Pensamiento algebraico temprano: el papel del entorno Logo

Referencias

Bednarz, N., C. Kieran y L. Lee (1996), Approaches to Algebra: Perspectives for Research and Teaching, Holanda, Kluwer Academic Publishers. Booth, L. R. (1984), Algebra: Children ́s Strategies and Errors, Windsor, Reino Unido, NFER-Nelson. Castro, E., L. Rico y E. Castro (1995), Estructuras aritméticas elementales y su modelización, Bogotá, Grupo Editorial Iberoamericana, pp. 45-79. Carraher, D., A. Schliemann y B. Brizuela (2000), “Early algebra, early arithmetic: Treating operations as functions”, en M. L. Fernández (ed.), Proceedings of the Twenty-Second Annual Meeting North American Chapter of the Inter- national Group for the Psychology of Mathematics Education, PME-NA XXII; Tucson, Arizona, 7 a 10 de octubre de 2000. ———————— (2001), “Operate You On Unknowns?”, PME 25 Psychology of Mathematics Education, Utrecht, Holanda, vol. 1, pp. 130-140. Carraher, D. y D. Earnest (2003), “Guess my rule revisited”, en Proceedings of the International Conference of the Psychology of Mathematics Education of the 27 Conference of the PME Psychology of Mathematics Education, Honolulu, vol. 1, pp. 173-180. Da Rocha Falcão, J. T. (1993), “A álgebra como ferramenta de representação e resolução de problemas”, en A. D. Schliemann, D. W. Carraher, A. G. Spinillo, L. L. Meira, y J. T. da Rocha Falcão (1993), Estudos em Psicologia da Educação Matemática, Recife, Editora Universitaría, UFPE. Durán Ponce, R. (1999), Reconocimiento de patrones en secuencias numéricas y de figuras por alumnos de sexto grado de primaria, tesis de Maestría, Departamento de Matemática Educativa, Cinvestav, IPN. Filloy, E. (1991), “Cognitive Tendencies and Abstraction Processes in Algebra Learning”, en F. Furinghetti (ed.), Proceedings of the fifteenth International Conference for the Psychology of Mathematics Education, vol. 2, pp. 48-55. ———————— (1993), “Tendencias cognitivas y procesos de abstracción en el aprendizaje del álgebra y de la geometría”, Enseñanza de las Ciencias, vol. 11, núm. 2, pp. 160-166. ———————— (1997), La observación en matemática educativa. Modelos teóricos locales y sistemas de signos, México, Notas del autor. ———————— (1999), “Modelos Teóricos Locales (MTL): Un marco teórico y metodológico para la observación experimental en matemática educativa”, en Aspectos teóricos del álgebra educativa, Grupo Editorial Iberoamericana, cap. 1. Filloy, E. y T. Rojano (1985a), “Obstructions to the Acquisition of Elemental Algebraic Concepts and Teaching Strategies”, en L. Streefland (ed.), Proceedings of the Ninth Annual Conference for the Psychology of Mathematics Education, Utrech, Holanda, State University of Utrecht, pp. 154-158. ———————— (1985b), “Operating unknown and models of teaching (A clinical study with 12-13 years old with a high proficiency in pre algebra)”, en S. K. Domarin y M. Shelton (eds.), Proceedings of the Sixth Annual Meeting for the Psychology of Mathematics Education, North American Chapter, Columbus, Ohio, EUA, Ohio State University, pp. 75-79. ———————— (1991), “Translating from natural language to the mathematical system of algebraic signs and vice-versa”, en R. Underhill (ed.), Proceedings of the thirteenth Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, vol. 2, pp. 29-35. Filloy, E., T. Rojano y L. Puig (2008), Educational Algebra. A Theoretical and Empirical Approach, Berlín, Heidelberg y Nueva York, Springer. Hoyles, C. y R. Sutherland (1989), Logo Mathematics in the Classroom, Londres y Nueva York, Routledge. ———————— (1989), Ways of learning in a computer based environment: Some findings of the Logo Maths Project, Londres, Institute of Education, University of London. Kaput, J., M. Blanton y L. Moreno (2008), “Algebra from a Symbolization Point of View”, en National Council of Teachers of Mathematics, Algebra in the Early Grades, Londres, Lawrence Erlbaun. Kaput, J. y M. Blanton (2000), “Generalization and progressively formalizing in a third-grade mathematics classroom: Conversations about even and odd numbers”, conferencia magistral presentada en PME-NA XXII; Tucson, Arizona, 10 de octubre de 2000. ———————— (2002), “Design principles for tasks that support algebraic thinking in elementary school classrooms”, Norwich, Reino Unido, vol. 2, pp. 104-112. Kieran, C. (1980), “The interpretation of the equal sign: Symbol for an equivalence relation vs. an operator symbol”, en R. Karplus (ed.), Proceedings of the Fourth Conference of the International Group for the Psychology of Mathematics Education, Berkeley, California, University of California, pp. 163-169. Kieran, C. y E. Filloy (1989), “El aprendizaje del álgebra escolar desde una perspectiva psicológica”, Enseñanza de las ciencias, vol. 7, pp. 229-240. Lee, L. (2001), “Early algebra —but which algebra?”, en Proceedings of the 12 ICM Study Conference, Australia, vol. 2, pp. 392-399. Mac Gregor, M. y K. Stacey (1993), “Seeing to pattern and writing to rule”, PME Psychology of Mathematics Education, Ibaraki, Japón. Mason, J., A. Graham, D. Pimm y N. Gower (1985), Routes of Roots of Algebra, Gran Bretaña, The Open University Press. ———————— (1989), “Mathematical abstraction as the result of a delicate shift of attention”, For the Learning of Mathematics, vol. 9, núm. 2, junio, pp. 2-8. NCTM (1989), National Standards for Mathematics, National Council of Teachers of Mathematics. Noss, R. (1986), “Constructing a conceptual framework for elementary algebra through LOGO programming”, Educational Studies in Mathematics, núm. 17, pp. 37-54. Radford, L. (1996), “The role of geometry and arithmetic in the development of algebra: Historical remarks from a didactic perspective”, en N. Bernardz, C. Kieran y L. Lee (eds.), Approaches to Algebra. Perspectives for Research and Teaching, Holanda, Kluwer Academic Publishers. Reggiani, M. (1994), “Generalization as a basic for algebraic thinking: Observations with 11-12 years old pupils”, en Proceeding of the XVIII PME Conference, Lisboa, Portugal, pp. 97-104. Sfard, A. y L. Linchevski (1994), “The Gains and Pitfalls of Reification —The Case of Algebra”, Educational Studies in Mathematics, vol. 26, pp. 191-228. Slavit, D. (1999). “The role of operation sense in transitions from arithmetic to algebraic thought”, Educational Studies in Mathematics, Holanda, Kluwer Academic Publishers, vol. 37, pp. 251-274. Schliemann, A., D. Carraher, B. Brizuela y D. Earnest (2003), “Algebra in elementary school”, en PME 27 Psychology of Mathematics Education, Honolulu, vol. 1, pp. 127-134. Sutherland, R. (1991), “Some unanswered research questions on the teaching and learning of algebra”, For the Learning of Mathematics, vol. 11, núm. 3, noviembre, pp. 40-46. Ursini, S. (1990), “El lenguaje aritmético-algebraico en un ambiente computacional”, Cuadernos de Investigación, núm. 15, IV, julio, México, PNFAPM, pp. 149- 156. Vergnaud, G. (1991), El niño, las matemáticas y la realidad: problemas de la enseñanza de las matemáticas en la escuela primaria, México, Trillas, caps. 9 y 11.