Uma abordagem didática interativa e visual no ensino de Mudança de Coordenadas em Integrais Múltiplas

Abstract

The research falls within the field of Mathematics Education, with the general objective of investigating how a pedagogical approach, based on the assumptions of Semiotic Representation Registers and supported by GeoGebra, can contribute to the teaching and learning processes of Changes of Coordinates in Multiple Integrals, in the context of Integral Calculus. Guided by the general objective, we constructed the following specific objectives: i) To analyze the use of Digital Technologies in the teaching of Changes of Coordinates in Multiple Integrals, in academic productions, focusing on the difficulties reported on the teaching and learning processes; ii) To analyze difficulties evidenced by students, based on a diagnostic test, in the change of semiotic representation registers in tasks that involve Changes of Coordinates in Multiple Integrals; and iii) To analyze knowledge mobilized by students when solving a sequence of tasks, which uses different representation registers, on Changes of Coordinates in Multiple Integrals. For the theoretical framework, we refer to Raymond Duval's Theory of Semiotic Representation Records (TRRS). As a methodological framework, contributions from Didactic Engineering were used, in which a literature review and field research were carried out, with a diagnostic test and sequence of tasks applied to Unimontes students from the 5th to the 8th period of the Mathematics Degree. The results show that GeoGebra enhances the visualization of integration regions, allowing students to explore relationships and understand integration limits and coordinate changes. However, challenges persist, mainly in the conversion between graphic and algebraic records, showing that pedagogical mediation can help include these tools in the learning process. Comparing the results of the diagnostic test with the analysis of the tasks performed, an evolution in the understanding of mathematical concepts was observed, but also the need for more frequent reviews aimed at the students' previous difficulties. It is concluded that the combination of TRRS and the use of Digital Technologies can favor learning, allowing a more fluid transition between the registers of semiotic representations. However, the analyzed data indicate that overcoming the difficulties related to the conversion between graphic and algebraic registers requires more structured pedagogical support. In addition, aspects such as the available technological infrastructure and teacher training for the use of these resources can directly influence the quality of this approach in teaching Change of Coordinates in Multiple Integrals.