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Artículos

Vol. 10 No. 1 (2007): Marzo

RELACIONES ENTRE ÁREA Y PERÍMETRO: CONVICCIONES DE MAESTROS Y DE ESTUDIANTES

Submitted
September 8, 2024
Published
2007-01-14

Abstract

In this research we examine the convictions of teachers and students regarding the existing relations between perimeter and area of a flat figure. The research is inserted in a classical position, explored for more than 60 years, but that today includes new factors. Particularly, the change of the convictions is studied, the language utilized to express that change, the degree of incident that have the given examples, and, particularly, we discuss the idea that the supposed relations between perimeter and area constitute an example of the not criticism attitude of the student that tends to confirm increases or decreases among entities put in relation.

References

  1. Azhari, N. (1998). Using the intuitive rule «Same of A, same of B» in conservation tasks Manuscrito no publicado, cit. en Stavy y Tirosh (2001).
  2. Battro, A. M. (1983). Il pensiero di Jean Piaget. Bologna, Italia: Pitagora. [Ed. original en español: 1969, Buenos Aires: Emecé].
  3. Beswick, K. (2004). The impact of teachers' perceptions of student characteristics on the enactemnent of their beliefs. En: Høines MJ., Fuglestad AB. (eds.) Proceedings of the 28th PME Intemational Conference. 2, 111-118.
  4. Brousseau, G. (1976). Les obstacles épistémologiques et les problèmes en mathémati- ques. En: Wanhamme W. & Wanhamme J. (eds.) [Se publicó nuevamente en Recher- ches en didactique des mathématiques 4(2), 1983, 165-198].
  5. Brousseau, G (1986). Fondements et Méthodes de la Didactique des Mathématiques. Recherches en didactique des mathématiques 7(2), 33-115.
  6. Brousseau, G (1989). Obstacles épistémologiques, conflicts socio-cognitifs et ingéniérie didactique. En: Bodnarz N. & Garnier C. (eds.) Les obstacles épístémologiques et le conflit socio-cognitif. Construction des savoirs (obstacles et conflits). Colloque internationale CIRADE, Université de Québec, Canadá.
  7. Chamorro, M. C. (1997). Estudio de las situaciones de enseñanza de la medida en la escuela elemental. Tesis de doctorado. UNED.
  8. Chamorro, M. C. (2001). Le difficoltà nell'insegnamento-apprendimento delle grandezze nella scuola di base. La matematica e la sua didattica 9(4), 332-351.
  9. Chamorro, M. C. (2002). Le difficoltà nell'insegnamento-apprendimento delle grandezze nella scuola di base. La matematica e la sua didattica 10(1), 58-77.
  10. Chevallard, Y. (1985) La transposition didactique. Du savoir savant au savoir enseigné. Grenoble: La Pensée Sauvage.
  11. D'Amore, B. & Fandiño, M. I. (2005). Cambios de convicciones en futuros profesores de matemática de la escuela secundaria superior. Espilion 58, 20(1), 25-43.
  12. D'Amore, B. & Fandiño, M. I. (2006). Area e perimetro. Aspetti concettuali e didattici. Trento, Italia: Erickson.
  13. D'Amore, B. & Maier, H. (2003). Producciones escritas de los estudiantes sobre argu- mentos de matemáticas. Espsilon. 18(2), 53, 243-262.
  14. Edwards, T. G & Hensien S. M. (1999). Changing instructional practice through action research. Joumal of Mathematics Teacher Education. 2(2), 187-206.
  15. Fennema, E. & Franke, M. L. (1992). Teachers' Knowledge and its Impact. En: D. Grows (Ed.). Handbook of Research on Mathematics Teaching and Learning. (pp. 147-164). New York: Macmillan Publishing Company.
  16. Fischbein, E. (1985). Intuizione pensiero analitico nell'educazione matematica. En: Artu- si Chini, L (Ed.). Numeri e operazioni nella scuola di base (pp. 8-19). Bologna, Italia: Zanichelli.
