Geometric interpretation of the signs of trigonometric ratios with Geogebra

Authors

  • Stephanie Chiquinquirá Díaz Urdaneta Asociación Aprender en Red. Grupo TEM - Tecnologías en la Educación Matemática
  • Juan Luis Prieto González Universidad del Zulia. Asociación Aprender en Red. Grupo TEM - Tecnologías en la Educación Matemática
  • Ana Del Valle Duarte Castillo Universidade Federal do Pará - UFPA

DOI:

https://doi.org/10.18542/amazrecm.v13i28.4907

Keywords:

trigonometric ratios, mnemonic devices, GeoGebra

Abstract

The teaching of Trigonometry has been characterized by an algebraic approach, which has made its study a memoristic and a mechanical process. A content where the previous can be evidenced is the signs of the trigonometric ratios, which tend to be treated through the use of mnemonic devices, action that limits its comprehension. With the aim of supporting the overcoming of this problem, in this paper it is described the design of an elaborated resource with the software GeoGebra and its application in a sequence to analyze and make sense of the Sine, Cosine and Tangent ratios. The design of the resource was based on the TPACK model (Mishra & Koehler, 2006). It is deemed pertinent that teachers have this style of resources in the sense that these help them in their teaching practices supported on technological environments like GeoGebra.

References

BORBA, M. D. C. Students’ understanding of transformations of functions using multirepresentational software. 1993.

Doctoral Dissertation - Cornell University Ithaca, NY. 1993.

BORBA, M. D. C. & VILLARREAL, M. Humans-with-media and the reorganization of mathematical thinking: information and communication technologies, modeling, experimentation and visualization. 1 ed. New York: Springer, 2005.

BRITO, A. & MOREY, B. Trigonometria: dificuldades dos professores de matemática do ensino fundamental. Revista Horizontes, v.22 , p. 65-70, 2004.

CHACÓN, A., SÁNCHEZ, A. & QUIRÓS, C. Comprensión de las razones trigonométricas: niveles de comprensión, indicadores y tareas para su análisis. Revista Electrónica Actualidades Investigativas en Educación, v. 7 (2), p. 01-31, 2007.

COUTINHO, Clara Pereira. TPACK: Em Busca de um Referencial Teórico para a Formação de Professores em Tecnologia Educativa. Revista Paidéi@. UNIMES VIRTUAL, Vol.2, Número 4, JUL. 2011. Disponível em http://revistapaideia.unimesvirtual.com.br.

DÍAZ, S. & PIETRO, J. El análisis de los signos de las razones trigonométricas con tecnologías. Una manera de trascender las reglas prácticas. Comunicación presentada en el VIII Congreso Venezolano de Educación Matemática. Coro, 2013.

DIKOVIĆ, L. Applications geogebra into teaching some topics of mathematics at the college level. Computer Science and Information Systems, v. 6 (2), p. 191-203, 2009.

DUVAL, R. Quel cognitif retenir en didactique des mathématiques. Recherches en Didactique des Mathématiques, v. 16 (3), p. 349-382, 1996.

FI, C.D. Preservice secondary school mathematics teachers' knowledge of trigonometry: cofunctions. Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, v. 2, p. 833-834, 2006.

FIALLO, J. Estudio del proceso de Demostración en el aprendizaje de las Razones Trigonométricas en un ambiente de Geometría Dinámica. 2010 Tesis Doctoral Universitat de València, Valencia, 2010.

FIALLO LEAL, J.E., GUTIÉRREZ RODRÍGUEZ, A. Unidad de enseñanza de las razones trigonométricas en un ambiente Cabri para el desarrollo de las habilidades de demostración. Comunicación presentada en X Simposio de la SEIEM. Huesca, 2007.

GUTIÉRREZ, R. & PRIETO, J.L. Deformación y reflexión de funciones con GeoGebra. El caso de las parábolas definidas por la expresión . Números, v. 88, p. 115-126, 2015.

HOHENWARTER, M. Dynamic investigation of functions using geogebra. Proceedings of Dresden International Symposium on Technology and its Integration into Mathematics Education 2006. Dresden, Germany: DES-TIME. Disponível em: Acesso em: 01/02/2015.

LABORDE, C., KYNIGOS, C., HOLLEBRANDS, K. & STASSER, R. Teaching and learning geometry with technology. En A. Gutiérrez & P. Boero (Eds.), Handbook of Research on the Psychology of Mathematics Education, pp. 275-304, 2006.

LU, Y. W. A. Linking geometry and algebra: a multiple-case study of uppersecondary mathematics teachers’ conceptions and practices of GeoGebra in England and Taiwan. 2008 Unpublished Master's thesis - University of Cambridge, Cambridge, 2008.

MISHRA, P., & KOEHLER, M. Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, v. 108 (6), p. 1017-1054, 2006.

NAVARRO, E. Curso Proedeutico de Matemática. 1ed. Caracas: Litho-Tip, 1970.

Published

2017-12-30

Issue

Section

Artigos Científicos