Spatial geometric thinking and its articulation with the visualization and manipulation of objects in 3D
DOI:
https://doi.org/10.23925/1983-3156.2023v25i2p258-277Keywords:
Spatial Geometric Thinking, Visualization, GeoGebra, Mathematics educationAbstract
This paper aims to build a conceptual framework that addresses spatial geometric thinking and the respective visualization skills required at different levels of the schooling process. Studies indicate that spatial geometric sills are essential for scientific thinking. It encompasses a set of cognitive processes through which humans can construct and manipulate mental representations of objects in space and is a skill directed towards understanding objects and their relations in the 2D and 3D worlds. The use of these spatial reasoning skills involves drawing, manipulating, and explaining objects and their relationships and should be developed from the first years of schooling. Based on this theoretical context, partial research results on surface representations that can be manipulated in three dimensions (3D) and obtained through GeoGebra will be presented in this paper. The underlying theory was Duval's Theory of Registers of Semiotic Representation, which allowed the analysis of activities developed by graduate students in Mathematics Education by observing and physically manipulating such representations to obtain the respective graphic and algebraic records. The conceptual framework constructed and presented in this article contributed to identifying other skills required in this study for the development of spatial geometric thinking.
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Cheng, Y.L., & Mix, K.S. (2014). Spatial Training Improves Children's Mathematics Ability. Journal of Cognition and Development, 15, 11 - 2.
Duval, R., & Moretti, T. (2012). Registros de representação semiótica e funcionamento cognitivo do pensamento Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Revemat: Revista Eletrônica de Educação Matemática, 7(2), pp. 266–297.
Duval, R. (2011). Registros de representações semióticas e funcionamento cognitivo da compreensão em matemática. In: MACHADO, S. D. de A. (Org.). Aprendizagem em Matemática: registros de representação semiótica. 8. ed. Campinas, SP: Papirus.
Duval, R. (2006). A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics, 61, 103-131.
http://dx.doi.org/10.1007/s10649-006-0400-z
Duval, R. (2000). Basic issues for research in Mathematics Education. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 24th Conference fo the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 55-69). Hiroshima, Japan: PME.
Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century: An ICMI study. Dordrecht: Kluwer.
Gardner, H. (1983). Frames of Mind: A Theory of Multiple Intelligences. New York: Basic Books.
Gutiérrez, A. (1992). Exploring the links between van Hiele levels and 3-dimensional geometry. Structural Topology, 18, 31–48.
Gutiérrez, A. (1996). Vizualization in 3-dimensional geometry: In search of a framework. In L. Puig & A. Guttierez (Eds.), Proceedings of the 20th conference of the international group for the psychology of mathematics education, vol. 1 (pp. 3–15). Valencia: Universidad de Valencia.
Kluppel, G. T. (2012). Reflexões sobre o ensino de geometria em livros didáticos à Luz da Teoria das Representações Semióticas segundo Raymond Duval. Dissertação (Mestrado em Educação). Universidade Estadual de Ponta Grossa. Ponta Grossa.
Fujita, T., Kondo, Y., Kunimune, S., Jones, K., & Kumakura, H. (2014). The influence of 3D representations on students’ level of 3D geometrical thinking. In P. Liljedahl, S. Oesterle, C. Nicol, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (PME38 & PME-NA36) (Vol 4, pp.25-32). Vancouver, Canada: PME.
Hitt, F. (1998). Difficulties in the articulation of different representations linked to the concept of function. The Journal of Mathematical Behavior, Volume 17, Issue 1.
Lowrie, T., Logan, T., & Ramful, A. (2016). Spatial Reasoning Influences Students' Performance on Mathematics Tasks. Mathematics Education Research Group of Australasia, 407-414.
Lorenzato, S. (2006). Laboratório de Ensino de Matemática na formação de professores. Campinas: Autores Associados.
Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175-197.
Mulligan, J., Woolcott, G., Mitchelmore, M. & Davis. (2018).Connecting mathematics learning through spatial reasoning. Math Ed Res J 30, 77–87. https://doi.org/10.1007/s13394-017-0210-x
Newcombe, N. S., Uttal, D. H. & Miller, D. I., (2013). Exploring and Enhancing Spatial Thinking: Links to Achievement in Science, Technology, Engineering, and Mathematics? Current Directions in Psychological Science, 22(5), 367–373. https://doi.org/10.1177/0963721413484756
Passos, C. L. B. (2006) Materiais manipuláveis como recursos didáticos na formação de professores de matemática. In: LORENZATO, S. (org): O laboratório de ensino de Matemática na Formação de Professores. Campinas, SP: Autores Associados, pp. 77–91.
Piaget, J. (1952). The origins of intelligence in children (Vol. 8, No. 5, pp. 18-1952). New York: International Universities Press.
Pittalis, M, Christou C. (2013). Coding and decoding representations of 3D shapes. In Psychology the Journal of Mathematical Behavior. DOI:10.1016/J.JMATHB.2013.08.004
Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205–236). Rotterdam: Sense.
van Hiele, P. (1999) Developing Geometric Thinking Through Activities that Begin with Play. Teaching Children Mathematics. February 1999. (pp. 310-316)
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