R. Ramos, A. Aguilar, F.M. León Rodríguez, O. García

Universidad Nacional Autónoma de México (MEXICO)
Problem Statement
This research has designed a mechanical device in order to prove that students can take ownership of the knowledge of a mathematical object.

Description of the mathematical object
In teaching of the scientific computing, there have been developed a considerable number of methods to solve systems of linear algebraic equations; the method of decomposition or matrix factorization, is one of the most used by its effectiveness and optimization of computer resources. This method consists of decomposition the matrix of coefficients of the system in two factors, the matrix L (from the word in English Lower) and the matrix U (from the word in English Upper); from where it takes his name, is to say, method of decomposition LU (Press, 2007). Once obtained the factors in which the matrix of coefficients of the system is decomposed; these factors are replaced in the proposed system and it is come to determine the corresponding solution.

This research focuses on the design of a didactic sequence, which for its implementation has relied on the use of a mechanical device in order to facilitate teaching and learning of the LU decomposition method; this device fulfills the functions of the elements that are used in the design of the didactic scaffolding; which is constituted by: an exposure of the mathematical object, using to describe it a mathematical discourse, diagrams, tables, graphics, software and symbolic language, other elements of the instructional scaffolding are, a combination of theory with practice, the necessary background structure for understanding the method, support elements such as keys or formulas, steps or description of the algorithm, and written reminders and encouragement for future tasks or motivation and finally an evaluation system that enables learning through the acquisition of tools and positive habits to continue learning throughout professional working life.

The didactic design described was used like mediator (Labatut, 2004) to the mechanical device that was constructed in order to facilitate the observation of a behavior model in the development of the method and this way caused in the student the development of its abilities in the construction of a general algorithm from the observations done in the provided university classroom of resources trims in the student. It is very probable that the student has not reached to develop the general construction of which consists the method of decomposition LU; nevertheless, if it is possible to be affirmed that every time that he makes use of the mechanism used in this research as a tool for the development and application of the method there are possibilities of solving in his professional life, as he done in the university classroom. This research allowed to reorient education under the theoretical principles of the used didactic scaffolding; causing in the student the formation of habits and attitudes that shape a human kind capable of becoming conscious agent of development, thereby encouraging creativity, capacity for independent learning, critical thinking, discipline and organization in the work, sense of personal and social responsibility.