Uma análise sobre o uso da metodologia de ensino-aprendizagem-avaliação de matemática por meio da resolução de problemas para a abordagem de números inteiros em uma turma do sétimo ano de uma escola pública municipal (Umbaúba-SE)

Abstract

This paper presents the results of a study aimed at analyzing the use of the Teaching Learning-Assessment of Mathematics through Problem Solving methodology for approaching integers in a seventh-grade class at a municipal public school in the city of Umbaúba, Sergipe. Problem Solving is understood here as the methodology proposed and advocated by Onuchic and Allevato (2021): Teaching-Learning-Assessment of Mathematics through Problem Solving methodology, in which knowledge construction occurs through the resolution of a generating problem. A mapping was conducted in the Brazilian Digital Library of Theses and Dissertations (BDTD) to identify previous research on the subject, leading to an examination of the works of Melo (2020), Lara (2021), Santos (2023), and Batista (2024). These studies contributed to the understanding of the theme and the adaptation of the generating problems applied. Participants included one Mathematics teacher and 27 seventh-grade students. Throughout the implementation, carried out over six meetings, the teacher assumed the role of an inquirer, encourager, and mediator, constantly circulating the classroom to observe each group's work, attending to dialogues, and encouraging students to both formulate conjectures and share their understandings of the proposed problems. Findings showed progress not only in students' comprehension of integers and their operations but also a shift in student posture; they took an active role in the teaching-learning process and built knowledge collaboratively through problem solving. During the applications, students demonstrated greater autonomy, confidence in their strategies and solutions, and appreciation for their peers' insights. Regarding the Teaching-Learning-Assessment of Mathematics through Problem Solving methodology, adaptations were made to the ten steps suggested by Onuchic and Allevato (2021); upon analyzing the implementation, it was concluded that the methodology was structured and developed using eight steps. Furthermore, assessment was present throughout the problem-application process, not only permeating but also contributing to the learning process. Both students and the teacher consistently utilized assessment during the methodological stages, connecting and analyzing the proposed strategies. Based on the collected data, it was found that the use of this methodology enabled a shift in both the students' posture as knowledge builders and the teacher's role as a mediator and inquirer. Additionally, the practice of assessment by both students and the teacher was identified, alongside the redefinition of errors, which were understood as part of the learning process, thereby transforming the classroom into an environment for the collective construction of knowledge.