Análise da Engenharia Didática sobre o Modelo de Complexificação da Sequência Generalizada de Fibonacci, uma abordagem num curso de formação inicial de professores

Abstract

The educational object is a review of an academic master's dissertation in science and mathematics education of the Federal Institute of Education, Science and Technology of the State of Ceara, bringing the application of two methodologies, being: Didactics, and other teaching - Theory of Didactic Situations. This review is divided into 3 topics: Methodology and the Fibonacci Model, Epistemic-Mathematical Field and Data Collection and Analysis. However, the process of Fibonacci sequence complexification, applied in the initial teacher training course, is carried out through didactic transposition.

A Didactic Engineering in the Research Process of the Generalization of the Padovan Sequence: An Experience in a Pre-Service Teacher Training Course

“…Finally, we conducted analyses based on the DE and TDS methodologies, aiming to investigate teaching situations, from the perspective of the French Didactics of Mathematics, highlighting other research developed in a similar context to ours: Oliveira, Alves e Silva (2019), Vieira, Alves and Catarino (2019), Alves and Dias (2018), Artigue (2018;1988), Oliveira (2018), Alves and Catarino (2017), Santos ( 2017), Almouloud (2016;2007), Perrin-Glorian and Bellemain (2016), Alves (2016;, Kidron (2014), Teixeira and Passos (2013), Margolinas (2012), Oliveira and Araújo (2012), Brousseau (2008;2002;2000;1986;1982;1976), and Laborde (1997).…”

“…Starting the data application, we distributed a list of exercises to the students, and advised them to interact with each other. Those activities were examined and discussed during resolution, when students formulated arguments aiming at their further examination, which was registered through video-recordings and photos (Oliveira, 2018).…”

As relações recorrentes n-dimensionais de Leonardo

“…Com base nos trabalhos de Harman (1981); Oliveira (2017), nesta seção serão introduzidas a notação e relações recorrentes n-dimensionais de Leonardo, definindo assim uma expressão generalizada em que n representa o número de variáveis.…”

Os quatérnios circulares hiperbólicos e os números hibrinomiais de Perrin

“…Os quatérnios foram desenvolvidos por William Rowan Hamilton (1805-1865), sendo portanto uma extensão dos números complexo. Assim, possuem duas estruturas quaterniônicas: quatérnio em R, com componentes reais, e os quatérnios complexos (biquatérnios) em C, com variáveis complexas, existindo quatro dimensões [14]. Dessa forma, tem-se que um quatérnio é definido por: q = a + bi + cj + dk, onde a, b, c e d são números reais e i, j, k a parte ortogonal na base R 3 .…”