O estudo da função afim a partir da interpretação global de propriedades figurais: uma investigação com estudantes do ensino médio

Abstract

The present investigation was based on Theory of Semiotic Representation Registers, idealized by Raymond Duval, which conceive that the learning of a math concept happens mainly from the articulation between differents semiotic representations registers. One of the aspects of this theory is the global interpretation of the properties of images that concerns articulating between register algebraic symbolic and graphic of a function, in order to identify the modifications on visual variables on the graphic register and their respectively symbolic units on algebraic symbolic register. Thus, the present research had the objective to analyze the students learning about linear function from didactic studies in relation to the global interpretation of the properties of images. Therefore, with the support of the Theory of Didactical Situations, and along the lines of Didactic Engineering, it was developed a linear function didactic studies related to global interpretation of the properties of images. This studies included the realization of an experiment, the problem solving, aspects of mathematical investigation and the use of Desmos and GeoGebra (Graphing Calc) applicants to smartphones. This research was developed by students form the 1st Teachers Training course class, in a public school in Paraná. The analyses showed that the research students started to recognize the linear function between differents representations registers and to transit between them, besides manifesting the development of a integrated vision between the visual variables of representation on the graphic register and their significant symbolic unit on the algebraic symbolic register.