Construction of the concept of solution of ordinary differential equations through analytical, graphical and numerical methods

This article presents the results of applying a sequence of activities based on the APOS theory to the teaching of ordinary differential equations (ODEs) with undergraduate mathematics students. Following a cognitive model called genetic decomposition (GD) in APOS theory, activities were designed to build the mental structures and mechanisms that a student must develop to construct the concept of solution to ODEs. The data were collected during six work sessions in which students solved ODEs using the separable variables method, the ODE´s slope field and Euler's numerical method jointly. The results show how students' interaction with the three solution methods and the use of GeoGebra software promotes the development of students' abilities to find solutions to ODEs.