Abstract:

This article aims to present the development and implementation of active methodologies in the teaching of Differential and Integral Calculus (DIC). It incorporates implementation guidelines, student feedback, and an analysis of student satisfaction regarding the employed methodology. The developed activities addressed the following topics: Transformation of Functions; Limits by Definition and Limits at Infinity; Continuous Functions and First and Second Derivative Tests; and Riemann Sums and the Fundamental Theorem of Calculus. For each activity, instructors are provided with implementation suggestions, including guidelines for environmental and task organization, learning objectives, core content, activity sequencing, estimated time, required materials, and GeoGebra constructions, alongside bibliographic references. These activities resulted in a compilation titled "Atividades para Cálculo Diferencial e Integral" (Activities for Differential and Integral Calculus), available on the GeoGebra platform (https://www.geogebra.org/m/x3eaprcv). The interventions, supported by GeoGebra’s dynamic resources, promoted group work, conceptual exploration, hypothesis formulation, and peer discussion. The research was conducted at two institutions: Université Claude Bernard Lyon 1 (LYON 1) in France and the Federal University of Technology - Paraná (UTFPR) in Brazil. Before and after each session, students completed satisfaction questionnaires regarding the lesson format and provided qualitative comments. Results indicate that Brazilian students showed greater receptivity to active methodologies, despite frequent algebraic difficulties that hindered problem-solving. In contrast, French students, while demonstrating superior mathematical proficiency and organization, exhibited resistance to collaborative work and the disruption of the traditional, competitive pace characteristic of classes préparatoires. Qualitative feedback reinforced these differences: Brazilian students predominantly provided positive feedback, highlighting improved understanding and collaboration. Conversely, French students were divided, with criticisms focused on a preference for traditional lectures, a perceived "slow" pace, and discomfort with group dynamics.The lower satisfaction levels among French students reflect a lack of familiarity with these methods, suggesting that increased exposure could mitigate discomfort in innovative learning scenarios. Additionally, the competitive nature and rigid scheduling of the French preparatory system likely contributed to this dissatisfaction. The findings suggest that active methodologies can enhance conceptual learning and student engagement; however, their acceptance depends heavily on institutional context, pedagogical culture, and prior familiarity with non-traditional approaches. This educational product seeks to support instructors in transitioning toward student-centered teaching and may be expanded with new activities in future research.

Keywords:

Mathematics Education, Active Methodologies, GeoGebra, Differential and Integral Calculus, Comparative Study.