Facilitando el aprendizaje de trigonometría a través de una interfaz tangible
Abstract
In mathematics education, studies reveal difficulties in the teaching-learning of trigonometry in secondary and higher education, where students are not encouraged to achieve a deep conceptual understanding of the associated concepts. Considering the importance of trigonometry for multiple disciplines, it becomes necessary to implement new approaches that foster students to take an active role in their own learning. Several studies demonstrate that incorporating digital technologies have a positive impact on students’ learning. However, most of the existing technologies do not consider the use of the body and multiple senses. Tangible User Interfaces (TUIs) in contrast, can host bodily interactions that apply principles of the Embodied Cognition Theory. Nonetheless, there is a lack of applications of TUIs for trigonometry education. This study consisted in designing and validating a tangible interface for the teaching-learning of basic concepts of trigonometry. The interface hosts a pedagogical experience that privileges exploration, the use of intuition, and fosters collaborative learning. A Pre-Test was applied to 119 students to determine previous knowledge, yielding a 29.1% performance. After two interventions with the interface, the results of a Post-Test reveal an increase of 37.1%, confirming the educational effectiveness of the interface and the pedagogical experience to facilitate learning of basic concepts of trigonometry.
References
Ambrose, S., Bridges, M., Dipietro, M., Lovett, M., & Norman, M. (2010). Seven ResearchBased Principles for Smart Teaching (Vol. 48). https://doi.org/10.1002/mop.21454
Bravo, U. (2016). Visual analogies: representation of the design process and its application in the field of education. Base Diseño e Innovación, 2, 42-49.
Brown, S. A. (2006). The trigonometric connection: Students’ understanding of sine and cosine. In Proceedings of 30th Conference of the International Group for the Psychology of Mathematics Education, vol. 1.
Camilleri, M. A., & Camilleri, A. C. (2017). Digital Learning Resources and Ubiquitous Technologies in Education. Technology, Knowledge and Learning, 22(1), 65-82. https://doi.org/10.1007/s10758-016-9287-7
Chin, J. P., Diehl, V. A., & Norman, L. K. (1988). Development of an instrument measuring user satisfaction of the human-computer interface. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems - CHI ’88. https://doi.org/10.1145/57167.57203
Council, D. (2014). Innovation by Design. Customer Relationship Management, p. 23. Design Council.
Curri, E. (2012). Using Computer Technology in Teaching and Learning Mathematics in an Albanian Upper Secondary School: The Implementation of SimReal in Trigonometry Lessons. Universitetet i Agder; University of Agder.
De Raffaele, C., Smith, S., & Gemikonakli, O. (2018). An Active Tangible User Interface Framework for Teaching and Learning Artificial Intelligence. Proceedings of the 2018 Conference on Human Information Interaction&Retrieval - IUI ’18, 535-546. https://doi.org/10.1145/3172944.3172976
Dockendorff, M., & Solar, H. (2018). ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra. International Journal of Mathematical Education in Science and Technology, 49(1), 66-84. https://doi.org/10.1080/0020739X.2017.1341060
Dodge, E., & Lakoff, G. (2005). Image schemas: From linguistic analysis to neural grounding. From Perception to Meaning: Image Schemas in Cognitive Linguistics, 57-91.
Driscoll, M. P. (2000). Psychology of learning for Instruction (2nd ed.). Allyn & Bacon.
Dumas, J. S., & Redish, J. (1999). A practical guide to usability testing. Intellect books.
Font, V., Bolite, J., & Acevedo, J. (2010). Metaphors in mathematics classrooms: Analyzing the dynamic process of teaching and learning of graph functions. Educational Studies in Mathematics, 75(2), 131–152. https://doi.org/10.1007/s10649-010-9247-4
Gentner, D., & Nielson, J. (1996). Anti-Mac Interface. Communications of the ACM, 39(8), 70-82. https://doi.org/10.1145/232014.232032
Hollan, J., Hutchins, E., & Norman, D. (1985). Direct manipulation interfaces. HumanComputer Interaction, 1, 311-338.
