Funções: uma análise acerca da abordagem em provas do nível 3 - 2ª fase da OBMEP

Abstract

This research aims to analyze how the subject of functions is addressed in Level 3 questions of the second phase of the Brazilian Mathematics Olympiad for Public Schools (OBMEP). Some of the purposes of this competition are to verify improvements in the teaching of mathematics in basic education, as well as to monitor the revelation of new talents in young students encouraged by participation in the event. The data analyzed here were collected through a bibliographic research, which involved building a description about the evolution of the idea of function over time, as well as aspects related to the creation and functioning of the OBMEP. Then the questions that address, even if implicitly, the subject of functions, from the first edition of the OBMEP, which occurred in 2005, to the 2018 edition, were analyzed. These questions were solved in full detail, where we tried to show connections between algebraic and geometric aspects of the concepts involved. Whenever possible, we resorted to the GEOGEBRA software apparatus to give a different approach to each question. The results obtained in this research point to the use of functions as central content in the questions, as well as facilitating content for solving problems of various subjects that are addressed in the test. In addition, we conclude that it is important to work on this subject in the classroom with different approaches and using questions designed with this perspective for a better development of these skills in students.