The aim of this study is to characterize ways of reasoning and arguing that first year university mathematics students exhibit in problem-solving activities from a course that emphasizes the importance of formulating conjectures and the search for different ways to support or validate them. The use of a Dynamic Geometry System in the representation of problems and in the formulation of conjectures or relationships that are important in the solution processes is highlighted. In this context, students have the opportunity to look for different ways to argue and support the relevance and validity of the conjectures. Results indicate that students extend their ways of reasoning so that allows them to move from empirical to formal arguments within problem solutions. [For the complete proceedings, see ED657822.]