The Padovan Sequence and the plastic number: a prior analysis and a priori
DOI:
https://doi.org/10.33448/rsd-v8i8.1212Keywords:
Didactic Engineering; linear sequence; Theory of Didactic Situations.Abstract
The present work presents the two initial phases of Didactic Engineering with the theme involving the study of the Sequence of Padovan and the plastic number which was the object of study primarily by Richard Padovan (1935-?) And Gérard Cordonnier (1907 - 1977). In order to transform the Padovan numbers into a content to be taught, a theoretical investigation will be carried out, presenting teaching guides and didactic transposition around this linear and recurrent sequence, so that there is greater exploitation in the academic teaching to the study of said sequence. Finally, academic improvements will be made through a historical, mathematical and epistemological context.
References
Almouloud, S. (2007). Ag Fundamentos da Didática da Matemática. São Paulo: Editora. UFPR.
Almouloud, S. & Coutinho, C.Q.S. (2008). Engenharia Didática: características e seus usos em trabalhos apresentados no GT-19/ANPEd. Revemat: Revista Eletrônica de Educação Matemática, 3(1):62-77.
Alves, F.R.V. (2016). Engenharia Didática para generalização da sequência de Fibonacci: uma experiência num curso de licenciatura. Educ. Matem. Pesq., São Paulo, 18(1):61-93.
Artigue, M. (1988). Ingénierie Didactique. Recherches en Didactique des Mathématiques. Grenoble: La Pensée Sauvage-Éditions, 9.3:281-308.
Artigue, M.; Douady, R.; Moreno, L.;Gomez, P. (1995). Ingenieria Didática em Educacion Matemática. Bogotá: Grupo Editorial Iberoamérica.
Barbosa, G. S. (2016). Teoria das situações didáticas e suas influências na sala de aula. Educação Matemática na Contemporaneidade: desafios e possibilidades. São Paulo. XII Encontro Nacional de Educação Matemática.
Brousseau, G. (1986). Theorisation des phénomènos d‟enseignement des mathématiques. These détat, Univesité de Bordeaus I.
Chevallard, Y.(1991). La transposición didáctica: del saber sabio al saber enseñado. Buenos Aires: Aique.
Douady, R. (1995). La ingeniería didáctica y la evolución de su relación con el conocimiento. Gomez, P. (org.) Ingenieria Didactica en Educación Matemática. Bogotá: Grupo Editorial Iberoamericano.
Falcón, S. & Plaza, Á. (2007). On the fibonacci k-numbers. Chaos, Solitons & Fractals, 32(5):1615-1624.
Ferreira, R. (2015). Números mórficos. Dissertação de Mestrado Profissional em Matemática. Universidade Federal da Paraíba, João Pessoa.
Iliopoulos, V. (2015). The plastic number and its generalized polynomial. Cogent Mathematics.
Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications. Wiley-Interscience.
Marohnic, T. S. (2012). Plastic Number: Construction and Applications. Advanced Research in Scientific Areas.
Pais, L. C.(2002) Didática da Matemática. Uma análise da influência francesa. 2a ed. Belo Horizonte: Autêntica.
Pereira, A.S., Shitsuka, D.M., Parreira, F.J. & Shitsuka, R. (2018). Metodologia da pesquisa científica. Ed. UAB/NTE/UFSM, Santa Maria/RS.
Seenukul, S. T. R. S., P;Netmanee (2015). Matrices which have similar properties to Padovan Q-Matrix and its generalized relations. Sakon Nakhon Rajabhat University Journal of Science and Technology, 7(2):90-94.
Santos, A.A.S; Alves, F.R.V. (2017). A Engenharia Didática em articulação com a Teoria das Situações Didáticas como percurso metodológico ao estudo e ensino de Matemática. Acta Scientiae, 19(3):447-465.
Santos, A.A.S. (2017). Engenharia Didática sobre o estudo e ensino da fórmula de Binet como modelo de generalização e extensão da sequência de Fibonacci. (Dissertação de Mestrado Acadêmico em Ensino de Ciências e Matemática). Instituto Federal de Educação, Ciência e Tecnologia do Estado do Ceará.
Sokhuma, K. (2013). Padovan q-matrix and the generalized relations. ResearchGate. 7:2777–2780.
Spinadel, Vera W.; Buitrago, Antonia Redondo. (2009). Towards van der Laan’s Plastic Number in the Plane. Journal for Geometry and Graphics, 13(2):163–175.
Stewart, I. (2000). L´Univers des Nombres. Paris: Belin pour la Science.
Voet, C & Schoonjans, Y. (2009). Benidictine thought as a Catalyst for 20th Century Liturgical Space-Motivations behind Dom Hans van der Laan ́s Ascetic Church Arquitectury. II Congresso International de Arquitectura Religiosa Contemporánea Entre El Concepto Y la Identidad-Ourense.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
1) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2) Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3) Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
