Static and dynamic representations in accessing a three-dimensional mathematical object
DOI:
https://doi.org/10.5007/1981-1322.2024.e100666Keywords:
Three-Dimensional Mathematical Object, Static and Dynamic Representation, Quadric SurfacesAbstract
This article is an excerpt from doctoral research, addressing access to three-dimensional mathematical objects which, as they are abstract, require representations to do so. Aiming to understand the potentialities and limitations of possible representations, a theoretical analysis and application of a teaching and learning situation were carried out. In the theoretical analysis, we propose a framework for the classification of different two- and three-dimensional representations, static and dynamic, and a priori assessment of the characteristics of each representation. When applying the teaching and learning situation, we observe what each representation reveals or hides about the properties of quadric surfaces. The strategy used for analysis consisted of crossing data from theoretical analysis and the cognitive behaviors of three participants. Dynamic representations present a much greater range of possibilities for producing mathematical knowledge than static representations. However, the results of this investigation suggest that the representations of a three-dimensional mathematical object can be used in a complementary way and based on an analysis of its characteristics, considering the concepts covered, the proposed activities and the student's prior knowledge.
References
Azuma, R., Baillot, Y., Behringer, R., Feiner, S., Julier, S., & MacIntyre, B. (2001). Recent advances in Augmented Reality. IEEE Computer Graphics and Applications, 21(6), 34–47. Recuperado de https://ieeexplore.ieee.org/document/963459
Bicer, A., Nite, S. B., Capraro, R. M., Barroso, L. R., Capraro, M. M., & Lee, Y. (2017). Moving from STEM to STEAM: The effects of informal STEM learning on students’ creativity and problem solving skills with 3D printing | Semantic Scholar. IEEE Frontiers in Education Conference (FIE), 1, 1–6. Recuperado de https://doi.ieeecomputersociety.org/10.1109/FIE.2017.8190545
Borba, M. C., Scucuglia, R., & Gadanidis, G. (2014). Fases das Tecnologias Digitais em Educação Matemática: Sala de aula e internet em movimento. Belo Horizonte: Autêntica.
Duval, R. (2003). Registros de Representação Semióticas e Funcionamento Cognitivo da Compreensão em Matemática. In S. D. A. MACHADO (Ed.), Aprendizagem em Matemática: registros de representação semiótica (pp. 11–33). Campinas - SP: Papirus.
Duval, R. (2012). Registros de representação semiótica e funcionamento cognitivo do pensamento. Tradução: Méricles Thadeu Moretti (M. T. MORETTI, Trans.). Revista Eletrônica de Educação Matemática - REVEMAT, 7(2), 266–297. Recuperado de DOI: 10.5007/1981-1322.2012v7n2p266
Fonda, C. (2013). A pratical Guide to Your First 3D Print. In E. CANESSA, C. FONDA, & M. ZENNARO (Eds.), Low-Cost 3D Printing for Science, Education and Sustainable Development (pp. 25–60). ICTP: ICTP—The Abdus Salam International Centre for Theoretical Physics. Recuperado de https://citeseerx.ist.psu.edu/document?repid=rep 1&type=pdf&doi=bd3869ba16fd0690d1348e25e67db9ac7c18dbe8#page=13
Hedler, L. W. M. (2020). Desenvolvimento do pensamento geométrico espacial GeoGebra, Impressora 3D e Abstração Reflexionante processo de abstração reflexionante. (Tese de Doutorado em Informática na Educação). Universidade Federal do Rio Grande do Sul.
Kirner, C., & Kirner, T. G. (2011). Evolução e Tendências da Realidade Virtual e da Realidade Aumentada. In M. W. S. Ribeiro & E. R. Zorzal (Eds.), Realidade Virtual e Aumentada: Aplicações e Tendências (pp. 10–25). Uberlândia - MG: SBC. Recuperado de https://x.gd/1GxEf
Notare, M. R., & Basso, M. V. de A. (2016). Geometria Dinâmica 3D – novas perspectivas para o pensamento espacial. RENOTE - Revista Novas Tecnologias na Educação, 14(2). Recuperado de DOI: 10.22456/1679-1916.70683
Parzysz, B. (1988). Knowing vs seeing. problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19, 79–92. Recuperado de https://doi.org/10.1007/BF00428386
Parzysz, B. (1991). Representation of space and students’ conceptions at high school level. Educational Studies in Mathematics, 22(6), 575–593. Recuperado de DOI: 10.1007/BF00312716
Pereira, L., Oliveira, D., Couto, I., Oliveira, A., & Silva, R. L. de S. da. (2017). Uma Ferramenta de Apoio ao Ensino de Cálculo com Realidade Aumentada. In Anais Do XXVIII Simpósio Brasileiro de Informática Na Educação (SBIE 2017), 1(1), 595. Recuperado de doi: 10.5753/cbie.sbie.2017.595
Ribeiro, L. O. M., Guterres, L. X., & Silveira, D. N. (2020). O Uso Da Realidade Aumentada Com Dispositivos Móveis Na Educação Matemática Como Potência Na Geometria Espacial. PLURAIS - Revista Multidisciplinar, 5(2), 40–57. Recuperado de DOI: 10.29378/plurais.2447-9373.2020.v5.n2.8922
Schaun, T. T. (2019). As Representações Tridimensionais das Superfícies Quádricas na Disciplina de Cálculo com Realidade Aumentada (Dissertação de Mestrado em Educação Matemática). Universidade Federal de Pelotas.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Nubia Lúcia Cardoso Guimaraes, Márcia Rodrigues Notare
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors hold the copyright and grant the journal the right for their articles' first publication, being their works simultaneously licensed under the Creative Commons Attribution License (CC BY), which allows the sharing of such works with its authorship acknowledged and its initial publication in this journal.
Authors are allowed to enter into separate additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or as a book chapter, with an acknowledgment of its initial publication in this journal).
