Formas de expresión de modelos mentales [cronotópicos] de alumnos y profesor en clase de geometría analítica de grado 10°

Abstract

The research problem consisted of studying the mental models and their forms of expression of students and teachers when together they solve Analytical Geometry activities. The general objective was to characterize, determine and establish and compare some features of the mental models [chronotopic] and their forms of expression of students and a teacher with the mathematical activities proposed in the classroom, in the development of Analytical Geometry activities of the 10th grade. Methodologies derived from the Chronotopy Program were used, whose emphasis was placed on the subdisciplines of Topia or Topo*, that is, Topography, Topology, Topometry and Toponomy. For the collection of information, the audiovisual record of 14 classes was made during the 2017-2 semester, non-participant observation was made. The methodology combined ethnographic moments with other types of research. The ethnographic phase allowed the collection of data that allowed studying manifestations of mental models. Due to the above, it became necessary to distinguish ethnographic moments from others such as the study from the grounded theory. For the analysis of the information, the methodology of the grounded theory was used, under the categories of the Chronotopy Program. For the systematization of the data, ATLAS.ti8 was used. The theoretical framework emphasized three theoretical components, which is why it was called the Theoretical Ψrider: Mental Models, Semiotics and the Chronotopy Program. The elements that allowed identifying mental models [chronotopic] stand out in this theoretical framework. Among the results of the analysis, some of them can be highlighted: 1. A characterization and an identification methodology of the forms of expression of the mental models [chronotopic] of students and teacher of grade 10 when they develop Analytical Geometry activities in the plane . 2. An interpretation of the forms of expression of the mental models [chronotopic] of students and their teacher in the described context. 3. The generation of a set of elements related to mental models [chronotopic] that need to be considered in the didactics of analytical geometry. Among the recommendations, the development of future research on the teaching and learning of Analytical Geometry and in particular on the recognition of other forms of mathematical expression that coexist in the classroom is proposed.