Aller directement au menu principal Aller directement au contenu principal Aller au pied de page
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 16 No 3 (2013): Noviembre

PROBLEMAS DE ESTIMACIÓN DE GRANDES CANTIDADES: MODELIZACIÓN E INFLUENCIA DEL CONTEXTO

DOI
https://doi.org/10.12802/relime.13.1631
Soumis
juillet 13, 2023
Publiée
2023-07-13

Résumé

Dans cet article on introduit les problèmes d’estimation de grands nombres. On s’est proposé d’étudier les processus de modélisation mathématique et l’influence du contexte de ces problèmes dans les résolutions des élèves de collège en Espagne. Grâce à une analyse qualitative, on est arrivé à trois catégories pour analyser les résultats: les réponses orientées à la question, les stratégies et le succès dans la résolution. On a analysé aussi les relations entre les stratégies proposées par les élèves et les contextes des situations dans les énoncés des problèmes, ainsi que la modélisation des situations à résoudre. D’après les données recueillies par notre étude, on déduit que le contexte peut influencer les propositions de résolution des élèves. On conclut que ce type de problèmes peuvent être utilisés pour introduire la modélisation dans la salle de classe.

Références

  1. Arcavi, A. (2002). The Everyday and the Academic in Mathematics. En M. Brenner & J.Moschkovich (Eds.), Everyday and Academic Mathematics in the Classroom (pp. 12–29). Reston(VA), USA: NCTM
  2. Ärlebäck, J. B. (2009). On the use of realistic Fermi problems for introducing mathematical modelling in school. The Montana Mathematics Enthusiast, 6(3), 331–364. DOI: 10.1007/9781-4419-0561-1_52
  3. Barth, H., Kanwisher, N. & Spelke, E. (2003). The construction of large number representations in adults. Cognition, 86, 201–221. DOI: 10.1016/s0010-0277(02)00178-6
  4. Booth J.L. & Siegler, R.S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41(6), 189–201. DOI: 10.1037/0012-1649.41.6.189
  5. Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62, 211–230. DOI: 10.1007/s10649-006-7834-1
  6. Codes, M., González, M. T., Monterrubio, M. C. & Delgado, M. L. (2011). El análisis matemático a través de las situaciones reales presentes en los libros de texto de educación secundaria. En M. M. Moreno, A. Estrada, J. Carrillo & T. A. Sierra (Eds.), Investigación en Educación Matemática. Comunicaciones de los Grupos de Investigación de la SEIEM. XIV Simposio de la SEIEM (pp. 173–186). Lleida, España: SEIEM.
  7. Doerr, H. & English, L. D. (2003). A modelling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.
  8. Doerr, H. M. (2006a). Examining the tasks of teaching when using students’ mathematical thinking. Educational Studies in Mathematics, 62, 3–24. DOI: 10.1007/s10649-006-4437-9
  9. Doerr, H. M. (2006b). Teachers’ ways of listening and responding to students’ emerging mathematical models. ZDM The International Journal on Mathematics Education, 38(3), 255–268. DOI: 10.1007/BF02652809
  10. English. L. D. (2006). Mathematical modeling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303–323. DOI: 10.1007/s10649005-9013-1
  11. Esteley, C. B., Villarreal, M. E. & Alagia, H. R. (2010). The overgeneralization of linear models among university students’ mathematical productions: A long-term study. Mathematical Thinking and Learning, 12(1), 86–108. DOI:10.1080/10986060903465988
  12. Freudenthal. H. (1983). Didactical Phenomenology Of Mathematical Structures. Dordrecht, Netherlands: Kluwer Academic Publishers Group.
  13. Gibbs, G. (2007). Analizing qualitative data. London, United Kingdom: SAGE Publications.
  14. Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(13), 170-218. DOI: 10.2307/749074
  15. Hildreth, D. J. (1983). The use of strategies in estimating measurements. Arithmetic Teacher,30(5), 50–54.
