Uso de artefactos concretos en actividades de geometría analítica: una experiencia con la elipse

Referencias

Artobolevski, I. (1964). Mechanisms for the Generation of Plane Curves. New York: Pergamon Press. Artobolevski, I. (1975). Mecanismos en la técnica moderna. Tomo 2, parte 1. Moscú: Ed. Mir. Arzarello, E. & Robutti, O. (2004). Approaching functions through motion experiments. Educational Studies in Mathematics, 57(3). Special issue. Bartolini, M. et al. (2004, July). Learning Mathematics with tools. Paper presented at the 10th International Congress on Mathematical Education (ICME-10), Copenhagen, Denmark. Bartolini, M. (2007) Experimental mathematics and the teaching and learning of proof. Research funded within the PRIN 2005019721 on "Meanings, conjectures, proofs: from basic research in mathematics education to curricular implications. Bartolini, M. et al. (2004, September). The MMLAB: a laboratory of geometrical instruments. Paper presented at the minisimposio Applicazioni della Matematica all’industria culturale, Venezia, Italy. Boero, P., Garuti, R. & Mariotti, M. (1996). Some dynamic mental processes underlying producing and proving conjectures. Proceedings of PME-XX, Vol. 2 (pp. 121-128). Valencia. Boero, P., Pedemonte, B. & Robotti, E.: (1997). Approaching Theoretical Knowledge Through Voices and Echoes: a Vygotskian Perspective. En E. Pehkonen (1997, Ed.) Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (pp. 81-88). Lahti Research and Training Center. Finland: University of Helsinki. Dennis, D. (1995). Historical Perspectives for the Reform of Mathematics Curriculum: Geometric Curve Drawing Devices and Their Role in the Transition to an Algebraic Description of Functions. Unpublished doctoral dissertation, Cornell University. Duval, R. (1995). Semiosis et Penseé Humain. New York: Peter Lang. Dyck, W. (1994). Katalog matematischer und matematisch-physikalischer Modelle, Apparate und Instrumente. New York: Georg OlmsVerlag, Zurich. Hoyos, V. (2006). Funciones Complementarias de los artefactos en el aprendizaje de las transformaciones geométricas en la escuela secundaria. Enseñanza de las ciencias, 24(1), 31–42. Hoyos, V. & Falconi, M. (2005). Instrumentos y matemáticas: historia, fundamentos y perspectivas educativas. México: Ed. UNAM. Hoyos, V., Capponi, B. & Génevès, B. (1998). Simulation of drawing machines on Cabri-II and its dual algebraic symbolization. En Inge Schwank (Ed.), Proceedings of CERME1, Alemania: Universidad de Osnabrueck. Kempe, A. B. (1877). How to Draw a Straight Line. London, England: Macmillan and Co. Mariotti, M.A., Bartolini Bussi, M., Boero, P., Ferri, F. y Garuti, R. (1997). Approaching Geometry Theorems in Contexts: From History and Epistemology to Cognition. E. Pehkonen (1997, Ed.) Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (pp. 180-195). Lahti Research and Training Center. Finland: University of Helsinki. Piaget, J. (1950). Introducción a la Epistemología Genética. “El pensamiento matemático”. Buenos Aires: Paidós. Schooten, F. van (1657). Exercitationum mathematicarum liber IV, sive de organica conicarum sectionum in plano descriptione. Lugd. Batav ex officina J. Elsevirii. Verillon, P. & Rabardel, P. (1995). Cognition and Artifacts: A Contribution to the Study of Thought in Relation to Instrumented Activity. European Journal of Psychology of Education, 10(1), 77-101. Vincent, J., Chick, H., & McCrae, B. (2002). Mechanical linkages as bridges to deductive reasoning: A comparison of two environments. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, 4 (pp. 313 – 320). Norwich, UK: PME.