Aprendizagem do conceito função afim por estudantes do Ensino Médio: possibilidades da organização do ensino

Abstract

This research, developed within the scope of the Graduate Program in Mathematics Education and Physics Teaching at the Federal University of Santa Maria (UFSM), has the problem: With regard to the organization of related function teaching in High School, can some elements be essential for student learning? From this, its general objective is to investigate elements that may prove to be essential for the learning process of the concept of related function for students in a high school class. The subjects of this research are first-year students of the Technical Course in Agriculture Integrated into High School, at a municipal school in Ijuí-RS. The actions were organized from the perspective of a didactic experiment, considering as instruments used to capture the empirical material records produced by students in portfolios, audio and video recordings of the classes developed and a questionnaire. As for the theoretical and methodological approach, it considers the Historical-Cultural Theory of Lev Semionovitch Vigotski, more specifically, the Activity Theory of Alexis Nikolaevich Leontiev and the Teaching Guiding Activity of Manoel Oriosvaldo de Moura. Teaching organized based on the assumptions of the Teaching Guiding Activity aims to enable students to become collectively involved in the search for solutions to teaching situations, which must consider the essence of the concepts and its logical-historical movement. This intentional organization of teaching can allow students to enter into activity, since the structure of the Teaching Guiding Activity considers the possible motives and needs of students in the development of proposed teaching situations with the aim of promoting learning, in our case, about the affine function, considering the conceptual links of algebraic knowledge: fluency, variable, field of variation, dependence and proportionality. The first situation, related to fluency, aimed to enable students to understand that everything changes, starting with observing photographs and their personal changes. The second, composed of the Pega Varetas game, aimed to provide students with an understanding of variables, the possible values that each variable can assume and the dependency relationship between quantities, introducing the intuitive notion of function. Finally, the third emerged through a real demand in the school context, related to dairy production and highlights the relationship between the related function and proportionality. As a result, the following are highlighted as essential elements for the appropriation of the concept of related function: the collective mode of organization; the proximity to the students’ historical-social context; the need that leads to greater student involvement and the reason for finding solutions.