  17. Gentner, D. (1983). Structure mapping: a theoretical framework. Cognitive Science 7. 156-166.
  18. Giovannoni, L. (1996). Misure di estensione superficiale nella scuola dell'infanzia. La matematica e la sua didattica 4, 394-423.
  19. Gudmundsdottir, S. (1996). The Teller, the Tale, and the One Being Told: The Narrative Nature of the Research Interview. Curriculum Inquiry 26(3), 293-300.
  20. Gudmundsdottir, S. (2001). Narrative research on school practice. En: V. Richardson (Ed.) (2001). Fourth Handbook for Research on Teaching. New York: Macmillan. 226- 240.
  21. Gudmundsdottir, S. & Flem, A. (2000). Voices of teachers in school reform. Keynote paper at a workshop on "Teachers' lives, narrative research, and school change". Haifa University, Israel, 18 de mayo de 2000. Obtenido en: http://www.sv.ntnu.no/ped/sigrun/ publikasjoner/voices.htm (23/05/05).
  22. Hoyles, C. (1992). Mathematics teaching and mathematics teachers: a meta-case study For the leaming of mathematics 12(3), 32-44
  23. lacomella, A. & Marchini, C. (1990). Riflessioni sul problema della misura. Periodico matematiche. 66, VI, 4, 28-52.
  24. Jaquet, F. (2000). Il conflitto area-perimetro I. L'educazione matematica 2(2), 66-77
  25. Jaquet, F. (2000). IIl conflitto area-perimetro II. L'educazione matematica 2(3), 126-143
  26. Krainer, K., Goffree, F. & Berger, P. (Eds.) (1999). On Research in Mathematics Teacher Education. Osnabrück, Alemania: Forschunginstitut für Mathematik Didaktik. Obtenido en: http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/cerme1. proceedings.html.
  27. Llinares, S. & Krainer, K. (2006). Mathematics (student) teachers and teacher educators as learners. En: A. Gutierrez, P. Boero (Eds.) Handbook of Research on the Psychology of Mathematics Education (pp. 429-459). Rotterdam, The Netherlands: Sense Publishers B.V. En prensa.
  28. Llinares, S. & Sánchez García, V. (2002). Imágenes sobre las matemáticas, su enseñan za y aprendizaje en estudiantes para profesores de secundaria y tareas matemáticas escolares. Revista de Educación 3, 443-461.
  29. Marchini, C. (1999). Il problema dell'area. L'educazione matematica 1(1), 27-48.
  30. Medici, D. (1999). Un problema e la sua analisi: frazione di terreno. En: L. Grugnetti & F Jaquet (Eds.). // Rally matematico transalpino. Quali apporti per la didattica? Actas de las jornadas de estudio sobre el Rally Matemático Trasalpino. Brigue, 1997-1998. Parma - Neuchâtel: Departamento de Matemática de la Universidad de Parma - IRDP de Neuchâtel.
  31. Medici, D., Marchetti, P., Vighi, P. & Zaccomer, E. (2005). Comparing perimeters and areas childrens' pre-conceptions and spontaneous procedures. Texto presentado al Cer-me 4: Obtenido en: http://cerme4.crm.es/Papers%20definitius/7/wg7listofpapers.htm
  32. Montis, A. M., Mallocci, P. & Polo, M. (2003). Congettura e argomentazione nella cos- truzione dei concetti di equiestensione e isoperimetria:. un percorso didattico dalla prima alla quinta elementare. L'educazione matematica 3, 1-12.
  33. Moreira, P. & Comiti, C. (1993). Difficultés rencontrées par des élèves de cinquième en ce qui concerne la dissociation aire/périmètre pour des rectangles. Petit x 34, 43-68.
  34. Moreira, P. (1996). À propos de l'apprentissage du concept d'aire. Petit x 43, 43-68.
  35. Outhred, L. & Mitchelmore, M. (1992). Representation of area: a pictorial perspective. XVI PME. 2, 194-201.
  36. Pehkonen, E. & Törner, G (1996). Introduction to the theme: Mathematical beliefs. Zentralblatt für Didaktik der Mathematik. 28, 99-100.
  37. Piaget, J. (1926). La rappresentazione del mondo nel fanciullo. Torino: Boringhieri, 1966. [Ed. original en francés: 1926, Paris: Alcan).
