Connecting arithmetic and geometric workspaces through the notion of approximation in Geogebra
Abstract
Through this research we analyzed the measures approximation in geometric objects with Geogebra ant high school level, and the results showed that high school students have weak notions of the concept of approximation, however its vast resources of arithmetic. These results permitted, on the one hand, analyze the potential they have for learning by connecting ideas geometric and arithmetic, and, on the other hand, better understand their strengths and difficulties. We frame this work in the theory of Duval representations (1993), as well as in the work of Núñez and Cortés (2008) on Interactive Technological Environments for Math Learning (ATIAM), and Kuzniak (2012, 2013), on the importance of transit in different Areas of mathematics.
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References
Aspinwall, L., Shaw, K. & Presmeg, N. (1997). Uncontrollable Mental Imagery: Graphical Connections between a Function and its Derivative. Educational Studies in Mathematics, 33(3), pp. 301-317.
Cortés, C., Guerrero, L., Morales Ch., & Pedroza, L. (2014) Tecnologías de la Información y la Comunicación (TIC): Aplicaciones Tecnológicas para el Aprendizaje de las Matemáticas. En: (2014) Agustín Carrillo (Ed.) Unión. Revista Iberoamericana de Educación Matemática. No 39. Septiembre 2014, pp. 141-161.
Cortés, C. & Núñez, E. (2007) Ambientes tecnológicos interactivos para el aprendizaje de las matemáticas. Memorias del IX Congreso Nacional de Investigación Educativa. México, 2007.
Chang, K., Males, L., Mosier, A. & Ginulates, F. (2011) Exploring US textbooks’ treatment of the estimation of linear measurements. ZDM, 43(5), pp. 697-708.
Duval, R. (1993) Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives, n°5, p. 37-65. IREM de Strasbourg.
Filloy, E., Puig, L. & Rojano. T. (2008). Educational algebra. A theoretical and empirical approach. Springer, USA.
Gooya, S., Khosroshahi, L. & Teppo, A. (2011) Iranian students’ measurement estimation performance involving linear and area attributes of real-world objects. ZDM, 43(5), pp. 709-722.
Guerrero, L. & Cortés, C. (2013) Ambientes tecnológico-interactivos para el aprendizaje de las matemáticas: investigaciones y experiencias en geometría y cálculo. En: Rojano, T. (Editora) Las tecnologías digitales en la enseñanza de las matemáticas. Ed. Trillas, México.
Guerrero, L. & Rivera, A. (2002) Exploration of patterns and recursive functions. En: Proceedings of the 24th PME-NA Conference, vol. 1. Athens, GA, USA.
Guerrero, L., Rojano, T., Maviriks, M. & Hoyles, C. (2011). Critical Moments in generalization tasks. Building algebraic rules in a digital sign system. En: Wiest, L. & Lamberg, T. (Eds.) Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Reno, NV: University of Nevada, Reno.
Hannighofer, J., Van den Heuvel-Panhuizen, M., Weirich, S. & Robitzsch, A. (2011) Revealing German primary school students’ achievement in measurement. ZDM, 43(5), pp. 651-665.
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. En: Lester, Jr., (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707-762). Greenwich, CT: Information Age Publishing.
Kuzniak, A. (2012) Understanding the nature of the geometric work through its developement and its transformations. 12th International Congress on Mathematical Education, COEX, Seoul, Korea.
Kuzniak, A. (2013) Travail mathématique et domaines mathématiques. To appear in A. Kuzniak et P. R. Richard (eds), Proceedings of the 3rd symposium Espace de Travail Mathématique. Université de Montréal.
Kuzniak, A. & Rauscher, J. (2011) How do teachers’ approaches to geometric work relate to geometry students’ learning difficulties? Educational Studies in Mathematics, Vol. 77, pp.129–147.
Núñez, E. & Cortés, C. (2008) Propuesta de una metodología de enseñanza usando ambientes tecnológicos interactivos. En: R. Pantoja, E. Añorve, C. Cortés y L. Osornio (Editores) Investigaciones y propuestas sobre el uso de la tecnología en educación matemática. Vol. 1, 121-231, Editorial AMIUTEM.
Rojano, T. (2001). Algebraic Reasoning with Spreadsheets. Proceedings of the International Seminar “Reasoning explanation and proof in school mathematics and their place in the intended curriculum”. Qualificactions and Curriculum Authority. Cambridge, UK, pp. 1-16.
SEP (2011). Programas de estudio 2011. Guía para el Maestro. Educación Básica. Secundaria. Matemáticas. Subsecretaría de Educación Básica de la SEP, México.
Smith, J., Van den Heuvel-Panhuizen, M. & Teppo, A. (2011) Learning, teaching, and using measurement: introduction to the issue. ZDM, Zentralblatt für Didaktik der Mathematik, 43, pp. 617–620.
Tanguay, D., Geeraerts, L., Saboya, M., Venant, F., Guerrero, ML. & Morales, Ch. (2013) An activity entailing exactness and approximation of angle measurement in a DGS. CERME 8. 6-10 de febrero, Turquía.
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