Mecanismos articulados: Geometría Dinámica y Cinemática en un entorno educativo STEM
Contenido principal del artículo
Resumen
Una propuesta concreta de uso de un Sistema de Geometría Dinámica en un entorno educativo STEM (Science, Technology, Engineering and Mathematics) en general y en la asignatura de Matemáticas en particular, consiste en el estudio, manipulación y generación de simulaciones digitales de mecanismos articulados.
En este artículo recopilamos propuestas que argumentan a favor del uso de modelos mecánicos o articulados de mecanismos, en particular los utilizados para dibujar o trazar curvas, como un medio de generación de ideas o nociones matemáticas complejas apoyados por las posibilidades de la Geometría Dinámica. Además, este enfoque supone un recurso muy efectivo para la introducción en el aula de contextos históricos de recreación de la experiencia científica.
Presentamos dos repositorios digitales de mecanismos articulados, la Kinematics Models For Design Digital Library y el Laboratorio delle Macchine Matematiche así como una revisión de propuestas didácticas del uso educativo de este tipo de mecanismos.Palabras clave:
Citado por
Detalles del artículo
Referencias
Abánades, M.Á., et al. (2014). An algebraic taxonomy for locus computation in dynamic geometry. Computer-Aided Design 56 22–33. DOI: https://doi.org/10.1016/j.cad.2014.06.008
American Association for the Advancement of Science AAAS. (1993). Benchmarks for science literacy. New York: Oxford Press.
Artobolevskii, I. I. (1964). Mechanisms for the generation of plane curves. Pergamon.
Banks, F., & Barlex, D. (2014). Teaching STEM in the secondary school: Helping teachers meet the challenge. Routledge.
Bolt, B. (1992). Matemáquinas: la matemática que hay en la tecnología (1ª ed.) Barcelona: Labor.
Bryant, J., & Sangwin, C. (2011). How round is your circle?: where engineering and mathematics meet. Princeton University Press. DOI: https://doi.org/10.1515/9781400837953
Bussi, M. G. B. (1998). Drawing instruments: Theories and practices from history to didactics. In Proceedings of the International Congress of Mathematicians (pp. 735-746).
Bussi, M. G. B. et al. (2004, July). Learning Mathematics with tools. Paper presented at the 10th International Congress on Mathematical Education (ICME-10), Copenhagen, Denmark.
Bybee, R. W. (August 26, 2010) What Is STEM Education? Science 329 (5995), 996. [doi: 10.1126/science.1194998]. DOI: https://doi.org/10.1126/science.1194998
Bybee, R. W. (2013). The case for STEM education: Challenges and opportunities. National Science Teachers Association.
Cortés, J. C.; Soto Rodríguez, H. A. (2012). Uso de Artefactos Concretos en Actividades de Geometría Analítica: Una Experiencia con la Elipse. Journal of Research in Mathematics Education, 1(2), 159-193. doi: 10.4471/redimat.2012.09
De Villiers, M. (1998). An alternative approach to proof in Dynamic Geometry. In R. Lehrer and D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space. Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 369–393.
Dennis, D. (1995). Historical perspectives for the reform of mathematics curriculum: Geometric curve drawing devices and their role in the transition to an algebraic description of functions. Cornell University, May.
Dennis, D. (2000). The role of historical studies in mathematics and science educational research. Handbook of research design in mathematics and science education, 799-813.
European Parliament. (2015). Encouraging STEM Studies for the Labour Market. Recuperado de: http://www.europarl.europa.eu/RegData/etudes/STUD/2015/542199/IPOL_STU(2015)542199_EN.pdf
Farouki, R. T. (2000). Curves from motion, motion from curves. CALIFORNIA UNIV DAVIS DEPT OF MECHANICAL AND AERONAUTICAL ENGINEERING.
Flórez, M., Carbonell, M. V., & Martínez, E. (2011). Design of Cycloids, Hypocycloids and Epicycloids Curves with Dynamic Geometry Software. Engineering Applications. EDULEARN11 Proceedings, 1011-1016.
Fontes, F. L. (2012). Instrumentos virtuais de desenho e a argumentação em Geometria. (Dissertação de Mestrado em Ensino de Matemática). Universidade Federal do Rio Grande do Sul. Porto Alegre. Brasil.
Gonzalez, H. B., & Kuenzi, J. J. (2012, August). Science, Technology, Engineering, and Mathematics (STEM) Education: A primer. Congressional Research Service, Library of Congress.