  38. Piaget, J. (1937). La costruzione del reale nel bambino. Firenze: La Nuova Italia, 1973. [Ed. original en francés: 1937, Neuchâtel: Delachaux & Niestlé].
  39. Piaget, J. & Inhelder, B. (1962). Lo sviluppo delle quantità fisiche nel bambino. Firenze: La Nuova Italia, 1971. [Ed. original en francés: 1962, Paris - Neuchâtel: Delachaux & Niestlé].
  40. Piaget, J., Inhelder, B. & Szeminska, A. (1948). La geometria spontanea del bambino. Firenze: Giunti Barbèra, 1976. [Ed. original en francés: 1948, Paris: PUF].
  41. Presmeg, N. (2002). Beliefs about the nature of mathematics in the bridging of everyday and school mathematical practices. En: G Leder, E. Pehkonen & G Törner (Eds.) (2002). Beliefs: A hidden variable in mathematics education? (pp. 293-312). Dordrecht: Kluwer Academic Publishers.
  42. Raths, J. (2001). Teachers' Beliefs and Teaching Beliefs. Early Childhood Research & Practice. 3, 1. Obtenido en: http://ecrp.uiuc.edu/v3n1/raths.html(05/03/05)
  43. Resnick, L. B. & Ford, W. W. (1981). Psicologia della matematica e apprendimento sco- lastico. Torino: Sei. [Ed. original en inglés: 1981, Hillsdale: Lawrence Erlbaum Associa- tes].
  44. Rogalski, J. (1979). Quantités physiques et structures numériques. Mesures et quantifca- tion: les cardinaux finis, les longeurs, surfaces et volumes. Bulletin de l'APMEP. 320, 563-586.
  45. Rouche, N. (1992). Le sense de la mesure. Bruxelles: Didier Hatier.
  46. Schoenfeld, A. H. (1983). Beyond the purely cognitive: beliefs systems, social cognitions and metacognitions as driving forces in intellectual performance. Cognitive science 7(4), 329-363.
  47. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacogni- tion and sense making in mathematics. En: A. D. Grows (Ed.) (1992). Handbook of research on mathematics leaming and teaching. (pp. 334-370). New York: MacMillan
  48. Skott, J. (1999). The multples motives of teacher activity and the roles of the teachers school mathematical images. In: O. Zaslavsky (Ed.) (1999). Proceedings of the 23rd PME International Conference. 4 (pp. 209-216).
  49. Speranza, F. (1987). La geometria dalle cose alla logica. En: B. D'Amore (Ed.) (1987). La matematica e la sua didattica. Bologna: Pitagora. 105-114.
  50. Stavy, R. & Tirosh, D. (2001). Perché gli studenti fraintendono matematica e scienze? Trento: Erickson.
  51. Strehle, E., Whatley, A., Kurz, K. A., Hausfather, S. J. & Stroudsburg, E. (2001). Narrati ves of collaboration: inquiring into technology integration in teacher eduaction. Joumal of Technology and Teacher Education 10(1), 27-47.
  52. Thompson, A. G (1992). Teachers' Beliefs and Conceptions: a Synthesis of the Resear ch. En: D. Grouws (Ed.) (1992). Handbook of Research on Mathematics Leaming and Teaching. (pp. 127-145). New York: Macmillan Publishing Company.
  53. Tierney C., Boyd, C. & Davis, G. (1990). Prospective Primary Teachers's Conception of area. XIV PME. 2, 307-315.
  54. Tirosh, D. & Graeber, A. (2003). Challenging and changing mathematics teaching class- room practice. En: A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick & F. K. S. Leung (Eds.) Second International Handbook of Mathematics Education (pp. 643-687). Dordre- cht: Kluwer Academic Publishers
  55. Törner, G. (2002). Mathematical beliefs. A search of a common ground: some theoretical considerations on structuring beliefs, some research questions, and some pheno- menological observations. En: G C. Leder, E. Pehkonen & G Törner (Eds.) Beliefs: A hidden variable on mathematics education? (pp. 73-94), Dordrecht-Boston-Londres: Kluwer Ac. P.
  56. Vihn, B. et al. (1964). L'épistemologie de l'espace. París: PUF.
  57. Vihn, B. & Lunzer, E. (1965). Conservations spaciales. Paris: PUF.

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