Operating with positive numbers in GeoGebra: didactic implications
DOI:
https://doi.org/10.23925/2237-9657.2022.v11i2p072-091Keywords:
numerical operations, mathematical objects, GeoGebraAbstract
In this article, the exploration of various numerical operations with GeoGebra is studied and discussed, as well as the application of some of them to create graphical representations of functions. Specifically, using the GeoGebra dynamic geometric environment, the operations of addition, subtraction, multiplication, division, and the square root are explored in the set of positive numbers, and the operations of multiplication, division and the square root are applied to the definition of graphical representations. Once the numerical operations have been explored, an analysis of the mathematical objects involved in these operations is carried out, highlighting the following three dimensions: 1) enumeration of the mathematical objects involved in each operation; 2) the relationships between operations and mathematical objects; 3) and application of these relationships to establish the complexity of operations.
References
Ausubel, D., Novak, J., & Hanesian, H. (1980). Psicologia educacional. Rio de Janeiro: Interamericana.
Fernandes, J. A. (1990). Concepções erradas na aprendizagem de conceitos probabilísticos. Dissertação (Mestrado em Educação), Universidade do Minho, Braga, Portugal.
Fernandes, J. A., & Vaz, O. (1998). Porquê usar tecnologia nas aulas de matemática? Boletim da SPM, 39, 43-55.
Fernandes, J. A., Alves, M. P., Viseu, F. & Lacaz, T. M. (2006). Tecnologias de informação e comunicação no currículo de Matemática do ensino secundário após a reforma curricular de 1986. Revista de Estudos Curriculares, 4(2), 291-329.
García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus tasks, International Journal of Mathematical Education in Science and Technology, 49(2), 227-252.
Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39(1-2), 127- 135.
Henriques, A., & Fernandes, J. A. (2015). O ensino da Estatística nas recentes orientações curriculares. In A. Borralho, E. Barbosa, I. Vale, H. Jacinto, J. Carvalho e Silva, & J. Latas (Orgs.), ProfMat2015: Matemática, currículo e desenvolvimento curricular (pp. 48-67). Évora: Associação de Professores de Matemática.
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale: Lawrence Erlbaum Associates.
MEC (2018). Base Nacional Comum Curricular - Educação é a Base. Brasília: Ministério da Educação.
Ministério da Educação e Ciência (2013). Programa e Metas Curriculares de Matemática: ensino básico. Lisboa: Autor.
Ministério da Educação e Ciência (2014). Programa e Metas Curriculares de Matemática A: ensino secundário. Lisboa: Autor.
NCTM (2000). Principles and standards for school mathematics. Reston: Autor.
Novak, J. D., & Gowin, D. B. (1996). Aprender a aprender. Lisboa: Plátano Edições Técnicas.
Petocz, P., & Reid, A. (2007). Learning and assessment in statistics. In B. Phillips, & L. Weldon (Eds.), The Proceedings of the ISI/IASE Satellite on Assessing Student Learning in Statistics. Voorburg: International Statistical Institute.
Skemp, R. R. (1993). The psychology of learning mathematics. Hillsdale: Lawrence Erlbaum Associates.
Soares, L. H. (2009). Aprendizagem significativa na educação matemática: uma proposta para a aprendizagem de Geometria Básica. Dissertação (Mestrado em Educação), Universidade Federal da Paraíba, João Pessoa, Brasil.
Viseu, F., Fernandes, J. A., Fernandes, M. C., Faria, M. S., & Duarte, P. (2009). Os mapas de conceitos na aprendizagem de Estatística por alunos do 10º ano do ensino profissional. In P. Dias, & A. Osório (Eds.), VI Conferência Internacional de TIC na Educação: Challenges 2009 (pp. 873-885). Braga: Centro de Competência da Universidade do Minho.
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-248.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Revista do Instituto GeoGebra Internacional de São Paulo
This work is licensed under a Creative Commons Attribution 4.0 International License.
Submission, processing, and publication of articles sent to the journal and registration of the DOI at Crossref is free of charge.
Authors retain their copyright and grant the journal the right of first publication of their article, which is simultaneously licensed under a Creative Commons - Attribution 4.0 International license CC BY that allows others to share the article by acknowledging its authorship and initial publication by the journal.
The GeoGebra journal encourages its authors to register their work with information and communication management systems aimed at researchers, such as Academia.edu, Mendeley, ResearchGate, etc.
10.23925
