Definir, buscar ejemplos, conjeturar… para probar si un número es feliz

  1. Angelina Alvarado Monroy 1
  2. María Teresa González Astudillo 2
  1. 1 Universidad Juárez del Estado de Durango (México)
  2. 2 Universidad de Salamanca (España)
Journal:
Avances de investigación en educación matemática: AIEM

ISSN: 2254-4313

Year of publication: 2014

Issue: 5

Pages: 5-24

Type: Article

DOI: 10.35763/AIEM.V1I5.73 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

More publications in: Avances de investigación en educación matemática: AIEM

Abstract

To instruct future mathematicians we need to confront them to tasks in which they must perform as if they were really mathematicians. In the task described below a group of students must understand a new definition: the happy number concept definition; they must extract information to generate examples that fit the definition, they must identify non-examples and find generic organizers to construct example spaces and finally solve a situation concerning these numbers. The interactions were first taped and then analyzed using the RBC-C model (Schwarz, Dreyfus, & Hershkowitz, 2009) to document how the process takes place. The results show that, although they did some conscious mistakes, the students confronted the task enthusiastically and they went on further the initial purpose

Bibliographic References

  • Alvarado, A., & González, M.T. (2010) La implicación lógica en el proceso de demostración matemática: estudio de un caso. Enseñanza de las Ciencias, 28(1), pp. 73-84
  • Alvarado, A., & González, M.T. (2013a) Interactive reconstruction of a definition. En B. Ubuz, C. Haser, M.A. Mariotti (eds.) Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education, 2276-2285. Antalya, Turquía
  • Alvarado, A., & González, M.T. (2013b) Generación interactiva del conocimiento para iniciarse en el manejo de las implicaciones lógicas. RELIME, 16(1), 37-63.
  • Bills, L., & Tall, D.O. (1998) Operable Definitions in Advanced Mathematics: The case of the Least Upper Bound, Proceedings of PME 22, Stellenbosch, South Africa, 2, 104–111.
  • Blanton, M., & Kaput, J. (2003) Developing elementary teachers' algebra eyes and ears. Teaching Children Mathematics, 10(2), 70-77.
  • Cobb (1995) Mathematical learning and small-group interaction: Four case studies. In P. Cobb & H. Bauersfeld (Eds.) The Emergence of Mathematical Meaning: Interaction in Classroom Cultures (pp. 25-129), Lawrence Erlbaum, Hillsdale.
  • Chevallard, Y. (1985). La transposition didactique; du savoir savant au savoir enseigné. Paris: La Pensée Sauvage.
  • Dreyfus, T., & Tsamir, P. (2004). Ben’s consolidation ok knowledge structures about infinite sets. Journal of Mathematical Behavior, 23, 271-300.
  • Edwards, B., & Ward, M. (2004). Surprises from Mathematics Education Research: Student (Mis)use of Mathematical Definitions. The Mathematical Association of America Monthly, 111, 411-424.
  • Gilboa, N. Dreyfus, T. & Kidron, I. (2011). A construction of a mathematical definition: the case of parabola. Proceeding of the 35PME (2), p.425-432. Turquía.
  • Goetting, M. (1995). The college students’ understanding of mathematical proof (Doctoral dissertation, University of Maryland, 1995). Dissertations Abstracts International, 56,3016A.
  • Hershkowitz, R., Schwarz, B.B. & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32, 195-222.
  • Kidron, I. (2008) Abstraction and consolidation of the limit procept by means of instrumented schemes: The complementary role of three different frameworks. Educational Studies in Mathematics, 69, 197-216.
  • Moore, R. C. (1994) Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249–266.
  • Pedemonte, B., & Buchbinder, O. (2011). Examining the role of examples in proving processes through a cognitive lens: the case of triangular numbers. ZDM, 43(2), 257-267.
  • Planas, N., & Morera, L. (2011). La argumentación en la matemática escolar: dos ejemplos para la formación del profesorado. In E. Badillo, L. García, A. Marbà & M. Briceño (Eds.), El desarrollo de competencias en las clases de ciencias y matemáticas (pp. 275-300). Mérida: Fondo Editorial Mario Briceño Iragorry. Universidad de los Andes.
  • Robinson, R. (1962). Definitions. London: Oxford University Press.
  • Schwarz, B.B., Dreyfus, T. & Hershkowitz, R. (2009). The nested epistemic actions model for abstraction in context. En B.B.Schwarz, T. Dreyfus & R. Hershkowitz (Eds.), Transformation of Knowledge through Classroom Interaction (pp. 11-42). London, UK: Routledge.
  • Selden, J., & Selden, A. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29, 123-151.
  • Steffe, L.P., & Wiegel, H.G. (1992) On reforming practice in mathematics education. Educational Studies in Mathematics, 23(5), 445-465.
  • Thompson, P. W. (1996). Imagery and the development of mathematical reasoning. In L. P. Steffe, B. Greer, P. Nesher, & G. Goldin (Eds.), Theories of learning mathematics (pp. 267-283). Hillsdale, NJ: Erlbaum.
  • Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Weber, K. (2001) Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101-119.
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