Explorando potencialidades no ensino de recorrências com os três momentos pedagógicos: história, teoria e aplicações

Abstract

This work aims to present a teaching proposal for numerical sequences and recurrence relations based on the methodology of the Three Pedagogical Moments (3PM). The study starts from the observation that many students face difficulties in learning this content, which demands more effective, meaningful methodologies connected to students’ realities. Numerical sequences, especially those defined by recurrence, are important not only for their theoretical value but also for their applicability in everyday situations, such as population growth, the functioning of technological systems, and financial mathematics. This is a qualitative and exploratory bibliographic research, which seeks to contribute to the existing gap regarding the application of the Three Pedagogical Moments in the teaching of sequences and recurrence. The theoretical framework includes authors from mathematics education and critical pedagogy, such as Delizoicov, Freire, Gomes, and Lima, among others. The study proposes a didactic sequence based on a generative theme — online betting — aiming to foster logical reasoning, pattern generalization, and the development of critical mathematical thinking. Theoretical findings indicate that the 3PM methodology — composed of the stages of initial problematization, knowledge organization, and knowledge application — is effective in mediating mathematical content in a more reflective, critical, and contextualized way. The analysis of previous studies (Ritter, 2017; Santos, 2023; Botelho, 2023; Cabral, 2023; Gaióski, 2019; Real, 2017) supports this conclusion, showing that the use of the 3PM in different educational contexts contributes to greater engagement, active student participation, and improved understanding of mathematical concepts. It is concluded that applying the Three Pedagogical Moments in teaching numerical sequences and recurrence relations can strengthen educational practices that are more integrated with students’ realities and committed to a mathematical education focused on citizenship. Therefore, the proposal developed here aims to be an effective contribution to mathematics teaching, articulating theory and practice with an emphasis on meaning-making and the intellectual emancipation of students.