HELPING STUDENTS TO LEARN PROBLEM SOLVING OF MATHEMATICS AT UNIVERSITY

The Tuning project aims to offer a concrete approach to implement the Bologna Process at higher education institutions and subject areas. In this project reference points are expressed in terms of learning outcomes and competences and a list of thirty generic competences is established. Problem solving is one of them, and it is connected to Mathematics in the sense that the last goal about Mathematics instructions is to analyze and solve problems.
The ability to solve problems depends not only on knowledge, but also on some intellectual processes. In this sense Polya’s work is well known. He showed that strategies for problem solving could be structured and taught. Other authors have reflected on Polya ideas and new interesting pieces of work have been carried out.
In this paper a tutorial action to teach students how to solve problems is analyzed. This action was based on Polya and Schonfield ideas and was carried out for three years with students who had failed in their first attempt to pass Mathematics II. This subject is in the first half of the second year of Telecommunication Engineering degree, at University of Oviedo. The action was developed in the second half of the year and its purpose was to teach students how to learn to solve problems. The subject is divided into three parts and three steps were considered for each. Firstly students had to solve a collection of selected problems individually. Secondly teachers read each solution paying attention to errors and mistakes. Finally, all students were called to a session where teachers remarked the main ideas and corrected the general mistakes. The solutions carried out by students were marked by teachers and given back to them. In case of necessity, students were seen individually about their doubts and concerns. After this process most of these students were successful during their next attempt.
In conclusion, these kinds of activities for students with some difficulties can be considered as positive for learning process, and similar actions should be considered in the design of study programs.