Esboço de gráficos nos ambientes papel e lápis e GeoGebra: funções afins e funções quadráticas

Abstract

When it comes to teaching linear and quadratic functions, we observed that the Mathematics teachers, guided by current textbooks, explore the construction of graphs by connecting points on the Cartesian plane. This method, while valid, does not guarantee an outline safe and does not imply the observation of important properties of these functions. With this in mind, this study aims to verify the efficiency of a screenplay produced in a explanatory and methodological booklet form. This script is a practical and efficient way to plot the graphs of polynomial functions of the 1st and 2nd grade using simple materials and essentials such as paper and pencil, and also a digital resource, the software GeoGebra. To check the efficiency of this route, we take a student group composed of individuals who attend high school in public schools and participant the Institutional Program for Scientific Initiation Scholarships Junior (PIBIC-Jr). The methodology consisted of questionnaires - before, during and after - the teaching intervention: lecture, referring to related functions and quadratic functions, highlighting the construction of their graphs, and use of a printed script, developed in the form of a explanatory booklet which worked the construction of graphs, using the principle of graph paper and pencil, and at another time, a dynamic geometry software. Using this software, and making a sketch of faster graphics, it became understandable graphical changes incurred when changing the coefficients of the functions. As a theoretical framework for the research exposed in this work, we rely on the contribution of the Theory of Didactic Situations, Guy Brousseau (2008), and representative forms of a function in the view of Raymond Duval (2009), in his Theory of Representation Registers Semiotics. The ten students participating in the study, seven had a breakthrough in the development of the trace graph of functions considered and understanding of their properties. Thus, one comes to the conclusion that it is possible to study and observe the properties of linear and quadratic functions taking into account specific issues pertaining to its graphics, both on paper and, especially, on the computer.