Iriarte, X., Aginaga, J., & Ros, J. (2014). Teaching Mechanism and Machine Theory with GeoGebra. In New Trends in Educational Activity in the Field of Mechanism and Machine Theory (pp. 211-219). Springer International Publishing. DOI: https://doi.org/10.1007/978-3-319-01836-2_23
Jahnke, H. N., Arcavi, A., Barbin, E., Bekken, O., Furinghetti, F., El Idrissi, A., ... & Weeks, C. (2002). The use of original sources in the mathematics classroom. In History in mathematics education (pp. 291-328). Springer Netherlands. DOI: https://doi.org/10.1007/0-306-47220-1_9
Laborde, C. et al. (2006) Teaching and learning Geometry with Technology. Handbook of research on the psychology of mathematics education: Past, present and future, p. 275-304. DOI: https://doi.org/10.1163/9789087901127_011
Manzano, F. J. (2016) Conicógrafos del Siglo XVII para la Educación Matemática del Siglo XXI. Revista TRIM, 10, pp. 47-60. Centro Tordesillas de Relaciones con Iberoamérica. Universidad de Valladolid.
Marginson, S., Tytler, R., Freeman, B., & Roberts, K. (2013). STEM: country comparisons: international comparisons of Science, Technology, Engineering and Mathematics (STEM) Education. Final Report.
Moon, F. C. (2003). Franz Reuleaux: Contributions to 19th century kinematics and theory of machines. Applied Mechanics Reviews, 56(2), 261-285. DOI: https://doi.org/10.1115/1.1523427
Mora Sánchez, J. A. (2007). Geometría Dinámica en Secundaria. Recuperado de http://jmora7.com/miWeb8/Archiv/2007%20Granada%20JAMora.pdf
OECD, (2007). PISA 2006: Science Competencies for Tomorrow’s World, Vol. 1.
OECD Publishing. (2012). Strengthening education for innovation . In OECD Science, Technology and Industry Outlook 2012 (pp. 206-208). OECD Pub.
Peron, G. C., de Cássia Silva, R., de Araújo Nunes, M. A., & Oliveira, A. B. S. (2011). Dynamical Simulation of a Valvetrain Mechanism: an Engineering Education Approach. Proceedings of COBEM 2011.
Quevedo, J. (2005). Informales e interactivas: Theatrum Machinarum. Matemáquinas en el Museo Universitario de Módena. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, (48), 81-90.
Reuleaux, F. (1885). The influence of the Technical Sciences upon General Culture. Columbia University, Henry Krumb School of Mines.
Rothwell, J. (2013). The hidden STEM Economy. Washington: Brookings Institution.
Sanchis, G. R. (2014). Historical Activities for the Calculus Classroom. - Module 1: Curve Drawing Then and Now," Convergence. June DOI: https://doi.org/10.4169/convergence20140602
Soto Rodríguez, H. A. (2010). Experimentación con un grupo de estudiantes de Bachillerato con hojas de trabajo relacionadas con la parábola y elipse usando artefactos concretos. (Tesis para obtener el título de Licenciado en Ciencias Físico Matemáticas). Universidad Michoacana San Nicolás de Hidalgo. Morelia, México.
Taimina, D., Pan, B., Gay, G., Saylor, J., Hembrooke, H., Henderson, D., ... & Paventi, C. (2007). Historical mechanisms for drawing curves. Hands On History: A Resource for Teaching Mathematics, 89-104. DOI: https://doi.org/10.5948/UPO9780883859766.011
Vincent, J., & McCrae, B. (2000). Mechanical Linkages, Dynamic Geometry Software and Mathematical Proof. In Proceedings of the International Conference on Technology in Mathematics Education (pp. 280-288). Auckland Inst. of Tech.
Vincent, J. (2003). Mathematical reasoning in a technological environment. Informatics in Education-An International Journal, (Vol 2_1), 139-150. DOI: https://doi.org/10.15388/infedu.2003.11
Yates, R. C. (1941) Geometrical Tools: A Mathematical Sketch and Model Book. Educational Publishers.
Zavala, J. C. C., & Rodríguez, H. A. S. (2012). Uso de artefactos concretos en actividades de Geometría Analítica: una experiencia con la elipse. REDIMAT, 1(2), 159-193.
Zimmermann, W., & Cunningham, S. (1991). Editor’s introduction: What is mathematical visualization. Visualization in teaching and learning mathematics, 1-7.
