The BREL method: its effectiveness for resolution set theory problems

Abstract

This article summarizes the research carried out in the field of mathematics didactics, whose main objective was to measure the effectiveness of the application of the two-dimensional BREL tables, in solving problems formulated in the domain of set theory by Students of the first year of the Institute of Higher Education "Our Lady of Lourdes" of Ayacucho. A pre- experimental design with pre-test and post-test was applied, whose stimulus “the use of the BREL table” was applied to the only section. To verify the research hypotheses, the statistical hypotheses H0: μd ≤ 0, H1: μd > 0 were used, where d (di) refers to the new variable formed by the subtraction of the exit grade in Student i minus the entrance mark that the same Student has; and for the comparison μd with 0 the t-test for related samples was used. The results corroborated the specific hypotheses that the Students at the end of the experiment, their exit exam scores significantly surpassed their entrance exam grades: for the dimension organization of the sets in the BREL tables, t = 16,462 with 29 gl and p = 0.00 <0.05; analysis of the logical sequence of operations with sets in the BRE table, t = 20.544 with 29 gl and p = 0.00 <0.05; and visualization of the operations with sets in the BREL table, t = 20.603 with 29 gl and p = 0.00 <0.05. In conclusion, the BREL table is a mathematical instrument that makes it possible in a short, fast, efficient and logical way to perform a series of actions: operations with sets, simplifications of complex formulations of sets, demonstrations of properties of set algebra and in that of solving exercises and problems with sets, without affecting the nature and mathematical rigor of the network of concepts in set theory.