Modelagem matemática e projetos na iniciação científica: conhecimentos matemáticos aplicados na solução de problemas no ensino médio

Abstract

Mathematical Modeling is considered a teaching method with research that includes the development of a model that can be applied to any area of knowledge, and teaching and its methods must keep up with scientific and technological advances, making it essential to expand Scientific Initiation in Basic Education. Therefore, this research had as its main objective to analyze how Mathematical Modeling can contribute to the development of Scientific Initiation projects, enabling the application of mathematical knowledge in Basic Education in order to favor the formation of conceptual thinking. As specific objectives, we intended to: understand the development of the study activity to promote conceptual thinking in adolescence; relate Mathematical Modeling and the mathematical concepts involved in the development of the project with the teaching of Mathematics for human development in its most advanced aspects; identify the criteria that students used in choosing a problem in the community; investigate the strategies used by students to solve the problem (prototypes, programming, research); to analyze, in the solutions presented, the representations that are used for mathematical models and the path taken for the development of higher psychological functions. This is a research that permeates the concepts of historical-critical Pedagogy and historical-cultural Psychology, as we consider that it is possible to guide an intentional, planned and systematized work for human formation with the application of appropriate mathematical knowledge with developments in other areas in Scientific Initiation projects. This work has a quantitative-qualitative approach of an applied nature and, according to the objectives, it is a research that seeks to understand the phenomena in their processuality and totality. For the technical analysis procedures, it fits into the research-training with the category of multi-referential thinking/doing and was carried out with 12 students from the three classes of the first year of High School, at the Escola Estadual Professora Guiomar de Almeida Peixoto. Data collection was carried out through the narratives of the practitioners recorded in the research/training diary constructed during the development of the project, considering the means of communication one-to-one, one-to-all and all-to-all on the various digital devices, with WhatsApp being the most used; collaborative dialogues and image records were also considered, as well as the ideas, concerns and meanings that emerged. In addition, to construct the mathematical model, the necessary mathematical concepts were applied and the GeoGebra program was used to analyze and validate the model through the graph of the situation identified in the semi-structured interviews. The other specific stages of the construction of the Scientific Initiation project, such as the logbook and the report, were assessed for analysis. A semi-structural questionnaire was also applied at the beginning of the research and another at the end for comparison; the last questionnaire had discursive questions about the learning developed and participation in the project. It was found that the practitioners carried out work that resulted in objectification, because it highlighted the relevance of awareness and reflection in the execution of activities that went beyond practice, as it involved ethical and symbolic values of the objectives, in addition to involving the formation, production and transmission of knowledge, as they were able to understand nature from the perspective of the cultural elements produced. As an educational product, a didactic manual for Mathematics teachers was prepared with a proposed didactic sequence for the development of Scientific Initiation projects.