Abstract:

Teaching through Problem Solving (PS) proposes that problem solving is not only the goal of learning mathematics, but can also be a means of learning mathematics. This means that a problem, and not the teacher's explanation, is the starting point for a student-centred work session in which certain mathematical concepts and skills must be applied. This perspective is related to other recognised theories such as Problem Based Learning (PBL), Inquiry Based Learning (IBL) and theories such as Mathematical Modelling.

The heuristic method of Problem Solving proposed by George Polya in the mid-20th century offers a working tool for the development of teaching through PS. Polya's four-stage method begins with the approach and analysis of the components of a problem proposed in class, the proposal of different ways of solving it, the resolution of the problem and the final reflection on the results and the process followed and its transferability to new situations.

In all cases, the problem presented to the students must be meaningful and have the potential to be solved from different perspectives, allowing the introduction and development of different mathematical concepts.

This paper presents an experience with Basic Education teachers in training from the University of Cordoba (Spain) and the University of Algarve (Portugal) in which Polya's Method was introduced through the resolution of an example problem, the participants were asked to apply it to a new mathematical problem and to present it in a final poster that was exhibited in class. The contributions of the participants from both universities in each of the four stages of the method are analysed and the different resolution strategies followed to solve the proposed problem are detailed. The experience confirms the potential of the method as a tool for learning mathematics through PS.

Keywords:

Problem Solving, Problem-based Learning, Mathematics Education, Teacher Training.