EXTENSION AS A TRAINING SPACE: EXPERIENCES WITH DIFFERENTIAL AND INTEGRAL CALCULUS IN THE BACHELOR'S DEGREE IN MATHEMATICS

Abstract

This article presents the experience of a university extension project, entitled "Mathematics in School," within the Differential and Integral Calculus 1 course of a Mathematics undergraduate program at a public university in Paraná. The project aimed to enrich the academic development of students, foster social and civic responsibility, and strengthen the relationship between the university and the external community. To this end, planning, preparation, implementation, and reflection activities were developed, including the study of the course syllabus contents, analysis of the intersection of these contents with Basic Education, recognition of applications of derivatives and integrals, reading of scientific articles, preparation of activities featuring Brazilian tourist attractions, validation in the Calculus classroom, and application in a second-year high school class. The project's activities focused on exploring the calculation of areas of irregular surfaces in real-world contexts, using manipulative teaching materials and digital technologies, aligning with skill EM13MAT307 of the National Common Curricular Base (BNCC). Among its contributions, it highlights the importance of university extension as a fundamental pillar in the comprehensive training of future mathematics teachers, connecting academic theory with pedagogical practice and social demands, and as a powerful platform for learning opportunities and knowledge production.