Analysis of inequalities graphs with a semiotic artefact

Overview & Synopsis

To enable students to perform a graphical analysis of inequalities graphs, a proper symbolic reading of these representations is required, which implies a linking between the graphs and their algebraic expression. We proposed to a high school student the use of an auxiliary line as a semiotic artefact to make connections between the locus of inequalities and their algebraic expression. Through an online questionnaire and an intervention, we observed that the student underused the given artefact and instead used the equation of the line that divides the plane to make the connection between algebraic and graph representations. We found that the semiotic mediation of the artefact allowed a local interpretation of the locus of the points on the auxiliary line, but the equation of the dividing line played a crucial role in associating the algebraic expression of the inequalities with their loci, which was the basis for the connection between the two types of representations.