A relevância do registro gráfico no ensino e na aprendizagem das equações diferenciais ordinárias

Considering the theory of registers of semiotic representation, we acknowledge the mobilization of different registers as a necessary element for the understanding of mathematical concepts. Studies report that the teaching and learning of ordinary differential equations (ODEs) usually happens through use and manipulation of symbolic-algebraic registers, as opposed to other varieties, such as the graphic register. Given this context, our article aims at discussing the importance of graphic registers for both teaching and learning of ODEs. Therefore, we devised a series of situations – directed at higher education students – which address the concept of ordinary differential equations by means of different registers of semiotic representation; favoring a qualitative approach to their solutions. Results indicate that the use of graphic registers to obtain information about an ODE’s solution enabled students to create connections between the equation, their family of solutions and their vector field. Thus, allowing students to recognize different representations of ODEs and to better understand the mathematical object at hand.