Perception of high school students about the straight line from a semiotic approach

Abstract

At the end of the Analytic Geometry course in high school it is desirable that students, from a semiotic approach, recognize mathematical objects, for example, the straight line, in different representations. As representations can be considered the drawings that carry the meanings of the object, the equations that algebraically describe such meanings and even the definition of the object itself. To observe this, a survey, printed and individual, was applied to a group of high school students, who had already taken Analytic Geometry. This article shows the data obtained and inferences from items 1 and 2, in which the students were asked to write the definition of a straight line and make representations of it. According to what was observed, in general they consider that the straight line is an "infinite succession of points" and the geometric representations stand out.