Função quadrática a partir da ideia fundamental de variação: um estudo com alunos da 1ª série do ensino médio

Abstract

The treatment of algebra restricted to operational techniques was one of the initial motivators of this work. When looking to the approach until then experienced in high school of the subject of mathematical functions, Quadratic Function, it is observed that this gets past by an approach in which it is primarily used the relations and notations of numerical sets to the detriment of an approach to its variational aspects. By reading the current educational normative document “Base Nacional Comum Curricular” (BNCC), was observed a concern in the development of fundamental mathematical ideas (equivalence, variation, interdependence, representation, order, proportionality and approximation) to convert them into objects of knowledge at school in Basic Education. Our guiding research question is: How can the fundamental idea of variation and covariational analysis contribute to the learning of the concept of quadratic function by 1st grade high school students? From the studies on, we obtained as a result of this Professional Master's research, an Educational Product (EP) in a sequence of activities format based on the didacticpedagogical organization of the Teaching Guiding Activities (TGA) of Moura (2016). We believe that our main objective was achieved through the didactic sequence developed and titled as “The Fundamental Idea of Variation for studying Quadratic Function using Lego parts and Uno Cards game”, which is composed of two investigative tasks that provided opportunities for discussions on the application and validation of the constructed product, culminating this way in the descriptive analyzes of the contributions to the learning of the concept of quadratic function by 1st grade high school students. From here we see the relevance of our work as potential for reapplication in the classroom by teachers who have a didactic intention of placing students as protagonists of their learning and of promoting the development of mathematical reasoning through practical situations that benefit the understanding of mathematical functional relationships linear and quadratic.