A análise didática de erros: Um estudo com equações do segundo grau

Abstract

The aim of this study is to understand the role of error in the teaching and learning process of mathematics. The research participants were first-year high school students and public school math teachers. This research is qualitative and the data collected were the productions made by students from four situations involving high school equations, in addition to structured interviews with teachers participating in the research. The study sought to highlight the types of errors made by students solving high school equations. We used as theoretical support the MADE - model of didactic analysis of errors, proposed by Torre (2007). The model offers us the possibility to analyze several types of errors that can occur at three moments in the process of resolving an issue, that is, errors at the time of entry, organization, and execution. The same author offers us theoretical support to do the didactic treatment of errors made by students, which consist of three phases: detection, identification, and correction of errors. Based on the students' resolutions, a high rate of errors was found, with this, we used the didactic treatment of errors that made it possible to improve their performance. It was possible to realize that due to the didactic treatment of the errors carried out, the scenario that used to be of several errors, became a significant reduction in them. With the teachers participating in the research, we seek to understand their perceptions about the student's error in the teaching and learning process. They understand that the error is important, but we note that they lack theoretical knowledge of what would be the best way to deal with the student's mistakes in the classroom, but they are uneasy when the error is evidenced by developing some strategy that they believe to be the correct one. In addition, some teachers perceive the error of their students, we can evidence in the testimonies given by the teachers characteristics that situate the error from a positive and a negative point of view.