International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
APA
In-text citation: (Alves et al., 2021)
Reference: Alves, F. R. V., Mangueira, M. C. D. S., Catarino, P. M. M. C., & Vieira, R. P. M. (2021). Didactic Engineering to Teach Leonardo Sequence: A Study on a Complexification Process in a Mathematics Teaching Degree Course. International Electronic Journal of Mathematics Education, 16(3), em0655. https://doi.org/10.29333/iejme/11196
AMA
In-text citation: (1), (2), (3), etc.
Reference: Alves FRV, Mangueira MCDS, Catarino PMMC, Vieira RPM. Didactic Engineering to Teach Leonardo Sequence: A Study on a Complexification Process in a Mathematics Teaching Degree Course. INT ELECT J MATH ED. 2021;16(3), em0655. https://doi.org/10.29333/iejme/11196
Chicago
In-text citation: (Alves et al., 2021)
Reference: Alves, Francisco Regis Vieira, Milena Carolina dos Santos Mangueira, Paula Maria Machado Cruz Catarino, and Renata Passos Machado Vieira. "Didactic Engineering to Teach Leonardo Sequence: A Study on a Complexification Process in a Mathematics Teaching Degree Course". International Electronic Journal of Mathematics Education 2021 16 no. 3 (2021): em0655. https://doi.org/10.29333/iejme/11196
Harvard
In-text citation: (Alves et al., 2021)
Reference: Alves, F. R. V., Mangueira, M. C. D. S., Catarino, P. M. M. C., and Vieira, R. P. M. (2021). Didactic Engineering to Teach Leonardo Sequence: A Study on a Complexification Process in a Mathematics Teaching Degree Course. International Electronic Journal of Mathematics Education, 16(3), em0655. https://doi.org/10.29333/iejme/11196
MLA
In-text citation: (Alves et al., 2021)
Reference: Alves, Francisco Regis Vieira et al. "Didactic Engineering to Teach Leonardo Sequence: A Study on a Complexification Process in a Mathematics Teaching Degree Course". International Electronic Journal of Mathematics Education, vol. 16, no. 3, 2021, em0655. https://doi.org/10.29333/iejme/11196
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Alves FRV, Mangueira MCDS, Catarino PMMC, Vieira RPM. Didactic Engineering to Teach Leonardo Sequence: A Study on a Complexification Process in a Mathematics Teaching Degree Course. INT ELECT J MATH ED. 2021;16(3):em0655. https://doi.org/10.29333/iejme/11196

Abstract

This paper presents a study based on didactic engineering and the theory of didactical situations on the complexification of the Leonardo sequence, addressing its numbers in a two-dimensional way, with the insertion of the imaginary unit i. This study is an excerpt from a masters’ thesis research done in the postgraduate programme in science and mathematics teaching of the Federal Institute of Ceará. It was conducted via Google Meet in an initial teacher education class in History of Mathematics. We will present a problem situation based on the research and the teaching methodologies assumed in it to evaluate the students’ investigative and intuitive side faced with the situation presented. We assessed the results according to the methodologies used and carried out an internal validation. Thus, we concluded that the students could build their knowledge themselves, becoming protagonists of this construction and obtaining an evolutionary understanding of the Leonardo sequence.

