Two-Column Demonstrations in Math Olympiad Geometry Problems: The Case of Honduras
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Abstract
In elementary plane geometry courses since the beginning of the 20th century, two-column demonstrations have been taught as a form of formal proof. Nevertheless, there is not much research on the use of this type of demonstrations in Mathematical Olympiad Problems. As a result, this study arises in which we analyzed Mathematics mistakes that students make when attempting to solve geometry problems in the Mathematical Olympiad before and after the implementation of two-column demonstrations in the problem-solving process. A total of 32 students from different departments of Honduras participated in the study. The place of study was the Virtual Math Competition (CVM) and the analysis is based on a method called Newman Error Analysis. In the pre-exam, the results show that students do not use two-column demonstrations for their answers, and the most common mistakes analyzed using the Newman Error are transformation, process skill, and encoding errors. On the other hand, in the final test, the use of two-column demonstrations by the students confirmed that this writing technique helps to order the information given in the problem.
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References
Department of Mathematics, University of Toronto. (2000). Writing Up Solutions. http://www.math.toronto.edu/barbeau/writingup.pdf
Djukić, D., Janković, V., Matić, I., & Petrović, N. (2011). The IMO Compendium: A Collection of Problems Suggested for the International Mathematical Olympiads: 1959-2009 Second Edition. Springer New York.
Bellanca, J., & Stirling, T. (2011). Classrooms without borders: Using internet projects to teach communication and collaboration. Teachers College Press.
Chen, E. (2021). Euclidean geometry in mathematical olympiads (Vol. 27). American Mathematical Soc.
Engel, A. (2008). Problem-solving strategies. Springer Science & Business Media.
Ramos Palacios, L. A. (2006). Una estrategia metodológica para desarrollar olimpiadas matemáticas en el nivel medio del sistema educativo hondureño. [Tesis de Maestría, Universidad Pedagógica Nacional Francisco Morazán].
Hang, K. H., & Wang, H. (2017). Solving problems in geometry: Insights and strategies for mathematical Olympiad and competitions (Vol. 10). World Scientific Publishing Company.
Herbst, P. G. (2002). Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49(3), 283-312. https://doi.org/10.1023/A:1020264906740
Idris, R. (2017). Mengatasi kesulitan belajar dengan pendekatan psikologi kognitif. Lentera pendidikan: jurnal ilmu tarbiyah dan keguruan, 12(2), 152-172. https://doi.org/10.24252/lp.2009v12n2a3
Moncada, J. M. (1904). Educación, trabajo y ciencia: (método de enseñanza integral). Retrieved from https://www.cervantesvirtual.com/nd/ark:/59851/bmcpk120
Newman, A. (1983). The Newman language of mathematics kit: Strategies for diagnosis and remediation. Sydney: Harcourt Brace Jovanovich Group.
Pérez, G. (1996). Historia de la educación superior de Honduras: antecedentes históricos 1733 – 1847
Pérez, G. (1997). Historia de la educación Superior de Honduras: Ciento cincuenta años de vida universitaria
Portillo, A. (2003). La Educación Superior en Honduras 1949-2000 Vol. III. Bosquejo Histórico de las Unidades Académicas (pp. 1-239).
Robert Osserman, Are proofs in high school geometry obsolete? J. Math. Behavior, to appear.
Valencia, M. R. M. (2014). Honduras: Origins, Development, and Challenges in the Teaching of Mathematics. Mathematics and Its Teaching In The Southern Americas: With An Introduction By Ubiratan D'ambrosio, 10, 265. https://doi.org/10.1142/9789814590570_0011
Weiss, M., Herbst, P., & Chen, C. (2009). Teachers’ perspectives on “authentic mathematics” and the two-column proof form. Educational Studies in Mathematics, 70(3), 275-293.
Wu, H. (1996). The role of Euclidean geometry in high school. Journal of mathematical behavior, 15(3), 221-238.
Xiong, B., & Lee, P. Y. (Eds.). (2007). Mathematical Olympiad in China: problems and solutions. World Scientific