Argumentação no ensino de operações com números inteiros

Abstract

When considering performance in external assessments, such as PISA, for example, we notice a huge number of students who are not achieving the desired level of proficiency in mathematics. We believe it is not possible to single out one person responsible for such a situation. In the present work, we highlight two fundamental variables in the teaching process, which have a strong influence on student learning, which are the teacher and the textbook. The teacher, being responsible for mediating the knowledge to be taught to the student and the textbook, a resource for consultation for both the student and the teacher, must present a solid knowledge not exclusively covering concepts and formulas, but also procedures and forms of reasoning that can justify them. In this perspective, we attribute a very important role to argumentation in mathematics teaching for this purpose, considering it as the expression of reasoning, in addition to contributing to the understanding of mathematical knowledge. In mathematics education, argumentation can be classified, according to Sales (2010) and Attie (2016), into two categories, explicative and justificative, and it is from this characterization that we outline the present study. In this way, the present research aims to identify the types of arguments used in the teaching of fundamental operations with integers, from speeches of basic education teachers and texts from textbooks, indicated by the Guide to the National Book and Teaching Material Plan, PNLD, 2020. As for the methodology, we consider that our research can be characterized as qualitative, with exploratory and descriptive aspects. Our data collection process was carried out in two parts, initially with the search and analysis of the didactic works, in a total of eleven books, and with the subsequent application of a questionnaire and semi-structured interviews, individually and remotely, with four teachers from the public school system working at the Elementary School level. From the analysis of the data collected, according to the technique of Content Analysis, we found that, for the most part, the authors of textbooks, despite having minimal resources for a justificative argumentation, show a shortage of repertoire in relation to the presentation of the content. In relation to the data obtained with the teachers, we observed two different scenarios in front of the class of these operations. For addition and subtraction, we point out that the main focus is on the justificative argumentation, through the use of contextualized situations to signify such operations, while in the multiplication, there is an inversion in this posture, in which the concentration resides in the explicative argumentation, attested by the recurrence directly to the rules and the absence of a logic validation for the procedures.