Didactic Engineering and an investigation of the Fibonacci Sequence hybridization process

• Autor(a) principal: Vieira, Renata Passos Machado
• Data de Publicação: 2021
• Outros Autores: Mangueira, Milena Carolina dos Santos, Alves, Francisco Regis Vieira, Catarino, Paula Maria Machado Cruz
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Revista de Ensino de Ciências e Matemática - REnCiMa
• DOI: 10.26843/rencima.v12n1a02
• Texto Completo: https://revistapos.cruzeirodosul.edu.br/rencima/article/view/2735
• topic: Engenharia Didática; Números Híbridos; Teoria das Situações Didáticas; Sequência de Fibonacci.; Didactic Engineering; Hybrid Numbers; Theory of Didactic Situations; Fibonacci sequence; Ingeniería Didáctica; Números híbridos; Teoría de las Situaciones Didácticas; Secuencia Fibonacci

This article presents data from research supported by the four phases of the Didactic Engineering research methodology, with the support of the dialectics of the teaching theory of Didactic Situations Theory. With that, the objective is to carry out an investigative study in the process of hybridization of the Fibonacci sequence and enable students to intuitive reasoning through teaching situations. For this, the set of hybrid numbers and the Fibonacci sequence are presented, with the aim of associating these two mathematical contents, proposing two teaching situations for students of the History of Mathematics course, of the Mathematics Degree course (initial training of teachers). The results were collected through recordings, teacher notes, photos and questions raised by the students, being analyzed according to the steps provided in the applied research and teaching methodology. Thus, based on these records, it was possible to reveal that despite the difficulties faced, students were able to build their own knowledge. Finally, there was an internal validation of the research, comparing the results obtained with those expected. It should be noted that this research is an excerpt from the dissertation of the Academic Masters in Science and Mathematics Teaching at the Federal Institute of Education, Science and Technology of Ceara.