Teaching-learning of Mathematics via Problem Solving: analysis of the problem solving process of undergraduates in initial formation

Abstract

This work aims to analyze the Problem Solving process of undergraduates in initial formation in the formative context of Teaching-Learning of Mathematics via Problem Solving (EAMvRP). Therefore, we dealt with the EAMvRP approach with 18 graduates from a public university in northern Paraná. The classes were recorded and transcribed and, together with the resolutions made by the undergraduates, they were qualitatively analyzed in a descriptive way. The analysis proceeded through a synthesis of the steps of Problem Solving in Proença (2018). The main results reveal that in the representation stage, properly understanding the semantic, linguistic and schematic knowledge favors the identification of information superfluous to the problem. We noticed that in the planning stage, the use of mathematical symbology collaborated to justify the resolution of the groups. In the execution stage, all groups had a visual-pictorial type of mind when they used drawings to develop their resolutions. Finally, in the last step – monitoring –, we identified that only one of the four resolutions that were analyzed developed this step satisfactorily, presenting a final answer to the problem. Thus, we can conclude that when developing the EAMvRP taking into account the steps of resolution of Proença (2018), the process becomes much richer, more interesting, collaborates in the identification of possible difficulties for students and, consequently, favors the development of a fruitful teaching of Mathematics.