Exploração, Proposição e Resolução de Problemas: pesquisas do GEPEP e suas possibilidades para a prática pedagógica

Abstract

This paper analyzes the possibilities of research developed by the Study and Research Group on Education and Postmodernity (GEPEP) in the Problem Exploration, Posing and Solving in pedagogical practice. The research follows a qualitative approach, aiming to seek meanings, interpret, and understand the information gathered. Initially, a documentary research was carried out, in which dissertations from GEPEP participants who worked on Problem Exploration, Posing and Solving were analyzed. The mapping of these studies helped to identify didactic movements that contributed to the development of a Continuing Education course for Mathematics teachers, focusing on activities of problem exploration, posing and solving in the form of Mathematical Narratives. The results showed that, in order to work with Problem Solving (PS) via Problem Exploration (PE), it is necessary to incorporate specific didactic movements, such as: the pursuit of refining problem resolution by addressing the problem at different levels of difficulty and depth; the generation of new problems based on the solution of the initial problem; and the idea that the discussion of the problem does not end with its (re)solution, as the teacher may revisit and deepen it at different moments and levels; additionally, the problem can serve as a starting point for generating new problems; furthermore, there is a dissatisfaction with merely finding a resolution, and, with this, the search for multiple resolution processes is encouraged, which help to deepen/refine the discussion, potentially resulting in new content, new problems, further work, new reflections and new syntheses; as well as the exploration of the problem, which may even spark debates on socio-political-cultural issues. In Problem Posing (PP) via Problem Exploration (PE), the following didactic movements are identified: the process of problematization precedes the posing of the problem, that is, it is necessary to become familiar with the problems generating-situation before posing the problem; additionally, mathematical concepts and content are developed based on the problems proposed by both teachers and students; moreover, it is essential to go beyond simply posing the problem, meaning that one should not limit the activity to posing and solving the problem; thus, the proposed problems can serve as a source for generating new problems through refinement and rewriting of the initial problem; in this way, problem posing can occur before, during and after the problem exploration and solving process; the proposed problems not only emphasize the discussion of mathematical processes and concepts but also reflect on socio-political-cultural issues. This study concludes that, in pedagogical practice via Problem Exploration-Posing-Solving, the work of problem exploration-problematization-posing enabled the problem or problems generating-situation to be discussed at various levels of depth, going further and further with the work of: exploring, problematizing, posing, rewriting/reformulating and solving problems. Furthermore, in the experience with Mathematics teachers, it was observed that the process of problem exploration led to a better understanding of the socio-political-cultural aspects surrounding the proposed problems.