Análise de processos de construções de modelos: o movimento de translação - Costa Junior, Edson Ferreira da (2021)
This work aims to analyze the construction processes of mathematical models carried out by first-year high school students, to represent the changes in the plane, specifically the horizontal movement. Geometric transformations, isometries, rigid movements and symmetries are common, either formally or in a simple way. With the purpose of mediating the work between these two extremes, a workshop was carried out, with the students developing the mutual teaching of algebra, geometry and arithmetic so that they could make use of creativity and mathematical language to descrive the actions observed. The workshop was supported by ideas about mathematical modeling, with the intention of mathematically interpreting and describing the horizontal translation movement through the manipulation of the concrete material, then providing a better visualization of the situation investigated by the participants. Therefore, two workshops were held with students during the 1st year of high school (14 – 15 years) in a public school in Goiás. It is important to emphasize that the objective was not to find the correct solution, the ideal answer, but to create a space of construction of significant knowledge where students, with the help of the teacher, were instructed to discover, criticize and question their decisions and the creation of a model based on the concrete world. To gather data, activity forms, questionnaires and audio recordings were used. Regarding the results, the arithmetic, algebraic and geometric approaches were analyzed when representing the phenomenon, and students showed difficulties related to the elementary operations and the use of symbology. It was noticed that students used one of the languages, the mathematics or the written mother tongue, or both, to solve problems by choosing the one that is more convenient for them to understand. It is possible to conclude that these difficulties are reflections of a mechanical teaching without meaning production in the previous grades. In addition, the research results can contribute to the interdisciplinary treatment of this topic and boost the development of mathematics, in addition to highlighting its applicability in everyday life.