ABSTRACT

The main aim of the study was to identify the ability to use mathematical notions in everyday life and the capacity to make connections starting from the poor results that Romania registers in the PISA tests. On the other hand, the results of the research applied to a group of 200 first-year students confirmed the inability to make connections between theory and real life. Linear algebra is an important discipline and very difficult for most students. The main obstacle is modeling the real problems in abstract concepts of algebra. So it is very important to help students understand how to „ translate” real-life problems in linear algebra concepts and then how to solve them using different examples and finally presenting the global theory. This research shows how it is possible for a professor to teach the algorithm for problem-solving in linear algebra and how to guide the students to find the solutions. We present the possibility of introducing the concepts of the compatibility of the systems of linear equations using examples and graphics.

Keywords: mathematical modelling, systems of equations, geometrical representation