The calculation of areas: an application of didactic engineering in the context of Mathematics Olympics

• Autor(a) principal: Santos, Ana Paula Rodrigues Alves
• Data de Publicação: 2018
• Outros Autores: Alves, Francisco Régis Vieira
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://doi.org/10.34624/id.v10i5.11133

This article presents a Didactic Engineering - ED developed in the context of the teaching of the Mathematical Olympiads. The application environment involved an Olympic group from a private school in Ceará-Brazil and was attended by two groups of students. It was developed an Olympic didactic situation - SDO - consisting of four items involving the calculation of areas of flat figures. Specifically, the calculation of areas with the aid of the Geogebra software was investigated in order to identify the intuitive categories of Fishbein during the application in the experimental phase of ED. In this investigation the ED was in a vision of complementarity that used the TDS in its phase of experimentation. Systematized data in the posterior analysis phase and internal validation indicate that: the identification of intuitive categories (affirmative, conjectura and anticipatory) does not occur in isolation, since we are talking about mentalprocesses. The students are surprised by the study of the calculation of areas, without the need of using formulas, but with the observation and analysis of the mathematical elements visualized in the SDO modeling. We verified that there is a guiding axis for the study of the congruence of triangles and the properties of the quadrilaterals that were described by the students. The two groups manifest difficulties in systematizing and formalizing their conjectures and the argumentsformulated in the initial phases of education foreseen in the TDS. However, we emphasize the essential character of mediation exercised by the teacher during the formulation phase. We observed that the mediator used the manifestation of conjectural and anticipatory intuitions so that there would be demonstrations and validations of mathematical concepts.