Estructuras y mecanismos mentales en la construcción de los conceptos área y perímetro de figuras planas en octavo grado

Abstract

The research of this master's thesis is focused on mental structures and mechanisms in the construction of the concepts Area and Perimeter of flat figures, under the framework of APOE theory. Describes how mathematical concepts can be constructed (learned) from mental structures of action, processes, objects and schema[pc] It is at the same time has its own research cycle that is comprised of three components that are theoretical analysis, teaching design and implementation, and observation, analysis and verification of data. The motivation is aimed at the difficulties that students present when building these concepts, since they see it as a simple algorithm or the repetition of a mathematical formula. To this end, a questionnaire was designed that was applied to a heterogeneous group of 20 students with whom the data collected was documented and analyzed based on the APOE theory research cycle. Considering the background and the study of historical epistemological aspects, in reported investigations, a Genetic Decomposition (DG) cognitive model is proposed through which a student can build a concept (Dubinsky, 1991) that makes it possible to explain those constructions and mental mechanisms, which hypothetically a student shows, by constructing the concept Area and Perimeter of flat figures as an object and to give viability to the DG.