El lenguaje logo, los niños y las variables

Referencias

Bednarz N, y Dufourdanvier B. (1991)… A study of external representations of change developed by young children, Proceedings of the Thirteenth PME—NA Conference, Blacksburg, Virginia, pp. 1407146. Booth L. (1984), Algebra: Children's Strategies and Errors, NFER-NELSON, Windsor. Galván MC., Ursini Si y Aguilar MC. (1995), Prefigurando la Idea de Discontinuidad en Ambientes Logo, Novena Reunión Centroamericana y del Caribe sobre Formación de Profesores e Investigadores en Matemática Educativa, (en prensa)… Healy L., Hoyies C. y Sutherland R. (1990), Critical Decisions in the Generali— zation process: a Methodology for Researching pupils Colaboration in Computer and Non Computer Environments, Proceedings of the Fourteenth PME Conference, México, Vol. 3, pp. 83—90. Hillel J . (1992), The Notion of variable in the context of the Turtle Graphics, in Hoyles C, y Noss R. (Eds.), Learning Mathematics and LOGO, MIT Press; pp 11—36. Hillel J. y Samurcay R. (1985), Analysis of a Logo Environment for learning the Concept of procedures With Variable, Research supported by Quebec Ministry of Education, FCAC Grant EQ 2539. Hoyles C. y Sutherland R. (1989), LOGO Mathematics in the Classroom, Routledge, Londres y Nueva York, Hoyles C. y Noss R (1987), Children Working in a Structured Logo Envi— ronment: From Doing to Understand ing, en Researches en Didactique des Mathematiques, 8, 12, pp. 131—174. Kchemann D. (1980), The Understanding of Generalized Arithmetic (Algebra) by Secondary School Children, PhD Thesis, Universidad de Londres, inglaterra. Leron U. y Zazkis R. (1986), Functions and vanables, Proceedings of the Second International Conference for Logo and Mathematics Education, London, U.K., pp. 1867192. Markovits Z, Eylon 8.8. y Bruckheimer M. (1988), Difficulties Students Have with the Function Concept, en Coxford AP. y Shulte A>P> (Eds), The ideas of Algebra K—12, pp. 43—60 Noss R. (1985), Creating a Mathematical Environment through Programming: A Study of Young Children Learning LOGO, PhD Thesis, Universidad de Londres, Inglaterra. Noss R. (1986), Constructmg a Concep— tual Framework for Elementary Alge- bra through LOGO Programming, en Educational Studies in Mathe matics, No. 17, pp. 335—357. Sutherland R. (1987), A Longitudinal Study of the Development of Pupils'Algebraic Thinking in a Logo environment, PhD Thesis, Universidad de Londres, Inglaterra. Sutherland R. (1989), Providing Compue ter Based Framework for Algebraic Thinking, en Educational Studies in Mathematics 20, pp. 317—344. Sutherland R. (1991), Some Unanswered Research Questions on the Teaching and Learning of Algebra, en For the Learning of Mathematics 11, 3, pp. 40-46. Sutherland R. (1992), What is Algebraic about Programming in LOGO?, en Hoyles C. y Noss R. (Eds.), Learning Mathematics and LOGO, MIT Press, pp. 37—54. Papert S. (1980), Mindst0rms: Children, Computers and Powerful Ideas, Basic Books Inc. Publishers New York… Ursini S. (1990), El Lenguaje Aritmé— tico—Algebraico en un Ambiente Computacional, en Cuadernos de Investigación, No. 15, IV, PNFAPM, México, pp. 534105. Ursini S. (1994a), Pupils'Approaches to Different Characterizations of Variable in LOGO, PhD Thesis, Universidad de Londres, Inglaterra. Ursini S. (1994b), Ambientes LOGO como apoyo para trabajar las Nociones de Variación y Correspondencia, l Simposio Metodologia de la Enseñanza de las Matemáticas. ITAM, México, pp. 124—128. Ursini S. (1995), General Method: A Way of Entering Algebra World, en Sutherland R. y Rojano T. (Eds) Kluwer (en prensa) Wagner S. (1981), An Analytical Framework for Mathematical Variables, Proceedings of the Fifth PME Conference, Grenoble, Francia, pp. 165—170.