Construção da parábola através de modelos lúdicos e computacionais

Abstract

Technological development is associated with systematic and organized knowledge, gathered during the entirety of human existence. The conics, in particular, the parabola, have a relevant presence in this development, although its study in basic education has been restrained to the manipulation of formulas without a context. This dissertation discusses the development of diverse activities related to the teaching of the parabola with the goal of relating theory and practice through its use in an academic context. This project was initially designed and developed for one class in their third year of high school at a public institution in Brazil. In order to introduce the characteristics and properties of the parabola, the use of physical and entertaining activities such as paper folding, along with resources from the geometrical environment, especially the program GeoGebra, were put to use to in order to achieve investigation, data analysis, a search for regularities, and identification and validation of the mathematical models. The diverse activities motivated the students to build a parabolic solar stove, which helped to connect theory and practice. In a second phase of experiment, the activities were applied in another public school, with the goal of involving a larger corpus of students within the fields of mathematics and the natural sciences. The activities developed used parabolic objects for reflection of sound waves and led to the elaboration of a project to build a parabolic bench in the school’s garden. It also presents a short analysis of the teaching and learning processes, based on the hypotheses of Piaget and Paulo Freire, about the role that mathematics has in human development and the aspects of mathematics education that utilize investigative processes and modeling. It was perceived the efficiency on the development of the competencies and abilities required nowadays and its viability to the realization of the scholarly activities.