The exploration of triangle properties in GeoGebra Discovery by elementary school students
DOI:
https://doi.org/10.23925/2237-9657.2023.v12i3p133-161Keywords:
GeoGebra Discovery, demonstration and proof, Plane GeometryAbstract
This research presents partial results of Doctoral research in Mathematics Education. We use a new version of GeoGebra, called GeoGebra Discovery. This is a qualitative investigation and the research participants are students enrolled in the 8th year of Elementary School. We present two activities of a didactic sequence, applied under the Design Experiments methodology and analyzed through the levels of understanding and development of van Hiele's geometric thinking (1984). The results indicate that the exploration and verification of conjectures of properties of the plane geometry, in particular of the triangle, using GeoGebra Discovery, can contribute to a dynamic, exploratory and significant learning of students.
Key-words: GeoGebra Discovery; demonstration and proof; plane geometry.
Downloads
Metrics
References
ABAR, C. A. A. P.; COTIC, N. S. GeoGebra: na produção do conhecimento matemático. 1. ed. São Paulo: Iglu Editora Ltda, 2014.
ALMOULOUD, S. A. Demonstration in geometry: historical and philosophical perspectives. Revista Pesquisa Qualitativa, v. 8, n. 18, p. 540-570, 7 out. 2020.
BALACHEFF, N. Aspects of proof in pupils’ practice of school mathematics,. En Pimm, D. (ed.), Mathematics, teachers and children, Hodder & Stoughton: Londres, p. 216-235, 1988.
BOTANA, F. et al. Hacia un autómata geómetra. La Columna de Matemática Computacional, v. 23, p. 343-371, 2020.
BROWN, A. L. Design Experiments: Theoretical and Methodological Challenges in Creating Complex Interventions in Classroom Settings. Journal of the Learning Sciences, v. 2, n. 2, p. 141-178, 1992.
COBB, P. et al. Design Experiments in Educational Research. Educational Researcher, v. 32, n. 1, p. 9-13, 1 jan. 2003.
COLLINS, A.; JOSEPH, D.; BIELACZYC, K. Design Research: Theoretical and Methodological Issues. Journal of the Learning Sciences, v. 13, n. 1, p. 15-42, jan. 2004.
DE VILLIERS, M. The Role of Proof in Investigative, Computer-based Geometry: Some personal reflections. In: KINHG, J.; SCHATTSCHNEIDER, D. (Eds.). Geometry Turned On! Dynamic Software in Learning, Teaching, and Research. Washington: The Mathematical Association of America, 1997. p. 15-24.
DE VILLIERS, M. Papel e funções da demonstração no trabalho com o Sketchpad. Tradução de Eduardo Veloso. Educação matemática, n. 62, 2001. Disponível em: <https://docplayer.com.br/35710051-Papel-e-funcoes-da-demonstracao-no-trabalho-com-o-sketchpad.html>. Acesso em: 20/03/2021.
DE VILLIERS, M. Using dynamic geometry to expand mathematics teachers’ understanding of proof. International Journal of Mathematical Education in Science and Technology, v. 35, n. 5, p. 703-724, set. 2004.
DE VILLIERS, M. Proof in Dynamic Geometry : More than Verification. Proceedings of the Ninth International Conference Mathematics Education in a Global Community, July, 2007.
DOERR, H. M.; WOOD, T. Pesquisa-Projeto (design research): aprendendo a ensinar Matemática. In: BORBA, M. C. (Ed.). Tendências internacionais em formação de professores de Matemática. Belo Horizonte: Autêntica. 2006. p. 113-128.
FUYS, D.; GEDDES, D.; TISCHLER, R. English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M. van Hiele. 1. ed. New York: [s.n.]. 1984. v. 1.
GOMBAUD, S. La démonstration, une approche historique et critique. 2007. Disponível em: <https://irem.univ-reunion.fr/IMG/pdf/Gombaud_Demonstration.pdf>. Acesso em: 10/08/2020.
HANNA, G. Proof, Explanation and Exploration: an Overview. In: JONES, K.; GUTIÉRREZ, Á.;
MARIOTTI, M. A. (Eds.). Educational Studies in Mathematics. [s.l.] Springer Nature, 2000. v. 44, p. 5-23.
HANNA, G.; DE VILLIERS, M. Proof and Proving in Mathematics Education. Dordrecht: Springer Netherlands, 2012. v. 15.
HANNA, Gila. Beyond verification : Proof can teach new methods. ICMI Symposium Rome 2008, 1–5. http://www.unige.ch/math/EnsMath/Rome2008/ALL/Papers/HANNA.pdf
HOHENWARTER, M.; KOVÁCS, Z.; RECIO, T. Determinando propiedades geométricas simbólicamente con GeoGebra. Revista de Didáctica de las Matemática, v. 100, n. 1, p. 79-84, 2019.
HOYLES, C. The Curricular Shaping of Students’ Approaches to Proof. For the Learning of Mathematics, 17(1), p. 7–16, 1997.
KOVÁCS, Z., RECIO, T., RICHARD, P. R., & VÉLEZ, M. P. GeoGebra Automated Reasoning Tools: A tutorial with examples. Aldon, G., Trgalova, J., Proceedings of the 13th International Conference on Technology in Mathematics Teaching, July 2017, 400–404. https://www.researchgate.net/publication/321162514%0AGEOGEBRA
MANSON, N. Is operations research really research? ORiON, v. 22, n. 2, p. 155-180, 2006.
MARIOTTI, M. A. Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, v. 44, n. 1-3, p. 25-53, 2000.
OLIVERO, F. The proving process within a dynamic geometry environment. University of Bristol, 2002.
PATSIOMITOU, S., BARKATSAS, A., & EMVALOTIS, A. Secondary Students ’ “ Dynamic Reinvention of Geometric Proof ” Through the Utilization of Linking Visual Active Representations. Journal of Mathematics and Technology, p. 43–56, 2010.
SIMON, H. A. The Sciences of the Artificial. 3. ed. [s.l.] MIT Press, 1996. v. 11.
USISKIN, Z., Van Hiele Levels and Achievement in Secondary School Geometry. Cognitive Development and Achievement in Secondary School Geometry Project. Chicago: Universidade de Chicago, 1982.
VAN HIELE-GELDOF, D. The Didactics of Geometry in the Lowest Class of Secondary School. English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M. van Hiele, editado por David Fuys, Dorothy Geddes, Rosamond Tischler como parte do projeto de pesquisa “An Investigation of the van Hiele Model of Thinking in Geometry among Adolescents”, Research in Science Education (RISE). Program of the National Science Foundation. Washington, D.C. 1984. (Trabalho original publicado em 1957.)
WALKER, D. Toward productive design studies. In: AKKER, J. VAN DEN et al. (Eds.). Education Design Research. 1. ed. New York: Routledge Taylor & Francis e-Library, 2006. p. 8-15.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 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.