Rethinking the teaching of differential equations through the constructivism paradigm

We report on rethinking the teaching of linear second order ordinary differential equations with constant coefficients by adopting a constructivist approach. In most cases teaching of linear second order ordinary differential equations, as seen in major textbooks, is done in a very procedural manner where the emphasis lies in identifying the type of equation and then apply a number of well established steps that will yield the solution. The problem gets exacerbated when one also considers the existence of computer algebra systems (CAS) such as maple or mathematica, which are capable of yielding the solution. In the rethought way of teaching, the student´s focus is shifted from applying the well defined pattern of steps, for attaining the solution of differential equations, to that of understanding the derivation of these steps. This is achieved by applying the skills derived from background knowledge, exploring the conceptual knowledge involved in attaining the solution, making hypotheses and testing them and consequently see the previously taught (ad-hoc) steps now been derived, been the product of all the previous activities.