Revisitando la noción de función real

Referencias

Blanco, L.J., Cárdenas, L.J., Figueiredo, C.A., Contreras, L.C. (2014). The Concept of Function and his Teaching and Learning. Far East Journal of Mathematics Education, 12(1), 47–78. Recuperado de http://pphmj.com/journals/fjme.htm/out.pdf Calvino, Italo. (2009). El libro de la naturaleza en Galileo. Ciencia 95, julio-septiembre, 50-53. [En línea] Cuevas, A. & Pluvinage, F. (2003). Les projets d’action pratique, éléments d’une ingénierie d’enseignement des mathématiques. Annales de didactique et de sciences cognitives, Strasbourg, IREM. Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Kluwer Academic Publishers. Dreyfus, T. (1990). Advanced Mathematical Thinking. In P. Nesher, & J. Kilpatrick. (Eds.). Mathematics and cognition: A research synthesis by the International Group for Psychology of Mathematics Education, 113–134. Cambridge, Great Britain: Cambridge University Press. Dubinsky, E. y, Harel, G. (1992). The Nature of the Process Conception of Function. En G. Harel y E. Dubinsky (eds.). The Concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America. Notes Series, 25, 85–106. Duval, R. (1998). Didáctica, Investigaciones en Matemática Educativa II. Editor F. Hitt. Gpo. Edit. Iberoamérica. México. Filloy E. y Rojano T. (1984). La aparición del lenguaje aritmético-algebraico. L’Educazione Matemática. Revista quadrimestrale a cura del Centro di Ricerca e Sperimentazione dell’Educazione matematica di Cagliari. Anno V n. 3 Diciembre 1984. Fillo, E,, Puig, L., Rojano T. (2008). Educational Algebra. A Theoretical and Empirical Approach. Springer. ISBN 978-0-387-71254-3. Goldenberg, P. (1988). Mathematics, metaphors and human factors: mathematical, technical and pedagogical challenges in the graphical representation of functions. Journal of Mathematical Behaviours. 7(2), pp. 135-174. Hart, K., Brown M., Kerslake D., Küchemann D., & Ruddock, G. (1985). Teacher's guide. Chelsea diagnostic mathematics test. London: NFER-Nelson. Hitt, F. (1988). “Obstacles related to the concept of function”. DME-PNFAPM CINVESTAV, México e Institute of education, University of London. U.K. pp. 1–7 Kieran, K., Garançon, M., Lee, L., Bolleau, A., (1993). Technology in the learning of functions: Process to object?. Proceedings of the International Conference for the Psychology of Mathematics Education. 1, 91–99. Pacific Grove. Ca. USA. Kjeldsen, T.H. y Petersen, H. P. (2014). Brindging History of the Concept of Function with Learning of Mathematics: Students´ Meta-Discursive Rules, Concept Formation and Historical Awareness. Science & Education, 23, 29–45. Kleiner, I. (1989). Evolution of the function concept: A brief survey. The college Mathematics Journal. 20(4), 282–300. Luzín, N. (1998). En: Ferreiros, J. (2003). Historia del concepto de función. La Gacete de la RSME, 6(21), 413–436. Markovits, Z., Eylon, B. S. & Bruckheimer, M. (1986). Functions today and yesterday. For the Learning of Mathematics. 6(2), 18–24. Markovits, Z., Eylon, B. S., & Bruckheimer, M.(1988). Difficulties students have with the function concept. In A. F. Coxford and A. P. Shulte (Eds.). The Ideas of Algebra. 1988 Yearbook, pp. 43–60. Reston, VA: NCTM. Martínez, A. M., (1993). Knowledge and Development of Functions in a Technology-Enhanced High School Precalculus Class: A Case Study. Doctoral Dissertation. The Ohio State University. Monna A. F. (1972/73). The Concept of Function in the 19th and 20th Centuries, in Particular with Regard to the Discussions between Baire, Borel and Lebesgue. Arch. Hist. Ex. Sci. 9. National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation standards for school mathematics. Reston, VA: The Author. National Council of Teachers of Mathematics. (1991). Professional standarts for teaching mathematics. Reston, VA: The Author. National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, D. C: National Academy Press. Nicholas, C.P. (1966). A dilemma in definition. American Mathematical Monthly, 73, 762–768. Norman, Alexander (1992). Teacher’s Mathematical Knowledge on the Concept of Function. The Concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America. Notes Series, 25, 215–232. Pluvinage, F. y Cuevas-Vallejo, C. Armando. (2006). Un acercamiento didáctico a la noción de función. Eugenio Filloy (ed.). Matemática Educativa, treinta años: Una mirada fugaz, una mirada externa y comprensiva, una mirada actual. Editorial Santillana, S.A. de C.V, Aula XX1 y CINVESTAV. México ISBN 10:970-29-1753-0. ISBN 13:978-970-29-1753-3 pp. 141-167. Rüting, Dieter. (1984). Some definitions of the Concept of Function from Joh. Bernoulli to N. Bourbaki. The Mathematical Intelligencer. 6(4). Selden, A., y Selden (1992). Research Perspectives on Conceptions of Function summary and overview. The Concept of Function: Aspects of Epistemology and Pedagogy. Mathematical Association of America. Notes Series, 25, 1–21. Sfard, A. (1989). Transition from operational to structural conception: the notion of function revisited. Proceedings of the Psychology of Mathematics Education. 3, 151–158. Paris, France. Sierpinska, Anna, (1992). On understanding the notion of function. The Concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America. Notes Series, 25, 23–58. Spivak, M. (1967). Calculus. USA: Benjamin, W.A. Youschkevitch, A. P. The Concept of Function up to the Middle of the 19th Century. Arch. Hist. Ex. Sci. 16 (1976) 37-85.