El concepto de serie numérica. Un estudio a través del modelo de Pirie y Kieren centrado en el mecanismo “folding back”

  1. M. Laura Delgado Martín 1
  2. Myriam Codes Valcarce 1
  3. M. Consuelo Monterrubio Pérez 1
  4. M. Teresa González Astudillo 1
  1. 1 Universidad de Salamanca (España)
Journal:
Avances de investigación en educación matemática

ISSN: 2254-4313

Year of publication: 2014

Issue: 6

Pages: 25-44

Type: Article

DOI: 10.35763/AIEM.V1I6.85 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

More publications in: Avances de investigación en educación matemática

Abstract

In this paper we present a research about the process followed by group of university students to build a numerical series and to determine its convergence. To this aim, the activity of the students is analyzed through the Pirie and Kieren model, while they are solving a task in their usual classroom. This theoretical frame can describe their progression through the different levels of the model. We have been able to prove in several situations that it is necessary to go back to inner levels using a mechanism called “folding back”, which can be caused by different reasons

Bibliographic References

  • Carlsen, M. (2010). Appropriating geometric series as a cultural tool: a study of student collaborative Learning. Educational Studies in Mathematics, 74, 95-116. doi: 10.1007/s10649-010-9230-0.
  • 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). Universidad de Salamanca, Salamanca, España. http://hdl.handle.net/10366/76452
  • Codes, M., Delgado, M. L., González Astudillo, M. T., & Monterrubio, M. C. (2013) Comprensión del concepto de serie numérica a través del modelo de Pirie y Kieren. Enseñanza de las Ciencias, 31(3), 135-154.
  • Codes, M., González, M.T., Delgado, M.L., & Monterrubio, M.C. (2013). Growth in the understanding of the concept of infinite numerical series: a glance through Pirie and Kieren theory. International Journal of Mathematical Education in Science and Technology, 44(5), 652-662.
  • Codes, M., & Sierra M. (2007). Actividad Rectángulos: Un ejemplo de aplicación de metodologías activas en el aula universitaria de matemáticas. Actas de las IVJornadas internacionales de Innovación Universitaria (2007). Madrid: Universidad Europea de Madrid.
  • Delgado, M. L., González, M. T., Monterrubio, C., & Codes, M. (2013). El mecanismo collecting para la comprensión del concepto de serie numérica. En A. Berciano, G. Gutiérrez, A. Estepa & N. Climent (Eds.), Investigación en Educación Matemática XVII (pp. 245-252). Bilbao: SEIEM.
  • Dubinsky, E., Weller, K., McDonald, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: an APOS-based analysis: part II. Educational Studies in Mathematics, 60, 253-266.
  • González-Martín, A. S., Nardi, E., & Biza, I. (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), 565-589.
  • Kidron, I. (2002). Concept definition, concept image, and the notion of infinite sum in old and new environments. En A. D. Cockbrun & E. Nardi (Eds.), 26th International Conference for the Psychology of Mathematics Education, 3, 209- 216.
  • McDonald, M. A., Mathews, D. M., & Strobel, K. H. (2000). Understanding sequences: A tale of two objects, En J. Kaput, A. H. Schoenfeld, & E. Dubinsky (Eds.), Research in collegiate mathematics education. IV. Conference Board of the Mathematical Sciences (CBMS), Issues in Mathematics Education, 8, 77-102
  • Martin, L. C. (2008). Folding back and the dynamical growth of mathematical understanding: Elaborating the Pirie–Kieren Theory. The Journal of Mathematical Behavior, 27, 64-85.
  • Martínez-Planell, R., Gonzalez, A. C., DiCristina, G., & Acevedo, V. (2012). Students’ conception of infinite series. Educational Studies in Mathematics, 81, 235-249.
  • Pirie, S., & Kieren, T. (1992). Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics, 23, 505-528.
  • Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in Mathematics, 26, 165-190.
  • Pirie, S., & Martin, L. C. (2000). The role of collecting in the growth of mathematical understanding. Mathematics Education Research Journal, 12(2), 127-146.
  • Tall, D. (1991). The psychology of Advanced Mathematical Thinking. En D. Tall (Ed.), Advanced Mathematical Thinking (pp. 3-21). Dordrecht: Kluwer Academic Publishers.
  • Warner, L. B. (2008). How do students’ behaviors relate to the growth of their mathematical ideas? Journal of Mathematical Behavior, 27, 206-227.
  • Weller, K., Brown, A., Dubinsky, E., McDonald, M., & Stenger, C. (2004). Intimations of infinity. Notices of the American Mathematical Society, 51(7), 741- 750.
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