Razones Trigonométricas con GeoGebra

JAVIER ANTONIO RIOS RIVERA, Jul 11, 2017

The comprehension of the trigonometrical reasons by means of the software GeoGebra in the context of the model of Van Hiele is an offer that searches by means of a study of cases, analyzes the comprehension of the trigonometrical reasons of the students of degree 10, where there arise contributions and such important elements as the used language and the meaning of the geometric and trigonometrical contents, pass through for certain processes of thought and levels of knowledge, well–balanced in experiences inside the practices of classroom. keeping in mind that the joint of the model in mind of Van Hiele with the concepts and pre-concepts established for the comprehension of the trigonometrical reasons, they arise hypothetical describers of the levels of reasoning by Van Hiele, thanks to the results of a diagnostic test and the questions related to the visualization of elements elaborated by means of the software GeoGebra. These strategies allow to deduce in what level the students are and this way from a module of learning there is claimed that they advance from a level to other one, by means of a series of cognitive activities in relation with the comprehension and the phases of learning of Van Hiele.

Table of Contents

  1. GENERAL OBJECTIVE
  2. SPECIFIC OBJECTIVES
  3. Levels of reasoning according to Van Hiele
  4. Learning Phases according to Van Hiele
  5. Learning Phases according to Van Hiele
  6. Learning Module
    1. Modulo de Aprendizaje: COMPRENSIÓN DE LAS RAZONES TRIGONOMETRICAS MEDIANTE EL SOFTWARE GEOGEBRA EN EL MODELO DE VAN HIELE
  7. Conclusions
  8. References

1.

GENERAL OBJECTIVE

Analyze the understanding of trigonometric ratios, in The context of the van Hiele model, using the GeoGebra software.


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2.

SPECIFIC OBJECTIVES

Design a diagnostic activity based on the visualization, the recognition of properties and definitions that allows recognizing the previous concepts to approach the trigonometric reasons. To determine the descriptors of the levels of reasoning of van Ice to locate a student at one of these levels, in Relation to the concepts associated with the trigonometric ratios, Using GeoGebra software. Design a learning module framed in the van Hiele model, which arises from the diagnostic activity, to achieve an advance in the understanding of trigonometric reasons, from GeoGebra software. Apply and evaluate a learning module to analyze the understanding of trigonometric ratios.


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3.

Levels of reasoning according to Van Hiele

Level 0: Visualization or recognition Perceives the figures as a whole Does not detect relationships between forms and parts Does not differentiate attributes and components. Level 1: Analysis Perceives the components and properties of Objects and figures as necessary conditions. Level 2: Ordination or Classification Describe the figures in a formal way. It indicates necessary and sufficient conditions. Level 3: Formal deduction Performs logical and formal deductions and demonstrations. It justifies the proposals put forward. Level 4: Rigor It knows the existence of different axiomatic systems and analyzes them to compare different geometries.


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4.

Learning Phases according to Van Hiele

Phase 1: Information Prior knowledge is determined in Reference to a certain theme. Phase 2: Guided guidance It is structured from a series of activities. Phase 3: Explanation It argues the procedures and each response obtained. Exchange of ideas and experiences. Phase 4: Free Orientation Activities aimed to deepening knowledge. Application and relationship between concepts and properties. Phase 5: Integration Synthesis of the related and studied. Integration of previous and acquired knowledge


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5.

Learning Phases according to Van Hiele

Phase 1: Information Prior knowledge is determined in Reference to a certain theme. Phase 2: Guided guidance It is structured from a series of activities. Phase 3: Explanation It argues the procedures and each response obtained. Exchange of ideas and experiences. Phase 4: Free Orientation Activities aimed to deepening knowledge. Application and relationship between concepts and properties. Phase 5: Integration Synthesis of the related and studied. Integration of previous and acquired knowledge


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6.

