Prática argumentativa no ensino de matemática: contribuições para o processo de resolução de problemas verbais

Abstract

Teaching mathematics is a sometimes complex task, since it requires the teacher to search for alternatives that allow students to abstract the concepts of this area, so that they can have possibilities to perceive the applicability of these concepts in everyday life. We understand that one option for this is the use of verbal mathematical problem solving as a methodological procedure for the teaching of mathematics. However, this resolution requires, for example, that the subject read the problem in order to understand it, since it presents itself by means of a statement, select a strategy to solve it and seek to validate the solution found, such actions being some difficulties that the students demonstrate to have, especially the of the sixth grade elementary school, a fact that is perceived in our own teaching practice. In the studies carried out, we realized that the argumentative practice promoted in the classroom could contribute to the students not only advancing in the process of solving verbal mathematical problems but also the possibility of developing metacognitive strategies that would allow them to have better conditions to deal with such problems in individual and future moments, but, above all, they were given the opportunity to participate more actively in these moments of resolution, having more effective possibilities to understand the mathematical content contemplated in the problem. Thus, we propose the following thesis: the solution of verbal problems, through argumentative practices, favors the development of metacognitive thinking in order to facilitate the development of skills and procedures for the resolution of these problems by the students involved in the discussion, thus favoring , the learning of mathematics. In this doctoral work we had as subjects of the research seven students of the sixth school year of a public school and the basic operations of mathematics as the content to be treated. The research was constituted as action-research and the analyzes were carried out based on Discursive Textual Analysis (DTA). Thus, we aim, initially, to identify the procedures used by the students in the stages that make up the resolution of a verbal problem. From there, we investigate if such procedures were developed to the point of being used again in new problems. Finally, we propose to verify, from the statements of the students, if these procedures were configured as metacognitive strategies. We also sought to verify how the discussion about the use of those strategies contributed to the development of metacognitive thinking. We conclude that, in fact, the use of argumentation in problem solving favors the teaching of mathematics, allowing metacognitive strategies, as well as other metacognitive movements, such as the construction of hypotheses, justifications and questions, to be socialized to the point of helping those involved in the discussions related to that resolution, and these strategies can be apprehended and used in future times, in addition to allowing the student to become more familiar with the type of problem being discussed, which also contributes to the development of metacognitive thinking about such task. For this, we note that it is indispensable that the teacher appropriates studies that allow him to understand a little about argumentation and its relation with the teaching of mathematics, in order to produce a planning that allows for discursive alternatives for the maintenance and fomenting the discussions. Although our actions were planned in such a way as to enable us to identify the metacognitive strategies used by students in our research, they also contributed to the students‟ understanding of the mathematical concepts involved in verbal problems applied in the classroom.