References

  • Almouloud, S. A. (2007). Fundamentos da didática da matemática [Fundamentals of mathematics didactics]. Editora UFPR.
  • Almouloud, S. A., & Silva, M. J. (2012). Engenharia didática: evolução e diversidade [Didactic engineering: evolution and diversity]. Revemat: Revista Eletrônica de Educação Matemática, 7(2), 22-52. https://doi.org/10.5007/1981-1322.2012v7n2p22
  • Almouloud, S., & Coutinho, C. Q. S. (2008). Engenharia Didática: características e seus usos em trabalhos apresentados no GT-19 / ANPEd 1 [Didactic Engineering: characteristics and its uses in works presented in GT-19 / ANPEd 1]. REVEMAT - Revista Eletrônica de Educação Matemática, 3(1), 62-77. https://doi.org/10.5007/1981-1322.2008v3n1p62
  • Alves, F. R. V., & Dias, M. A. (2017). Formação de professores de matemática: um contributo da engenharia didática [Mathematics teacher training: a contribution from didactic engineering]. REVEMAT, 12(2), 192-209. https://doi.org/10.5007/1981-1322.2017v12n2p192
  • Alves, F. R. V., & Vieira, R. P. M. (2020). The Newton fractal’s Leonardo sequence study with the Google Colab. International Electronic Journal of Mathematics Education, 15(2), 1-9. https://doi.org/10.29333/iejme/6440
  • Alves, F. R. V., Catarino, P. M., Vieira, R. P. M., & Mangueira, M. C. dos S. (2020). Teaching recurrent sequences in Brazil using historical facts and graphical illustrations. Acta Didactica Naposcencia, 13(1), 1-25. https://doi.org/10.24193/adn.13.1.9
  • Alves, F. R. V., Vieira, R. P. M., da Silva, J. G. A., & Mangueira, M. C. S. (2019). Engenharia Didática para o ensino da Sequência de Padovan: um estudo da extensão para o campo dos números inteiros. In F. A. M. F. Gonçalves (Ed.), Ensino de ciências e educação matemática 3. Atena Editora. https://doi.org/10.22533/at.ed.0901922112
  • Artigue, M. (1995). Ingeniería didáctica en educación matemática. Un esquema para la investigación y la innovación en la enseñanza y el aprendizaje de las matemáticas [Didactic engineering in mathematics education. An Outline for Research and Innovation in Mathematics Teaching and Learning]. Una empresa docente & Grupo Editorial Iberoamérica.
  • Brousseau, G. (1986). La relation didactique: le milieu [The didatic relationship: The environment]. Actes de la IVème Ecole d'Eté, 54-68.
  • Catarino, P. M., & Borges, A. (2019). On Leonardo numbers. Acta Mathematica Universitatis Comenianae, 89(1), 75-86.
  • Harman, C. (1981). Complex Fibonacci numbers. The Fibonacci Quarterly, 19(1), 82-86.
  • Oliveira, R. d., Alves, F. R. V., & Paiva, R. (2017). Identidades bi e tridimensionais para os números de Fibonacci na forma complexa [Two- and three-dimensional identities for Fibonacci numbers in complex form]. Revista Eletrônica Paulista de Matemática, 11, 91-106. https://doi.org/10.21167/cqdvol11ic201723169664rrofrvarebp91106
  • Oliveira, R. R. de, Andrade, M. H. De, & Alves, F. R. V. (2018). Função geradora e equação característica no contexto de investigação histórica do modelo de Fibonacci fundamentada na Engenharia Didática [Generating function and characteristic equation in the context of historical investigation of the Fibonacci model based on Didactic Engineering]. Boletim Cearense de Educação e História da Matemática, 5(41), 41-50. https://doi.org/10.30938/bocehm.v5i14.30
  • Oliveira, R. R. de. (2018). Engenharia didática sobre o modelo de complexificação da sequência generalizada de Fibonacci: Relações recorrentes n-dimensionais e representações polinomiais e matriciais [Didactic engineering on the generalized Fibonacci sequence complexification model: n-dimensional recurrent relations and polynomial and matrix representations] [Master’s dissertation in Science and Mathematics Teaching], Instituto Federal de Educação, Ciência e Tecnologia do Estado do Ceará, Fortaleza.
  • Pommer, W. M. (2013). A Engenharia Didática em sala de aula: Elementos básicos e uma ilustração envolvendo as Equações Diofantinas Lineares [Didactic Engineering in the classroom: Basic elements and an illustration involving Linear Diophantine Equations]. S. N.
  • Rodrigues, G. R., & Alves, F. J. C. (2019). Avaliação do uso de uma sequência didática no ensino de matrizes através da programação em blocos por um grupo focal [Evaluation of the use of a didactic sequence in the teaching of matrices through programming in blocks by a focus group]. Revista de Estudos e Pesquisas sobre o Ensino Tecnológico, 5(12), 30-50. https://doi.org/10.31417/educitec.v5i12.758
  • Shannon, A. G. (2019). A note on generalized Leonardo numbers. Notes on Number Theory and Discrete Mathematics, 25(3), 97-101. https://doi.org/10.7546/nntdm.2019.25.3.97-101
  • Slisko, J. (2020). Lo que pueden aprender los estudiantes a partir del error de Fibonacci al resolver el problema “El león en el pozo” [What Students Can Learn from the Fibonacci Error in Solving the “Lion in the Well” Problem]. Góndola, enseñanza y aprendizaje de las ciencias, 15(2), 216-238. https://doi.org/10.14483/23464712.16041
  • Vieira, R. P. M., Alves, F. R. V., & Catarino, P. M. M. C. (2019a). Relações bidimensionais e identidades da sequência de Leonardo [Two-dimensional relationships and identities in the Leonardo sequence]. Revista Sergipana de Matemática e Educação Matemática, 4(2), 156-173. https://doi.org/10.34179/revisem.v4i2.11863
  • Vieira, R. P. M., Mangueira, M. C. dos S., Alves, F. R. V., & Catarino, P. M. M. C. (2020). A forma matricial dos números de Leonardo [The matrix form of Leonardo’s numbers]. Ciência e Natura, 42, 1-13. https://doi.org/10.5902/2179460X41839
  • Vieira, R. P., Alves, F. R., & Catarino, P. M. (2019b). Uma exploração da sequência de padovan num curso de licenciatura em matemática [An exploration of the padovan sequence in an undergraduate mathematics course]. Indagatio Didactica, 11(4), 261-279. https://doi.org/10.34624/id.v11i4.10641

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