Learning Module

Nuestra práctica docente en el municipio de Sahagún, departamento de Córdoba, Colombia nos ha permitido evidenciar que algunos estudiantes del grado décimo tienen dificultades para comprender los conceptos relacionados con las razones trigonométricas, dado que no logran comprender, en años anteriores, ciertos conceptos previos necesarios para la comprensión de las primeras ideas acerca de la trigonometría. En este sentido, notamos una desarticulación entre lo que se supone debe estar comprendido y las nuevas ideas que se deben desarrollar en el grado décimo. De acuerdo con el modelo de van Hiele, se propusieron unos descriptores hipotéticos para reconocer en qué nivel se encontraban los estudiantes y qué conceptos se debían tener en cuenta para el paso de un nivel al siguiente; estos descriptores sirvieron de insumo para el diseño de las actividades del módulo enmarcadas en las fases de aprendizaje y la visualización de elementos elaborados en el software GeoGebra.

  • 1. Modulo de Aprendizaje: COMPRENSIÓN DE LAS RAZONES TRIGONOMETRICAS MEDIANTE EL SOFTWARE GEOGEBRA EN EL MODELO DE VAN HIELE

6.1.

Modulo de Aprendizaje: COMPRENSIÓN DE LAS RAZONES TRIGONOMETRICAS MEDIANTE EL SOFTWARE GEOGEBRA EN EL MODELO DE VAN HIELE

Modulo de Aprendizaje COMPRENSIÓN DE LAS RAZONES TRIGONOMETRICAS MEDIANTE EL SOFTWARE GEOGEBRA EN EL MODELO DE VAN HIELE
– JAVIER ANTONIO RIOS RIVERA

7.

Conclusions

Achievement of proposed objectives for the understanding of trigonometric ratios using GeoGebra software 2. Location of students in level 3 van hiele reasoning model 3. Management of the GeoGebra tool as a driving force for learning 4. Significant contributions to mathematics, especially to trigonometry Learning module for the understanding of trigonometric ratios, using GeoGebra software Input for basic and average mathematics teachers Validity of van hiele model for the understanding of trigonometric ratios Study reference for future undergraduate and postgraduate work


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8.

References

Algarín, D. and Leal, J. (2013). Characterization of Van Hiele's levels of reasoning specific to the processes of description, definition and demonstration in the learning of trigonometric ratios. Scientific Review, 56-60. Retrieved from http://cibem.semur.edu.uy/7/actas/pdfs/260.pdf Araya, A., Monge, A. and Morales, C. (2007). Understanding the trigonometric ratios: Levels of understanding, indicators and tasks for analysis. Current research in education, 7 (2), 1-31. Retrieved from http://www.redalyc.org/pdf/447/44770207.pdf Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics. Ausubel, D., Novak, J. and Hanesian, H. (1976). Educational psychology: a cognitive point of view. Mexico: Trillas. Available at: http://cmapspublic2.ihmc.us/rid=1J3D72LMF- 1TF42P4-PWD / learning% 20significtivo.pdf   Ausubel, D. (1983). Theory of meaningful learning. FACTS OF CEIF. Available in: Http: //www.xn--delegacin233 M7hb.bligoo.mx/media/users/20/1002571/files/240726/Aprendizaje_significativo.pdf Ausubel, D., Novak, J. and Hanesian, H. (1993). Educational psychology, a point of view cognitive. Mexico. Trillas. Baquero, R. (1999). Vigotsky and school learning. Madrid. Spain: Aique Grupo Editor S.A. Available at: http://cmapspublic3.ihmc.us/rid=1MQLSN4JP-17YHV2W-14J7/art%C3%ADculo.pdf Bravo, M., González, N. and Paz, A. (2014). Didactic sequences for the learning of Trigonometric reasons (undergraduate thesis). Cali, Colombia: Catholic University of Manizales. Recovered from: http://repositorio.ucm.edu.co:8080/jspui/bitstream/handle/10839/845/Martha%20Piedad%20Bravo%20Pineda.pdf?sequence=1


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