Euclid's geometric algebra
El álgebra geométrica de Euclides. An experience in the teaching of the algebra
Article Sidebar
PDF (Español (España))
FLIP
By submitting a text to the Journal Horizontes Pedagogicos, the authors agree that exclusive rights to reproduce by any means and distribute the article, is granted to the Faculty of Education of the Corporación Universitaria Iberoamericana.
Authors will obtain the permissions to reproduce copyrighted texts or illustrations that they will use in their writings.
Main Article Content
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.
Downloads
Article Details
Bher, Merlyn, Erlwanger, S. & Nichols, E. (1980). How children view the equals sign. Mathematics Teaching 92, 13-15.
Booth, L. R. (1984). Algebra: Children's Strategies and Errors: A Report of the Strategies and Errors in Secondary Mathematics Project. Nfer Nelson.
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic.
Delval, J. (2000). Descubrir el pensamiento en los niños. Introduccion a la práctica del método clínico. Barcelona: Paidós.
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.
Filloy, E. & T. Rojano. (1989). Solving equations: The transition from arithmetic to algebra, For the Learning of Mathematics 9(2), 19-25.
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.
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.
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.
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.
Katz, V. (Ed.) (2000). Using history to teach mathematics. An International Perspective. The Mathematical Association of America.
Katz, V. K. (1986). Using History in Teaching Mathematics. For the Learning of Mathematics 6(3), 13-19.
Kieran, C. (1992). The learning and Teaching of school algebra, In D. A. Grouws (Ed.) Handbook of Research on mathematics Teaching and Learning, MacMillan, New York, 390-419.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics 12, 317-326.
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.
Mason, J., Graham, A., Pimm, D. y Gower, N. (1985). Routes to Roots of Algebra. Gran Bretaña: The Open University Press.
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.
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.
Sfard, A. & Linchevski, L. (1994). The Gains and Pitfalls of Reification. The Case of Algebra. Educational Studies in Mathematics 26, 191-228.
