Problem-solving and mathematical competence: A look to the relation during the study of Linear Programming

This study seeks reflection on the approaches of 11th grade students to Linear Programming problems, discussing the approaches taken at different moments of the teaching process. It aims to analyze: How is the students' mathematical competence characterized in relation to problemsolving; What differences can be identified in the resolutions at different moments of the teaching and learning process. We adopt a qualitative and interpretative methodology, analyzing the approaches of two pairs of students with different mathematical backgrounds. The analysis is guided by P ' olya's stages of solving a problem and aspects of the understanding of mathematical competence. The results show different approaches to the problems depending on the teaching moment and different competences. The mathematical background impacts the students' success when they implement routine procedures, however it does not seem to determine the students' competence to reason about a problem.