Skip to main navigation menu Skip to main content Skip to site footer

Artículos

Vol. 8 No. 2 (2005): Julio

¿CÓMO PIENSAN LOS ALUMNOS ENTRE 16 Y 20 AÑOS EL INFINITO? LA INFLUENCIA DE LOS MODELOS, LAS REPRESENTACIONES Y LOS LENGUAJES MATEMÁTICOS.

Submitted
December 5, 2024
Published
2005-07-31

Abstract

The ideas, results and reflections that we develop, are product of studies and part of investigations (Garbin 2000, 2003, 2005 and Garbin & Azcárate, 2001) that have intended to contribute with the debate of the problems of the mathematical infinite in their potentialactual duality (Fischbein, Tirosh & Hess (1979), Sierspinska (1987), Tall (1980), Tirosh, (1991), Moreno & Waldegg (1991), Tsamir & Tirosh, (1994), D’ Amore (1997), Tall (2001), Fischbein, 2001) that generates the influence of the representations and different mathematical languages on the perceptions of the infinite and mathematical reasoning associates, and in the weaknesses and inconsistencies of the student’s answers to problems in which infinite processes are present.

References

  1. Aline, R. y Schwarzenberger, R. (1990). Research in teaching and learning mathematics at an advanced level. En Tall, D. (Ed.), Advanced Mathematical Thinking. Kluwer Academic Publisher. Dordrecht/Boston/London.
  2. Bliss, J., Monk, M. y Ogborn, J. (1983). Qualitative Data Analysis for Educational Research. Croom Helm. London.
  3. Fischbein, E. (1982). Intuition and proof. For the Learning of Mathematics 3 (2), 9-19.
  4. Fischbein, E. (2001). Tacit models and infinity. Educational Studies in Mathematics, 2- 3 (48), 309-329.
  5. Fischbein, E., Tirosh, D. y Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics, 10, 2-40.
  6. D’amore, B. (1997). L’infinito in didattica de la matematica. Matematica e la sua Didattica 3, 289-305.
  7. Dreyfus, T. (1990). Advanced mathematical thinking. En Nesher, P. y Kilpatrick, J. (Ed), Mathematics and Cognition (pp 113-134). Cambridge University Press.
  8. Duval, R. (1996). Quel cognitif retenir en didactique des nathématiques? Recherches en Didactique des Mathématiques 6 (3), 349-382.
  9. Duval, R. (1999). L’Apprendimento in matematica richiede un funzionamiento cognitivo specifico?. La matematica e la sua Didattica 1, 17-42.
  10. Garbin, S. (2000). Infinito actual: inconsistencias e incoherencias de estudiantes de 16-17 años. Tesis doctoral. Universitat Autònoma de Barcelona. España.
  11. Garbin, S. (2003). Incoherencias y conexiones: el caso del infinito actual con estudiantes universitarios. Primera fase del estudio. ALME, Vol. 16.
  12. Garbin, S (2005). Ideas del infinito, percepciones y conexiones en distintos contextos: el caso de estudiantes con conocimientos previos de cálculo. Enseñanza de las Ciencias, 23.1, 61-80.
  13. Garbin, S. y Azcárate, C. (2001). El concepto de infinito actual: Una investigación acerca de las incoherencias que se evidencian en alumnos de bachillerato. Suma, 38, 53-67.
  14. Moreno, L.E. y Waldegg, G. (1991). The conceptual evolution of actual mathematical infinity. Educational Studies in Mathematics 22 (3), 211-231.
  15. Nuñez, E. (1994). Subdivision and small infinities Zeno, paradoxes and cognition. Actas del PME 18 (3), 368-375.
  16. NCTM (2000). Principios y Estándares para la Educación Matemática. Edición española por la Sociedad Andaluza de Educación Matemática Thales.
  17. Rucker, R. (1995). Infinity and the Mind. Princeton University Press.
  18. Sierspinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics 18, 371-397.
  19. Tall, D. (1980). The notions of infinite measuring numbers and its relevance to the intuition of infinity. Educational Studies in Mathematics 11, 271-284.
  20. Tall, D. (1990). Inconsistencies in the learning of calculus and analysis. Focus on Learning Problems in Mathematics 12, 49-64.
  21. Tall, D. (1995). Cognitive Growth in Elementary and Advanced Mathematical Thinking. Actas del PME 19, Vol. 1, 61-75.
  22. Tall, D. (2001). Natural and Formal Infinities. Educational Studies in Mathematics 48 (2/ 3), 199-238.
  23. Tall, D. y Vinner, S. (1981). Concept image and concept definition in mathematics with particular references to limits and continuity. Educational Studies in Mathematics 12 (2), 151-169.
  24. Tirosh, D. (1990). Inconsistencies in students’mathematical constructs. Focus on Learning Problems in Mathematics, 12, 111-129.
  25. Tirosh, D. (1991). The role of students’intuitions of infinity in teaching the cantorian theory. En Tall, D. (Ed), Advanved Mathematical Thinking (pp. 199-214). Kluwer Academic Publisher. Dordrecht/Boston/London.
  26. Tsamir, P. y Tirosh, D. (1994). Comparing infinite sets: intuitions and representations. Actas del PME 18, 4, 345-352.

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 > >> 

You may also start an advanced similarity search for this article.