On the occasion of having to design an introductory course of mathematics for the University (UNGS, Buenos Aires, Argentina) we took into account the perspective of mathematical modelling. In this article we present the theoretical framework that we elaborated on to design our course. This framework allowed us to adapt the generic perspectives of modelling and problem solving to the characteristics of our students. In the second part of our article, we describe the resulting introductory course based on the theoretical aspects previously mentioned and we show some results, from the course, which evidence a positive attitudinal change in the students.