Avanços e concepções no cálculo de volumes: uma análise histórica e detalhada desde os primeiros prismas até as integrais duplas

Abstract

The aim of this research is to explore the concept of volume in a comprehensive way, from both a mathematical and pedagogical point of view. The methodology used involved a critical analysis of Davydov and Libâneo's theories, followed by an exploration of the evolution of volume formulas, from initial simplifications to more complex generalizations. The question that guided the research was: How can we promote a deeper understanding of the concept of volume and its relevance through a dynamic teaching approach? The results highlight the importance of adapting to students' needs, stimulating curiosity and autonomy, interdisciplinarity and the evolution of mathematical thinking. The contribution that this research sought to achieve was to inspire educators, students and researchers to explore the vast possibilities of studying volume and mathematics in general.