Ensino-aprendizagem de sistemas lineares na formação do professor de Matemática via exploração, resolução e proposição de problemas

Abstract

The present work aims to analyze the contributions of the teaching-learning methodology of Mathematics through Problem Solving, together with the Multiple Representations of Algebra in the teaching of Linear Systems. In this study, the content of Linear Systems was chosen, looking for an investigation in the field of Algebra that contemplates both basic and higher education, since the great problem perceived in the teaching of Algebra, revealed in the literature, deals with the distance between Algebra degree in Mathematics and Algebra taught in Basic Education. The research is characterized as qualitative (BOGDAN; BIKLEN, 1994; YIIN, 2016), in the modality of pedagogical research (LANKSHEAR; KNOBEL, 2008). The research was developed in a class of the 5th period of the Degree in Mathematics of a Federal University in Paraíba, where the class teacher was the researcher herself. The pedagogical research was chosen because there is interest not only in raising data, but also in improving the pedagogical practice of the teacher as a researcher and, above all, to contribute to the training of students in Mathematics from new ideas of Algebra, as well as by theoretical-practical experiences provided by the teaching- learning methodology of Mathematics through the Resolution, Exploration and Proposition of Problems. For this, a Workshop was used as a data collection tool, with activities planned in the light of Friedlander and Tabach (2001) and developed using the teaching-learning methodology of Mathematics through Exploration, Resolution and Problem Proposition (ANDRADE, 1998; 2017). The descriptions and analyzes of the meetings point out that although the students seem to have theoretical conceptions that correspond to the current perspectives of Problem Solving, their use as teaching methodology was something new for them, since these conceptions were very limited. That is, students had theoretical principles on problem solving in mathematics teaching, but had no practical experience of such a perspective. Thus, we realized that students understood and incorporated Exploration and Problem Solving to work with Problem Solving. This was evident in the seminars held by the students, since they did not finish the activity getting the answer to the problem, instead, they tried to go further, seeking new results and new syntheses. In this sense, when dealing with the teaching of Linear Systems, students' progress was noted, especially in the transition between the representations, since they began to use mathematical language to express the resolutions of the problems, not immediately resorting to judgment and error as in beginning of the workshop. Therefore, the results showed that the Multiple Representations of Algebra and the transition between them favor a learning of Linear Systems with greater understanding. It is concluded, therefore, that the teaching- learning methodology of Mathematics through the Proposition, Resolution and Exploration of Problems contributes to the construction of a new posture against the teaching of Linear Systems.