O ensino dos números complexos por meio de uma proposta metodológica de sala de aula invertida - Mendes, João Anderson (2020)
The text presented here refers to a master's research report whose goal was to investigate whether the use of the "Inverted Classroom" methodology favors the learning of high school students, especially regarding the teaching of a mathematical concept: complex numbers. This work's guiding methodology was shaped by the qualitative action research. The methodological procedures were carried out in the following ways: implementation of a sequence of activities, composed of a video prepared by the teacher / researcher with data for the study of the complex numbers representation in the Argand-Gauss plan, the concept of module and the argument of a complex number; application of a questionnaire to assess students' methods of study, and development of a control activity over the discussed subjects. The responses to the questionnaire and to the control activity allowed discussion / validation of the studied concepts and the main difficulties found. Finally, there was the institutionalization of the trigonometric form of complex numbers. The theoretical framework used to analyze the results consisted of the very bases of the "Inverted Classroom" concept, proposed by Jonathan Bergmann and Aaron Sams, in addition to contributions from Perrenoud's concepts of competence and Raymond Duval's semiotic representation records. The discussions between students in class, about their pre-class studies, indicated the potential of the used methodology to enable students to realize misconceptions and seek ways to advance their knowledge. These conditions helped the teacher / researcher to identify learning obstacles and take them into account in his teaching proposals. Another result that could be verified was how autonomously students acted during their studies, a factor that can favor the construction of a new competence. The employed methodology also allowed students to vary the representation records of complex numbers in order to succeed in improving the knowledge of the studied concepts