AMBIENTES INFORMAIS E ENSINO EXPLORATÓRIO: PROFISSÕES COMO SITUAÇÕES MATEMÁTICAS GERADORAS

Abstract

Mathematics is present in people's daily lives, whether in formal settings (such as in school) or informal settings (at home, on the street, in the neighborhood, and in everyday tasks). Its importance is undeniable. Therefore, this research analyzed the presence of mathematics in informal environments and how mathematics can be addressed in the classroom of a rural school, using the Exploratory Teaching Approach. The theoretical framework begins by differentiating formal, non-formal, and informal education, followed by an explanation of the Exploratory Teaching approach, employing the lesson in three phases: task introduction, autonomous work, and collective discussion. To value the environment in which the research was applied, a study on Rural Education was conducted, highlighting the importance of valuing its culture and knowledge. The methodology applied in the research has a qualitative bias, of exploratory nature and bibliographic survey. As an analysis method, Data Triangulation is used, according to Duffy (2007), which combines different methods, data, or investigations. The guiding question of the research is: how to relate the mathematics present in informal environments to the mathematics used in the classroom? The objective is to understand how the mathematics present in informal environments can contribute to the teaching and learning of mathematics in the school environment using the Exploratory Teaching approach. Therefore, the didactic sequence: Mathematics in Professions: An Exploratory Teaching Approach, available on the website: https://www3.unicentro.br/ppgen/dissertacoes/ was applied, which was the educational product developed and applied in a state school, with a class of 20 students from the 2nd and 3rd grades of high school. The field research started with a questionnaire in which students investigate the mathematics present in their family members' professions. From there, it is proposed to include a phase focused on investigating the student's informal environment within the Exploratory Teaching Approach, preceding the other phases, thus utilizing four phases: investigation of the task context, presentation of the task, autonomous student work, and collective discussion. In the “investigation of the task contexto” phase, it was possible to define “generative mathematical situations,” which were the professions of farmer and construction worker, that supported the construction of the mathematical tasks to proceed with the implementation of the other phases. Afterward, the analysis of the responses obtained from the task resolutions is conducted, promoting the connection between the use of mathematics by professionals and school mathematics.. As a result, it was found that using the mathematics present in professions within an Exploratory Teaching approach promoted motivating classes in which students perceived the relationship between everyday mathematics and formal mathematics, enabling the discovery and construction of knowledge by the students.