Cognitive construction of the solution set of a system of linear equations with two unknowns

Abstract

In this research, we propose a genetic decomposition for the solution set of a system of linear equations with two unknowns, by means of a transit from a homogeneous to a non-homogeneous linear system, in a Cartesian geometric context. To validate our genetic decomposition, we designed instruments that we applied to students from a secondary school mathematics teacher training program. Thus, and by using implicative statistics, we were able to confirm the mental constructions and mechanisms considered in our genetic decomposition. The results show lack of understanding of what a solution for a system is, difficulties in articulating the geometrical and algebraic aspects, and the convenience of using an alternative strategy in the case of systems of three or more linear equations.