Perspectivas sobre a equação do segundo grau e suas concepções no ENEM

Abstract

This work was developed with the objective of investigating how the notion of high school equation is conceived in Basic Education from its different conceptions. To do so, we started with the development of a historical study and, later, we analyzed how this concept is appro ached in mathematics books. So, we establish a dialogue of such studies with the perspectives of Mathematics Education, in order to appreciate the knowledge necessary for pedagogical practice in teaching equations. Hence, after presenting the categorization of equation conceptions, proposed by Ribeiro (2013), we carried out a survey in the National High School Exam. As methodological steps, we restricted our research to the last 10 years of the exam and probed, within the issues of the area of Mathematics and its technologies, only those that dealt with our object of study. Thus, aiming to understand how the exam contemplates the equations of the second degree from their different conceptions, we proceeded to a detai led analysis of each selected question, classifying them according to their relevance to these conceptions. Finally, we verified, in our results, a frequent approach to the geometric design, a reasonable work with questions that articulate characteristic elements of the pragmatic, procedural and applicational conceptions and a low focus on the structural design.