C. (2009). Um modelo de ensino dos conceitos de cálculo para os cursos de engenharia fundamentado em uma epistemologia histórica e baseado na metodologia da engenharia didática: Validação por meio do conceito de integral [A model for teaching calculus concepts for engineering courses based on a historical epistemology and based on the methodology of didactic engineering: Validation through the concept of integral] [PhD thesis, Universidade Federal do Ceará].
Becker, F. (2019). Construção do conhecimento matemático: Natureza, transmissão e gênese [Construction of mathematical knowledge: Nature, transmission and genesis]. Bolema: Boletim de Educação Matemática [Bulletin: Mathematics Education Bulletin], 33(65), 963-987. https://doi.org/10.1590/1980-4415v33n65a01
Bergmann, J., & Sams, A. (2018). Sala de aula invertida: Uma metodologia ativa de aprendizagem [Flipped classroom: An active learning methodology]. LTC.
Borges Neto, H. (2016). Uma proposta lógico-construtiva-dedutiva para o ensino de matemática [A logical-constructive-deductive proposal for teaching mathematics] [Thesis, Universidade Federal do Ceará].
Davis, P. J., & Hersh, R. (1981). The mathematical experience. Birkhäuser.
Descartes, R. (1983). Discurso do método; meditações; objeções e respostas; as paixões da alma; cartas [Method discourse; meditations; objections and responses; the passions of the soul; cards]. Abril Cultural.
Doruk, M. (2019). Preservice mathematics teachers’ determination skills of proof techniques: The case of integers. International Journal of Education in Mathematics, Science and Technology, 7(4), 335-348.
Felício, M. S. N. B., Menezes, D. B., & Borges Neto, H. (2020). Formação Fedathi generalizável [Generalizable Fedathi formation]. Boletim Cearense de Educação e História da Matemática [Ceará Bulletin of Education and History of Mathematics], 7(19), 24-40. https://doi.org/10.30938/bocehm.v7i19.2906
Ferraz, A. P. C. M., & Belhot, R. V. (2010). Taxonomia de Bloom: Revisão teórica e apresentação das adequações do instrumento para definição de objetivos instrucionais [Bloom’s Taxonomy: Theoretical review and presentation of the instrument’s adjustments to define instructional objectives]. Gestão e Produção [Management and Production], 17(2), 421-431. https://doi.org/10.1590/S0104-530X2010000200015
Ferreira, J. (2013). A construção dos números [The construction of numbers]. SBM.
Guidorizzi, H. L. (2001). Um curso de cálculo [A calculus course]. LTC.
Lima, E. L. (2013a). Análise real volume 1: Funções de uma variável [Real analysis volume 1: One-variable functions]. IMPA.
Lima, E. L. (2013b). Curso de aanálise [Analysis course]. IMPA.
Menezes, D. B. (2018). O ensino do cálculo diferencial e integral na perspectiva da sequência Fedathi: Caracterização do comportamento de um bom professor [The teaching of differential and integral calculus in the perspective of the Fedathi sequence: Characterization of the behavior of a good teacher] [PhD thesis, Universidade Federal do Ceará].
Morais Filho, D. C. (2016). Um convite à matemática: Com técnicas de demonstração e notas históricas [An invitation to mathematics: With demonstration techniques and historical notes]. SBM.
Mowahed, A. K., Song, N., Xinrong, Y., & Changgen, P. (2020). The influence of proof understanding strategies and negative self-concept on undergraduate Afghan students’ achievement in modern algebra. International Electronic Journal of Mathematics Education, 15(1), em0550. https://doi.org/10.29333/iejme/5886
Muniz Neto, A. C. (2013). Tópicos de matemática elementar: Números reais [Elementary math topics: Real numbers]. SBM.
Papert, S. (1986). Logo: Computadores e educação [Logo: Computers and education]. Brasiliense.
Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton University Press.
Sousa, F. E. E. (2015). A pergunta como estratégia de mediação didática no ensino de matemática por meio da sequência Fedathi [The question as a didactic mediation strategy in mathematics teaching through the Fedathi sequence] [PhD thesis, Universidade Federal do Ceará].
Souza, M. J. A. (2013). Sequência Fedathi: Apresentação e caracterização [Fedathi Sequence: Presentation and characterization]. In Sequência Fedathi: Uma proposta pedagógica para o ensino de matemática e ciências [Fedathi Sequence: A pedagogical proposal for teaching mathematics and science] (pp. 15-48). Edições UFC.
Weber, K. (2015). Effective proof reading strategies for comprehending mathematical proofs. International Journal of Research in Undergraduate Mathematics Education, 1(3), 289-314. https://doi.org/10.1007/s40753-015-0011-0
Xavier, D. O. (2020). Raízes: Postura docente virtual a partir de uma perspectiva Fedathiana [Roots: Virtual teaching posture from a Fedathian perspective] [Master’s thesis, Universidade Federal do Ceará].

How to cite this article

APA

Araújo, C. H. D., & Menezes, D. B. (2022). Mathematical proof and epistemological obstacles: Assumptions of the methodological teaching proposal of the Fedathi sequence. International Electronic Journal of Mathematics Education, 17(4), em0707. https://doi.org/10.29333/iejme/12315

Vancouver

Araújo CHD, Menezes DB. Mathematical proof and epistemological obstacles: Assumptions of the methodological teaching proposal of the Fedathi sequence. INT ELECT J MATH ED. 2022;17(4):em0707. https://doi.org/10.29333/iejme/12315

AMA

Araújo CHD, Menezes DB. Mathematical proof and epistemological obstacles: Assumptions of the methodological teaching proposal of the Fedathi sequence. INT ELECT J MATH ED. 2022;17(4), em0707. https://doi.org/10.29333/iejme/12315

Chicago

Araújo, Carlos Henrique Delmiro, and Daniel Brandão Menezes. "Mathematical proof and epistemological obstacles: Assumptions of the methodological teaching proposal of the Fedathi sequence". International Electronic Journal of Mathematics Education 2022 17 no. 4 (2022): em0707. https://doi.org/10.29333/iejme/12315

Harvard

Araújo, C. H. D., and Menezes, D. B. (2022). Mathematical proof and epistemological obstacles: Assumptions of the methodological teaching proposal of the Fedathi sequence. International Electronic Journal of Mathematics Education, 17(4), em0707. https://doi.org/10.29333/iejme/12315

MLA

Araújo, Carlos Henrique Delmiro et al. "Mathematical proof and epistemological obstacles: Assumptions of the methodological teaching proposal of the Fedathi sequence". International Electronic Journal of Mathematics Education, vol. 17, no. 4, 2022, em0707. https://doi.org/10.29333/iejme/12315