Uma análise do uso da metodologia de ensino-aprendizagem-avaliação de matemática por meio da resolução de problemas para a abordagem de produtos notáveis em turmas do nono ano de uma escola pública municipal (Aracaju-Sergipe)

Abstract

This text presents the result of a research study whose objective was to analyze the use of the Teaching-Learning-Assessment Methodology of Mathematics through Problem Solving to approach notable products in a ninth-grade class at a municipal public school in Aracaju, Sergipe. The theoretical framework adopted is the proposal de Onuchic and Allevato (2021), whose methodology simultaneously integrates the processes of teaching, learning, and assessment. The methodological approach adopted is a case study, in order to identify implications caused by the use of the methodology in the approach to notable products. Initially, a survey was conducted in the Brazilian Digital Library of Theses and Dissertations (BDTD) and in the repository of the Coordination for the Improvement of Higher Education Personnel (CAPES) for familiarization with the theme. The works selected for examination were those by Kucinskas (2024), Morais (2022), Trento (2019), Silva (2018), and Soares (2018). Subsequently, in light of the proposal of Onuchic and Allevato (2021), the Teaching-Learning-Assessment Methodology through Problem Solving is presented, as well as the steps indicated by the authors for its implementation, in addition to an association between the studies and the methodology. The research subjects were one Mathematics teacher and thirty-one students, having as a source the guidelines proposed in the textbook by Giovanni Junior (2022) concerning the teaching of notable products. Next, a typification of the problems present in the textbook adopted for use in the school was carried out, based on Dante (2005), and it was found that the typification of the textbook problems did not evidence the presence of generating problems suitable for the application of the methodology to approach the object of knowledge. However, this survey allowed the identification of paths for the creation/adaptation of generating problems, which resulted in the selection of problem situations aligned with the recommendations of Onuchic and Allevato (2021). The applications took place in six meetings, and their analysis made it possible to verify that the use of the methodology may favor the construction of mathematical knowledge by mobilizing prior knowledge and teamwork through the appreciation of the strategies developed by the students, which enables the teacher to act as a mediator of the teaching process, working mainly through questioning. The records produced by the students made it possible to identify not only the results obtained, but also the paths to the resolution, the mistakes made, and the strategies mobilized to overcome them, constituting relevant elements for the assessment process. Furthermore, it was observed that adaptations in the methodological script of Onuchic and Allevato (2021) did not compromise the teachinglearning-assessment process. Thus, based on the collected data, it is possible to infer that Problem Solving as a teaching-learning-assessment methodology may contribute to the approach to notable products, especially when it articulates representations of geometric objects of knowledge with algebraic ones.