Hornecker, E., & Buur, J. (2006). Getting a grip on tangible interaction. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems - CHI ’06, 437-446. https://doi.org/10.1145/1124772.1124838
Houde, S., & Hill, C. (1997). What do Prototypes Prototype? Handbook of HumanComputer Interaction, 367-381. https://doi.org/10.1016/B978-044481862-1.50082-0
Ishii, H., & Ullmer, B. (1997). Tangible Bits: Towards Seamless Interfaces Between People, Bits and Atoms. Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems, 234-241. https://doi.org/10.1145/258549.258715
Jetter, H. C., Reiterer, H., & Geyer, F. (2014). Blended Interaction: Understanding natural human-computer interaction in post-WIMP interactive spaces. Personal and Ubiquitous
Computing, 18(5), 1139-1158. https://doi.org/10.1007/s00779-013-0725-4
Johnson, M. (2013). The body in the mind: The bodily basis of meaning, imagination, and reason. University of Chicago Press.
Kepceoğlu, I., & Yavuz, I. (2016). Teaching a concept with GeoGebra: Periodicity of trigonometric functions. Educational Research and Reviews, 11(8), 573-581. https://doi.org/10.5897/err2016.2701
Lakoff, G. (2009). The Neural Theory of Metaphor. Ssrn. https://doi.org/10.2139/ssrn.1437794
Lakoff, G., & Núñez, R. E. (2000). Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (1st ed.). New York, NY, USA: Basic Books.
Marshall, P. (2007). Do tangible interfaces enhance learning? Proceedings of the 1st International Conference on Tangible and Embedded Interaction, 163-170. https://doi.org/10.1145/1226969.1227004
Mesa, V., & Goldstein, B. (2016). Conceptions of Angles, Trigonometric Functions, and Inverse Trigonometric Functions in College Textbooks. International Journal of Research in Undergraduate Mathematics Education, 3(2), 338-354. https://doi.org/10.1007/s40753-016-0042-1
Mushipe, M., & Ogbonnaya, U. I. (2019). Geogebra and Grade 9 Learners’ Achievement in Linear Functions. International Journal of Emerging Technologies in Learning (IJET), 14(08), 206-219. https://doi.org/10.3991/ijet.v14i08.9581
Pecher, D., Boot, I., & Van Dantzig, S. (2011). Abstract Concepts: Sensory-Motor Grounding, Metaphors, and Beyond. Psychology of Learning and Motivation, 54, 217-248. https://doi.org/10.1016/B978-0-12-385527-5.00007-3
Resnick, M., Myers, B., Nakakoji, K., Shneiderman, B., Pausch, R., Selker, T., & Eisenberg, M. (2005). Design Principles for Tools to Support Creative Thinking. NSF Workshop Report on Creativity Support Tools, (Creativity Support Tools), 25–35.
Scarlatos, L. (2002). An application of tangible interfaces in collaborative learning environments. SIGGRAPH ’02, 125-126. https://doi.org/10.1145/1242073.1242141
Shaer, O., & Hornecker, E. (2010). Tangible User Interfaces: Past, Present, and Future Directions. Foundations and Trends® in Human–Computer Interaction, 3(1-2), 1-137. https://doi.org/10.1561/1100000026
Skinner, B. F. (1976). About Behaviorism. Vintage.
Thompson, P. W., Carlson, M. P., & Silverman, J. (2007). The design of tasks in support of teachers’ development of coherent mathematical meanings. Journal of Mathematics Teacher Education, 10(4–6), 415-432. https://doi.org/10.1007/s10857-007-9054-8
Vygotsky, L. S. (1980). Mind in society: The development of higher psychological processes. Harvard university press.
Weber, K. (2005). Students’ understanding of trigonometric functions. Mathematics Education Research Journal, 17(3), 91-112. https://doi.org/10.1007/BF03217423
Zengin, Y. (2018). Incorporating the dynamic mathematics software GeoGebra into a history of mathematics course. International Journal of Mathematical Education in Science and Technology, 49(7), 1083-1098. https://doi.org/10.1080/0020739X.2018.1431850
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