O uso didático da calculadora gráfica Desmos via exploração-proposição-resolução de problemas: uma experiência na licenciatura em matemática

Abstract

This thesis addresses the didactic use of the Desmos graphing calculator through the Problem Exploration-Posing-Solving approach, based on an experience in a Mathematics teaching degree program. In this classroom methodology, we take Problem Posing as the starting point, which is considered one of the most challenging aspects to implement in teaching. Observing how Digital Technologies can be effectively incorporated into this practice, the research also reflects on the limited attention given to Problem Posing when using technological tools. Thus, we analyze how these methodological approaches can guide the use of digital teaching resources. The central research question was: How does the Problem Exploration-Posing-Solving methodology enhance the didactic use of the Desmos graphing calculator? The objective was to analyze how this methodology can improve the educational use of the tool. The qualitative, pedagogical research was conducted in the Mathematics Teaching Practice II course, part of a Mathematics degree program, under the guidance of the researcher as professor-researcher. Thirteen teaching candidates participated in the study, with data collected through written activity records, Desmos screenshots, WhatsApp group interactions, classroom activity audio recordings, and a field journal. Data analysis was carried out using Thematic Analysis. The study unfolded over two main phases, totaling 20 sessions. During the first phase (10 sessions), participants were introduced to the Teaching-Learning methodology via Problem Exploration-Posing-Solving and the use of the Desmos graphing calculator, fostering an initial reflective understanding of Mathematics teaching. This phase was crucial for planning the second phase, which focused on conducting a workshop where activities developed using Desmos were guided by the Problem Exploration-Posing-Solving methodology. The results indicate that the didactic use of the Desmos graphing calculator can significantly enhance Problem Exploration-Posing-Solving activities. Simultaneously, it became evident how this methodology qualified the didactic use of the Desmos tool. This approach guided the educational application of the graphing calculator, facilitating graph manipulation, the expansion of the numerical field from integers to reals, pattern recognition, conjecture formulation, and the development of mathematical concepts—elements often constrained in traditional pencil-and-paper activities. The research also identified challenges faced by the teaching candidates, particularly regarding Didactic Coherence in Problem Posing. This highlights the need for an Educational Framework to optimize the didactic use of the Desmos graphing calculator via the Problem Exploration-Posing-Solving methodology. This approach has the potential to enhance Mathematics teaching, fostering a favorable environment for learning and deeper mathematical knowledge construction.