Difficulties experienced by students in the interpretation of the solutions of ordinary differential equations that models a problem

In this work we analyzed some of the difficulties that arise when the student interpret the solutions of Ordinary Differential Equation (ODE) when they are expressed in graphical and algebraic form. The investigation was carried out with Engineering students who were at the end of a first course of ODE, who realized some activities in a graphical dynamic environment that included the interpretation of the solutions represented in algebraic and graphic form of a ODE that models the behavior of a population. One the one hand, even though the students dominated some algebraic tools to solve a ODE, they did not use them to interpret the behavior of the solutions within the graphical registry. On the other hand, when they working with the field of directions to obtain data on the solutions of the ODE its use was only local, that is to say, focused its attention on relatively small regions of the field of directions.