LIMIT AND CONTINUITY IN CALCULUS: AN APPROACH TO THE FORMAL DEFINITION USING GEOGEBRA

Abstract

This article proposes an alternative methodology for teaching and learning limits and continuity of functions using the GeoGebra software as a pedagogical resource. The proposal aims to explore the potential of GeoGebra to support the understanding of abstract concepts through interactive graphical visualizations, contributing to a more dynamic and meaningful learning process. For the theoretical foundation, a brief literature review was conducted, addressing studies that highlight the importance of digital technologies in mathematics education. The research emphasizes the role of problem solving as a central element in the learning process and discusses how the use of GeoGebra can enhance this practice, making the content more accessible and engaging for students. The results indicate the effectiveness of the software as a supporting tool in the teaching of calculus, demonstrating its ability to facilitate the construction of concepts and to encourage students’ active participation.

Author Biographies

Kairon Ruanndy Rodrigues de Brito, UFPA

Bachelor’s Degree in Mathematics from UEPA. Specialist in Calculus and Applied Mathematics from Faculdade Focus. Master’s student in Mathematics and Statistics at UFPA.

Lorrana Bárbara dos Santos Rodrigues, UFPA

Bachelor’s Degree in Mathematics Education from the State University of Pará. Specialist in Teaching Mathematics for Secondary Education – Mathematics in Practice from UNIPAMPA. Master’s student in Mathematics and Statistics at the Federal University of Pará.

Paulian Ramos da Silva , UFPA

Master’s student at the Federal University of Pará (UFPA), with a Bachelor’s Degree in Mathematics. Conducts research in the field of Statistics, with emphasis on statistical inference, estimation theory, maximum likelihood methods, the Cramér–Rao lower bound, the delta method, probabilistic modeling, statistical data analysis, and computational methods applied to parameter estimation and statistical simulation.

Eusom Passos Lima, UEPA

Educator and researcher working in the field of Mathematics and Education, dedicated to teaching, teacher training, and reflection on contextualized pedagogical practices. His work values the relationship between school mathematics, social reality, and local knowledge, contributing to the strengthening of learning and teaching practices in different educational contexts.

Eldon Ricardo Souza Pereira, UEPA

Undergraduate Degree – Specialization in Mathematics Education.

Sérgio Junior Bezerra Nobre, UEPA

Undergraduate student in Mathematics Education (Licentiate) at UEPA.

Alexia Bianca Veiga da Silva

Specialist in Methodology of Teaching Mathematics from Uniter. Bachelor’s Degree in Mathematics Education from UEPA.

Daniel Matias Santos, UEPA - Universidade do Estado do Pará

UEPA – State University of Pará.

Ana Carolina Cardoso Miranda, UFPA

Master’s Degree in Statistics from the Federal University of Pará.

Alessandra Liz Rebelo Carneiro, UFPA

Master’s student in Applied Mathematics.

References

ABAR, C. A. A. P. A Transposição Didática na criação de estratégias para a utilização do GeoGebra. Revista do Instituto GeoGebra Internacional de São Paulo, [S. l.], v. 9, n. 1, p. 59–75, 2020 DOI: https://doi.org/10.23925/2237-9657.2020.v9i1p59-75

ÁVILA, Geraldo. Análise matemática para licenciatura. 1.Ed. Editora Edgard Blucher LTDA. São Paulo, 2001.

BRITO, Daniel Alves. Aprendendo geogebra. Amazon. 2023.

CORRÊA, Francisco J. L. A. Introdução à Análise Real. Faculdade de Matemática UFPA. Belém, 2006.

FEITOSA, Francisco Eteval da Silva; RODRIGUES, Roberta dos Santos. Uma sequência didática para o ensino de limite e continuidade. REDEMA. Juiz de Fora, 2023.

LIMA, Elon L. Curso de análise, vol 1. 14. ed. Projeto Euclides. Rio de Janeiro: Instituto de matemática pura e aplicada, 2016.

MESSIAS, Maria A. V.; BRANDEMBERG, João C. Discussões sobre a relação entre limite e continuidade de uma função: Investigando imagens conceituais. Bolema, 2015

NAGAMINE, André. Definição formal de limites: o GeoGebra pode ajudar?. Brazilian Journal of Development. Curitiba, 2023.

JÚNIOR, José Firmino de Melo. Um Universo interdisciplinar chamado cálculo diferencial e integral: Concepções e Aplicações. TCC. Instituto Federal da Paraíba. Cajazeiras, 2020.

SOUSA, Jakson Ferreira de. Uso do Geogebra no ensino da Matemática. 2018. Dissertação (Mestrado) – Curso de Ensino, Universidade do Vale do Taquari - Univates, Lajeado, 12 dez. 2018. Disponível em: http://hdl.handle.net/10737/2482

How to Cite

Ruanndy Rodrigues de Brito, K. ., Bárbara dos Santos Rodrigues, L. ., Ramos da Silva , P. ., Passos Lima, E. ., Ricardo Souza Pereira, E. ., Junior Bezerra Nobre, S. ., Bianca Veiga da Silva, A. ., Matias Santos, D., Cardoso Miranda, A. C., & Liz Rebelo Carneiro, A. . (2026). LIMIT AND CONTINUITY IN CALCULUS: AN APPROACH TO THE FORMAL DEFINITION USING GEOGEBRA. RECIMA21 - Revista Científica Multidisciplinar - ISSN 2675-6218, 7(4), e747648. https://doi.org/10.47820/recima21.v7i4.7648