Comprensión del concepto de serie numérica a través del modelo de Pirie y Kieren

Bibliographic References

• BAGNI, G. T. (2005). Infinite series from history to mathematics education. International Journal for Mathematics Teaching and Learning, June. Disponible en línea <http://www.ex.ac.uk/cimt/ijmtl/bagni.pdf> (consulta, febrero del 2007).
• CODES, M. (2010). Análisis de la comprensión de los conceptos de serie numérica y su convergencia en estudiantes de primer curso de universidad utilizando un entorno computacional. Tesis doctoral, Salamanca: Universidad de Salamanca.
• CODES, M., M. T. GONZÁLEZ, L. DELGADO y M. C. MONTERRUBIO (2012). Growth in understanding the concept of infinite series: a glance through Pirie and Kieren Theory. Proceedings of ICME 12, Seúl (Corea), pp. 2660-2669.
• GÓMEZ-CHACÓN, I. M. (2000). Affective influences in the knowledge of mathematics. Educational Studies in Mathematics, 43(2), pp. 149-168.
• GONZÁLEZ-MARTÍN, A. S. (2010). The concept of series: teachers' conceptions and teaching practices. Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (PME34), 3, pp. 33-40, ISSN: 0771-100X.
• GONZÁLEZ-MARTÍN, A. S. y M. CAMACHO (2004). Legitimization of the graphic register in problem solving at the undergraduate level. The case of the improper integral. Proceedings of the 28th Conference of the International. Group for the Psychology of Mathematics Education (PME 28), Bergen (Noruega), Vol. 2, pp. 479-486.
• GONZÁLEZ-MARTÍN, A. S., E. NARDI E I. BIZA (2011). Conceptually-driven and visually-rich tasks in texts and teaching practice: the case of infinite series. International Journal of Mathematical Education in Science and Technology, 42(5), pp. 565-589.
• KIDRON, I. (2002). Concept definition, concept image, and the notion of infinite sum in old and new environments. En: A. D. Cockbrun y E. Nardi (eds.). 26th International Conference for the Psychology of Mathematics Education, 3, Norwich, England: School of Education and Professional Development, University of East Anglia, pp. 209-216.
• KIDRON, I., N. ZEHAVI y E. OPENHAIM (2001). Teaching the limit concept in a CAS environment: students' dynamic perceptions and reasoning. 25th PME Conference, 3, pp. 241-248.
• KYRIAKIDES, A. O. (2010). Engaging everyday language to enhance comprehension of fraction multiplication. En: V. Durand-Guerrier, S. Soury-Lavergne y F. Arzarello (eds.). Proceedings of the Sixth Conference of European Research in Mathematics Education. Lyon, France: CERME, pp. 1003-1012.
• MANU, S. S. (2005). Growth of mathematical understanding in a bilingual context: analysis and implications. En: H. L. Chick y J. L. Vincent (eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 3, pp. 289-296.
• MARTIN, L. C. (2008). Folding back and the dynamical growth of mathematical understanding: Elaborating the Pirie-Kieren Theory. The Journal of Mathematical Behavior, 27, pp. 64-85.
• MARTIN, L. C. y S. PIRIE (2003). Making images and noticing properties: The role of the computer in mathematical generalisation. Mathematics Education Research Journal, 15(2), pp. 171-186.
• PIRIE, S. (1988). Understanding - Instrumental, relational, formal, intuitive⋯, How can we know? For the Learning of Mathematics, 8(3), pp. 2-6.
• PIRIE, S. y T. KIEREN (1989). A recursive theory of mathematical understanding. For the Learning of Mathematics, 9(3), pp. 7-11.
• PIRIE, S. y T. KIEREN (1992). Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics, 23, pp. 505-528.
• PIRIE, S. y T. KIEREN (1994). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in Mathematics, 26, pp. 165-190.
• WALTER, J. y S. GIBBONS (2010). Student Problem-Solving Behaviors: Traversing the Pirie-Kieren Model for Growth of Mathematical Understanding. Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education.