Aprendizagem significativa em uma perspectiva crítica para o cálculo diferencial e integral: o estudo de derivadas a partir de uma unidade de ensino potencialmente significativa

Abstract

This research explored the teaching of derivatives through the lens of Ausubel’s theory of meaningful learning (2003), from the critical perspective of Moreira (2019). It consists of a qualitative, exploratory, and applied study, and follows the methodological approach of Educational Design Research. The central objective was to examine how pedagogical strategies based on Potentially Meaningful Teaching Units may contribute to teaching derivatives in a Software Engineering undergraduate program, aiming for students' critical meaningful learning. The research was carried out at a university in Paraná, Brazil, involving two groups of participants. The first group consisted of second-year students with a bachelor's degree in Software Engineering who had already completed the differential and integral calculus subjects, while the second group included first-year students who were enrolled in the same subject. Data collection methods included bibliographic reviews, theoretical and practical exploration, questionnaire administration, classroom recordings, and reflective journal entries. Following the EDR framework, the study was carried out in three phases: 1st) analysis/exploration, encompassing a literature review and a questionnaire applied to the first group; 2nd) design/development, involving the planning and implementation of PMTUs; and 3rd) evaluation/reflection, which entailed systematic data analysis and the development of the research product. Data were analyzed using Content Analysis techniques. It has been observed that deficiencies in basic mathematics and reliance on rote learning are factors that hinder the learning of Differential and Integral Calculus. The results indicate that PMTUs foster critical meaningful learning of derivatives in Calculus. Furthermore, they offer a valuable approach for mathematics educators focused on fostering student learning that transcends mechanical processes to become meaningful. This methodology supports teaching practices that enable students to find relevance in their learning, connect new information with prior knowledge, and comprehend the interdependence of calculus concepts and their broad applications. As a product of this research, an e-book was developed, featuring the activities implemented, key insights from the investigation, and practical guidelines for designing and applying PMTUs in the teaching of Differential and Integral Calculus. This resource aims to support educators and researchers in enhancing critical meaningful learning. In conclusion, pedagogical strategies based on Potentially Meaningful Teaching Units significantly advance the promotion of meaningful learning from a critical perspective of derivative concepts.