Difficulties in the appropriation of the concept of computability in Systems Engineering students

Abstract

The study was carried out in the city of Bogotá, during the first semester of the year 2020, at the higher education institution Escuela Tecnológica Instituto Técnico Central, in the subject discrete mathematics. The population consisted of 26 students. The mixed approach of the research has a sequential design and its objective was to analyze the relationship between the levels of appropriation of the concept of computability and the difficulties experienced by students around four variables. One of the main difficulties in the appropriation of the concept of computability comes from the mathematics of computability and specifically is related to the understanding of mathematical concepts, symbolism and algebraization; it also requires the holistic vision of the existing isomorphism between set theory, propositional logic, logical circuits and Boolean algebra. The results show that the difficulties characterized are close to the levels of appropriation (identified) around the concept of computability. The limitations corresponded to the crisis generated by the Covid 19, where it was not possible to apply the instruments in person. The teaching of mathematics in current times will not be the same as before, where the emphasis was on continuous mathematics; there is a new look towards the discrete and the finite. Finally, a series of guidelines for mathematics teaching in the XXI century in engineering faculties are proposed.