Estratégias utilizadas por estudantes da licenciatura em matemática para resolver problemas da geometria analítica: a eminente dificuldade da articulação entre as representações das secções cônicas

Abstract

Considering the context of research in Mathematics education supported by digital technologies, we present results of a study that aimed to discuss difficulties that undergraduate Mathematics students have in Analytic Geometry, specifically in conic sections, from the perspective of the Theory of Semiotic Representation Registers. The justification for this investigation is based on the need to understand how future teachers articulate concepts of conic sections, observing registers and transformations of semiotic representations. We qualitatively analyzed students’ responses in the first assessment instrument of the Mathematics III course, taught by the second author at the Federal University of Pernambuco. The analysis integrates literature reviews from the authors’ Doctoral and Postdoctoral research, focusing on mathematics teaching and learning with the use of technologies. We identified difficulties in the conversion between algebraic and geometric representations of conic sections, reflecting gaps in basic education.