Teaching and learning of calculus: exploring the three worlds of Mathematics (Olhar de Professor, 2021)
This paper brings a theoretical investigation, in a qualitative perspective, understood as a bibliographic study, developed with the objective to describe the Three Worlds of Mathematics theory, proposed by David Tall, and connect it with relevant aspects to the teaching and learning of Calculus. In this sense a general view was built on the Conceptual Embodied, Operational Symbolic and Formal Axiomatic worlds and that are related specifically with this mathematical knowledge field were presented. The results led to the conclusion that in opposition to the mechanical and repetitive process used to calculate limits, derivatives and integrals that an alternative pedagogical approach can be built. In this regard, a suggestion is made for the introduction of the study of Calculus starting from met-before related to geometry, arithmetic and algebra, that belong to embodied and symbolic reality, perceived in the worlds inhabited by the students that are starting their path at the university.
Keywords: Three worlds of mathematics. Higher education. Calculus.