THE ZONE OF PROXIMAL DEVELOPMENT WHEN LEARNING THE LU DESCOMPOSITION METHOD AS AN ACTIVITY IN THE CLASSROOM

The research has consisted in setting into practice the concept of Zone of Proximal Development (ZPD), in the Numerical Methods subject applied to the Lower and upper (LU) descomposition method. In the sociocultural learning model of Vygotsky, it is stated that the learning and development processes interact with each other, considering the learning as a development factor. Vigotsky highlights this strong relation between development and learning and stated the ZPD concept. With the postulates referring to the sociocultural model theory we proposed the activities in the investigation that were:
Construction of the educational scaffolding, reciprocal teaching, social learning conduction and collaboration between companions. The first activity consisted in presenting the development for obtaining the general formulas for the LU descomposition method, including the case solving. The second activity was the topic presentation carried out by the students, and the last two activities were the numerical solution of a case within the engineering context, organizing the activities among the students and the teacher as a workshop and forming working teams. The activities and the results were registered. One of the remarkable observations was that the students could not defeat the obstacle of the distance determined by their real and potential capacity: showing a dependence in the position where their potential capacity is found and showing a regular behavior according to that position. This leads us to conclude that they continued depending on the expert’s help that in the investigation was represented by the teacher’s notes that the students used for solving the problems, however we observed an approximation in the construction of the significant knowledge.