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| dc.creator | Delgado Fernández, Joaquín | |
| dc.creator | Butto Zarzar, Cristianne | |
| dc.date | 2016-04-28 | |
| dc.date.accessioned | 2023-03-20T15:56:53Z | |
| dc.date.available | 2023-03-20T15:56:53Z | |
| dc.identifier | https://horizontespedagogicos.ibero.edu.co/article/view/17205 | |
| dc.identifier.uri | https://biblioteca-repositorio.clacso.edu.ar/handle/CLACSO/215792 | |
| dc.description | A study based on Eculid´s geometric algebra is presented and a didactical sequence is presented where students identify simple algebraic expressions, such as the distributive law, the square of a binomial and solution of the quadratic equation. Our theoretical framework is base on Jankvist´s proposal where history of mathematics is used as in a historical-genetic purpose. The experimental phase was conducted with students of the first year of a ublic school of the preparatory level, located in the State of Morelos in México. The stages of the study include: a) application of an initial questionnaire, b) didactical sequence supported with ad hoc clinical interview and, c) final questionaire. Our results show that students are able to identify the distributive law as a conservation of area. Clinical interview shows tha in some cases students identify the biinomial formula as the sum of areas of rectangles composing a square, although they do not express completely their thinking in algebraic terms. | en-US |
| dc.description | Se reportan resultados de un estudio basado en un modelo de enseñanza que incorpora aspectos relacionados con el método de aplicación de las áreas (Euclides vol. II). En dicho modelo se recupera esta tradición geométrica para explicitar la vinculación de los aspectos geométricos y algebraicos e intentar construir significados de manera conectada. Objetivos: 1. Investigar la factibilidad de un abordaje: álgebra geométrica, 2. Verificar la viabilidad del método de aplicación de las áreas como un tratamiento didáctico que considere aspectos del desarrollo histórico del pensamiento algebraico. Metodología de tipo cualitativo, participantes: once estudiantes de primer año de bachillerato de una escuela pública de Morelos, México. Etapas del estudio: aplicación de un cuestionario inicial, secuencia didáctica y un cuestionario final. Los resultados revelan que los alumnos logran identificar las áreas simples y plantear la ecuación cuadrática y aplicar la fórmula para resolver la ecuación, pero cometen errores al sustituir la propia incógnita en el lado derecho de la fórmula. Se concluye que el abordaje del estudio permite el manejo de relaciones algebraicas básicas que conducen a las ecuaciones cuadráticas. Palabras clave: Historia de la matemática, álgebra geométrica de Euclides, método de aplicación de las áreas. | es-ES |
| dc.format | application/pdf | |
| dc.language | spa | |
| dc.publisher | Corporación Universitaria Iberoamericana | es-ES |
| dc.relation | https://horizontespedagogicos.ibero.edu.co/article/view/17205/767 | |
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| dc.relation | /*ref*/Filloy, E, y Rojano, T. (1985). Obstructions to the Acquisition of Elemental Algebraic Concepts and Teaching Strategies. En Proceedings of the Ninth Annual Conference of the Psychology of Mathematics Education, North American Chapter. Ohio, US. | |
| dc.relation | /*ref*/Filloy, E. & T. Rojano. (1989). Solving equations: The transition from arithmetic to algebra, For the Learning of Mathematics 9(2), 19-25. | |
| dc.relation | /*ref*/Furinghetti, F. & Radford, L. (2002). Historical Conceptual Devlopments and the Teaching of Mathematics: From Phylogenesis and Ontogenesis Theory to Classroom Practice. In Handbook of International Research in Mathematics Education. Lyn D. English (Ed.) Routledge. | |
| dc.relation | /*ref*/Jankvist, U. Th. & Kjeldsen, T. H. (2011). New Avenues for History in Mathematics Education: Mathematical Competencies and Anchoring. Sci. & Educ. 20, 831-862. doi: 10.1007(s11191-010-9315-2. | |
| dc.relation | /*ref*/Jankvist, U. Th. (2009). A categorization of the “whys” and “hows” of using history in mathematics education. Educ. Stud. Math 71, 235-261. doi: 10.1007/s10649-008-9174-9. | |
| dc.relation | /*ref*/Kaput, J. y M. Blanton. (2000). Generalization and progressively formalizing in a third-grade mathematics classroom: conversations about and old numbers. In plenary presentation at PME-NA XXII; Tucson, AZ; October 7-10, 2000. | |
| dc.relation | /*ref*/Katz, V. (Ed.) (2000). Using history to teach mathematics. An International Perspective. The Mathematical Association of America. | |
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| dc.relation | /*ref*/Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics 12, 317-326. | |
| dc.relation | /*ref*/Radford, L. (2014). Reflections on History of Mathematics (Chap 7). In Mathematics and Mathematics Education: Searching for Common Ground. Advances in Mathematics Education. M.N. Fried, T. Dreyfus (Eds.) Springer. | |
| dc.relation | /*ref*/Mason, J., Graham, A., Pimm, D. y Gower, N. (1985). Routes to Roots of Algebra. Gran Bretaña: The Open University Press. | |
| dc.relation | /*ref*/Radford, L y Guérette, G. (2000). Second Degree Equations in the Classroom. A Babylonian Approach Using History to Teach Mathematics: An International perspective. The Mathematical Association of America, Victor Katz, Editor, The United States of America. pp 69-75. | |
| dc.relation | /*ref*/Radford, L. (2001). The historical origins of algebraic thinking. In R. Sutherland, T. Rojano, A. Bell & R. Lins (Eds.), Perspectives on School Algebra (pp. 13-63). Dordrecht: Kluwer. | |
| dc.relation | /*ref*/Sfard, A. & Linchevski, L. (1994). The Gains and Pitfalls of Reification. The Case of Algebra. Educational Studies in Mathematics 26, 191-228. | |
| dc.source | Horizontes Pedagógicos; Vol. 17 No. 2 (2015); 53-64 | en-US |
| dc.source | Horizontes Pedagógicos; Vol. 17 Núm. 2 (2015); 53-64 | es-ES |
| dc.source | 2500-705X | |
| dc.source | 0123-8264 | |
| dc.subject | History of mathematics | en-US |
| dc.subject | algebra Euclidean geometry | en-US |
| dc.subject | method of application areas | en-US |
| dc.subject | Método de aplicación de las áreas. Algebra geometrica de Euclides | es-ES |
| dc.subject | Historia de la matemática. | es-ES |
| dc.title | Euclid's geometric algebra: An experience in the teaching of the algebra | en-US |
| dc.title | El álgebra geométrica de Euclides.: Una experiencia en la enseñanza del álgebra | es-ES |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Articles | en-US |
| dc.type | Artículos | es-ES |
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