Del infinito potencial al actual: un recorrido histórico a través de la metáfora conceptual

Referencias

Aristóteles. (trad. 1985). The complete Works of Aristotle. The revised Oxford translation. In J. Barnes (Ed.). New Jersey, United States: Princeton University Press. Arquímedes. (trad. 1897). The Sand Reckoner of Archimedes. New York: Cambridge University Press. Arrigo, G. y D'Amore, B. (1999). Lo veo, pero no lo creo: obstáculos epistemológicos y didácticos para la comprensión del infinito actual. Educación Matemática, 11(01), 5-24. Arrigo, G. y D’Amore, B. (2004). Otros hallazgos sobre los obstáculos en la comprensión de algunos teoremas de Georg Cantor. Educación Matemática, 16 (2), 5-20. Bagni, G.T. (2004). Exhaustion argument and limit concept in the History of Mathematics: educational reflections. In Furinghetti, F, Kaiser, S. & Vretblad, A. (Eds.), Proceedings of HPM–2004, History and Pedagogy of Mathematics, Uppsala, 94–103. Bagni, G.T. (2006). History of Calculus from Eudoxus to Cauchy. Historical investigation and interpretation and mathematics education. In Furinghetti, F. Kaiser, S. & Tzanakis, C. (Eds.), Proceedings of HPM–2004 & ESU–4, Revised edition (pp. 529–536). Crete: Emedia, University of Crete. Bell, E. T. (2003). The Development of Mathematics. Dover Publications, New York. Bell, J. L. (2008). A primer of infinitesimal analysis. New York: Cambridge University Press. Bolzano, B. (1991). Las paradojas del infinito. D.F., México: Universidad Nacional Autónoma de México. Bussotti, P., Tapp, C. (2009). The influence of Spinoza’s concept of infinity on Cantor’s set theory. Studies in History and Philosophy of Science, 40, 25-35. Cobb, P., Yockel, E. & Wood, T. (1992). A constructivist alternative to the representational view of the mind in mathematics education. Journal for Research in Mathematics Education, 23(1), 2-33. Comrie, B. (1976). Aspect. Cambridge Textbooks in Linguistics. Dauben, J. W., (1990). Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton University Press, Princeton, NJ. Durán, A. (2003). Euler y los infinitos (grandes y pequeños). Recuperado el 2 de mayo 2020 de http://upcommons.upc.edu/e-prints/bitstream/2117/1985/1/ mblanco_paper_icehve.pdf Eves H., Carroll V. (1966). An introduction to the foundations and fundamental concepts of matemathics, New York: Holt, Rinehart and Winston. Fauconnier, G. & Turner, M. (2002). The way we think. New York: Basic Books. Fischbein, E. (2001). Tacit models and infinity. Educational studies in Mathematics, 48, 309- 329. Flusberg, P., Matlock, T. & Thibodeau, S. (2019). The role of metaphor in communication and thought. Language and Linguistics Compass, 13(5). Font, V. (2007). Epistemología y Didáctica de las Matemáticas. En F. Ugarte (ed.) Reportes de investigación. n. 21, serie C, II Coloquio Internacional sobre la Enseñanza de las Matemáticas (pp. 1-48). Lima, Perú: PUCP Galilei, G. (trad.1954). Dialogues concerning two new sciences, Dover Publications, New York. Gallese, V. & Lakoff, G. (2005). The brain’s concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22 (3), 455-479. Guthrie, W. K. C. (2000). A History of Greek Philosophy. Cambridge University Press. Jech, T. (2011). Set Theory, Stanford Encyclopedia of Philosophy. Lakoff, G. & Núñez, R. (2000). Where Mathematics comes from. New York: Basic Books. Lucrecio. (trad. 1985). De la naturaleza de las cosas. Barcelona, España: Orbis. Noblit & Hare (1998) Metha-etnography: synthesizing qualitative studies. Sage Publications, California. Núñez, R. (2005) Creating mathematical infinities: Metaphor, blending, and the beauty of transfinite cardinals. Journal of Pragmatics, 37, 1717-1741. O’ Connor, J. J., & Robertson, E. F. (2002). Mac Tutor History of Mathematics. Recuperado el 2 de Mayo de 2010 de http://www. history.mcs.stand.ac.uk/HistTopics/Infinity.html Paéz, T. D. (2013) Las matemáticas a lo largo de la historia. Madrid, España: Visión Libros. Robinson, A. (1966). Non-standard Analysis. Princeton University Press. Rohrer, T. (2006). Image Schemata in the Brain. En From Perception to Meaning: Image Schemas in Cognitive Linguistics, Beate Hampe and Joe Grady, eds., Berlin: Mouton de Gruyter. 165-196. Rosch, E., Thompson, E. y Varela, F. (1991). The embodied mind: Cognitive science and human experience. MIT Press, Cambridge, MA. Sanhueza, D. (2015). Consideraciones sobre el infinito en la filosofía de Kant. Revista de Filosofía, 71, 151-162. Sfard, A. (2008). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4-13. Skolem, T. (1934). Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschließlich Zahlenvariablen, Fundamenta Mathematicae. 23 (1), 150–161. Stillwell, J. (2010). Mathematics and its history. Springer Science+Business Media. New York, USA. Tall, D. (1991). The Psychology of Advanced Mathematical Thinking. En Tall, D. (Ed.) Advanced Mathematical Thinking, Kluwer: Hollad, 3-21.Wilson & Gibbs (2007).