Practice, Perception, and Analysis of Teaching and Learning Conception in Differential and Integral Calculus from the Perspective of Teachers and Students: A Comparison Between Brazil and France

This paper aims to understand the teaching and learning practices and perceptions regarding the subject of Differential and Integral Calculus 1 (DIC1) based on the current French model, as implemented at Université Claude Bernard Lyon 1 (LYON 1), and the Brazilian model, as observed at the Federal University of Technology—Paraná (UTFPR). Five tutorial groups were studied at LYON 1. At UTFPR, four classes of DIC1 were analyzed. Teaching activities were observed, and teachers responded to a questionnaire regarding the frequency with which they implemented certain activities and their beliefs about which activities contribute most to student learning. Students responded to the same questionnaire, reflecting on how often their instructors employed these activities and which ones they believed were most beneficial for learning. There was general agreement between teachers and students about the instructional methodologies used in class; however, discrepancies emerged between observed practices, stated methodologies, and the activities considered essential for learning. In engineering programs, the time allocated to problem-solving—individually or on the board—emerged as a key aspect that may inspire changes and improvements in the Brazilian model. In contrast, group work and mathematical software may serve as avenues for improvement in the French model.