Throughout several years, an exploration concerning the methods that students of different educational levels use to solve problems or tackle some contents has been developed. It has been found that students tend to construct resolution procedures in which they emphasize diverse important aspects about concepts and that have very little relationship with the usage of algorithms or stereotyped procedures. Nevertheless, some teachers have the tendency to use algorithmic procedures to solve the same problems. Therefore, an important problem is detected; there seems to be an important difference between the expectations of teachers and students regarding the mathematical work, which impedes an effective communication and understanding in the educational work. Besides, it has been observed that, as the professor settles in the teaching function, there is an abandonment of the intuitive reasonings in the mathematical work and “formal” procedures are privileged. Also, the existence of believes about the things that student should know before solving a problems is stated.