Exploring the use of GeoGebra’s CAS view to determine repeating decimal periods in mathematics education

Authors

DOI:

https://doi.org/10.23925/2237-9657.2025.v14i1p267-276

Abstract

The article explores the use of the GeoGebra CAS view to determine the period length of repeating decimals, a relevant topic for mathematics education that can be enhanced through educational technologies. The text presents the mathematical concepts involved in determining the period of infinite, periodic rational numbers, particularly applying Fermat's Little Theorem to identify the period length of rational numbers with prime denominators. Specific commands within the GeoGebra CAS Window are highlighted, enabling students to explore numerical and symbolic operations, which can encourage the formulation of conjectures and problem-solving. The study concludes that the CAS Window is an effective tool for investigative learning in mathematics, though it has limitations in certain contexts.

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Author Biography

Marcio Vieira Almeida, Pontíficia Universidade Católica

He has academic training and experience in the areas of Mathematics, Mathematics Education, and Educational Technologies. He holds a Ph.D. in Mathematics Education from the Pontifical Catholic University of São Paulo (2017). He graduated with a degree in Mathematics Education from the University of São Paulo (2009). He has experience in the field of Mathematics Education, focusing primarily on the following topics: digital technologies in mathematics education, computational thinking, artificial intelligence, and teacher training. From 2022 to 2024, he served as a Visiting Professor in the PROFMAT Program at the Federal Institute of Education, Science, and Technology of São Paulo (IFSP) - São Paulo campus. He is currently a Professor at the Graduate Program in Mathematics Education at PUC-SP.

References

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Torres, A. C. A. (2013). Cálculo Simbólico también es posible con GeoGebra . UNIÓN - REVISTA IBEROAMERICANA DE EDUCACIÓN MATEMÁTICA, 9 (34). Disponível em: https://www.revistaunion.org/index.php/UNION/article/view/796

Gonçalves, W. V. (2023). Amadurecendo como professor, pesquisador e colaborador com o GeoGebra. Revista Do Instituto GeoGebra Internacional De São Paulo, 12(2), 221–238. https://doi.org/10.23925/2237-9657.2023.v12i2p221-238

Hefez, A. (2016) Arimética. Rio de Janeiro: SBM.

Sampaio, J. C. V. (2024) Dízimas periódicas e o teorema de Etiénne Midy. In. XI BIENAL DE MATEMÁTICA. Disponível em: https://sbm.org.br/xi-bienal/wp-content/uploads/sites/31/2024/07/XI_BM_MINICURSO_Joao_Sampaio.pdf

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Published

2025-06-08

How to Cite

Almeida, M. V. (2025). Exploring the use of GeoGebra’s CAS view to determine repeating decimal periods in mathematics education. Journal of the GeoGebra International Institute of São Paulo, 14(1), 267–276. https://doi.org/10.23925/2237-9657.2025.v14i1p267-276

Issue

Vol. 14 No. 1 (2025)

Section

Proposals for Action

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