Uma análise praxeológica sobre a presença de sólidos geométricos em provas do ENEM de 2017-2020

Abstract

This dissertation presents a research in which had as a main objective analyzing what are the mathematical praxeologies related to geometric solids present in Enem tests from 2017 to 2020. The reason for this object is due to the fact that evaluations, such as the National High School Exam (Enem), influence and are influenced by the curricular and didactic guidelines present in official documents for high school, such as the National Curricular Parameters for High School (PCNEM), Complementary Educational Guidelines to the National Curricular Parameters (PCN+). Enem is a largescale assessment at the national level, serving as an indication for the analysis/creation of public policies at this level of Brazilian education; for the admission of students from all over the country to public and private universities, in some cases even to institutions abroad. By taking into account the importance of this exam, in addition to the problem about the teaching of geometry, more specifically, the geometric solids and instigated by the research problem present in the Anthropological Theory of Didactics (ADT), we seek to understand how this mathematical object lives in this evaluation and under what conditions and restrictions this occurs. Thus, through a qualitative research of documentary character, we are based on the assumptions of Chevallard and Gáscon, to analyze the epistemological, economic and ecological dimensions related to our research problem. In the economic and ecological dimensions, we analyzed the presence of geometric solids in national high school curriculum documents (PCNEM and PCN+), in addition to analyzing two 2nd year mathematics textbooks of the same level of education, approved by the current PNLD's at the time of conclusion of the tests chosen for analysis (PNLD 2015 and PNLD 2018). In the analysis of these dimensions, we noticed an emphasis given to metric geometry, mainly by textbooks, containing a considerable number of tasks aimed at calculating surface area and volume measurements of solids. Or even, to discover measures that are not explicit. Carrying out these analyzes enabled the elaboration of our Praxeological Reference Model (PRM) and, as the name itself explains, this model served as a reference for our praxeological analysis of the Enem exams from 2017 to 2020, in which we infer that there is a predominance of tasks related to calculating volume measurements.