  16. Hogan, T. P. & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities? Mathematical Thinking and Learning, 5(4), 259–280. DOI: 10.1207/S15327833MTL0504_02
  17. Jones, M. G., Gardner, G. E., Taylor, A. R., Forrester, J. H. & Andre, T. (2012). Students’ accuracy of measurement estimation: Context, units, and logical thinking. School Science and Mathematics, 112(3), 171–178. DOI: 10.1111/j.1949-8594.2011.00130.x
  18. Jurdak, M. & Shahin, I. (1999). An ethnographic study of the computational strategies of a group of young street vendors in Beirut. Educational Studies in Mathematics, 40(2), 155–172. DOI: 10.1023/A:1003894908704
  19. Jurdak, M. & Shahin, I. (2001). Problem solving activity in the workplace and the school: the case of constructing solids. Educational Studies in Mathematics, 47(3), 297–315. DOI: 10.1023/A:1015106804646
  20. Jurdak, M. (2006). Contrasting perspectives and performance of high school students on problem solving in real world situated, and school contexts. Educational Studies in Mathematics, 63(3), 283–301. DOI:10.1007/s10649-005-9008-y
  21. De Lange, J. (1996). Using and applying mathematics in education. In A. J. Bishop (Ed.), International Handbook of Mathematics Education (pp. 49–97). Dordrecht, Netherlands: Kluwer Academic Publishers Group.
  22. Lesh, R. & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2), 157–189. DOI: 10.1080/10986065.2003.9679998
  23. Lesh, R. & Zawojewski, J. S. (2007). Problem solving and modeling. In F. K. Lester (Ed.), The second handbook of research on mathematics teaching and learning (pp. 763-804). Charlotte (NC), USA: Information Age Publishing.
  24. Lester, F.K. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25(6), 660–675. DOI: 10.2307/749578
  25. Martínez, M. (2008). Contextualización y enseñanza de las matemáticas en la educación primaria. En R. Cantoral, O. Covián, R. M. Farfán, J. Lezama, & A. Romo (Eds.), Investigaciones sobre Enseñanza y aprendizaje de las Matemáticas. Un reporte iberoamericano (pp. 613-641). México (DF), México: CLAME.
  26. Nunes, T., Schliemann, A. D. & Carraher D. W. (1993). Street mathematics and school mathematics. Cambridge, United Kingdom: Cambridge University Press.
  27. Palm, T. (2006). Word problems as simulations of real-world situations: A proposed framework. For the Learning of Mathematics, 26(1), 42–47.
  28. Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67(1), 37–58. DOI: 10.1007/s10649-007-9083-3
  29. Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: Pupils’ interactive modelling processes. En S. Ruwisch & A. Peter-Koop (Eds.), Mathematics education for the third millennium: Towards 2010 (pp. 454-461) Sydney, Australia: MERGA.
  30. Pólya, G. (1945). How to solve it. Princeton (NJ), USA: Princeton University Press.
  31. Puig, L. (1996). Elementos de resolución de problemas. Granada, España: Ed. Comares.
  32. Puig, L. (2008). Presencia y ausencia de la resolución de problemas en la investigación y el currículo. En R. Luengo, B. Gómez, M. Camacho & L. J. Blanco (Eds.), Actas del XII Simposio de la Sociedad Española de Investigación en Educación Matemática. Badajoz, España: SEIEM.
  33. Reys, R. E., Rybolt, J. F., Bestgen, B. J. & Wyatt, J. W. (1982). Processes used by good computational estimators. Journal for Research in Mathematics Education, 13, 183-201.
  34. Segovia, I. & Castro, E. (2009). La estimación en el cálculo y en la medida: fundamentación curricular e investigaciones desarrolladas en el departamento de didáctica de la matemática de la universidad de granada. Electronic Journal of Research in Educational Psychology, 7(1), 499-536.
  35. Segovia, I., Castro, E., Castro, E. & Rico, L. (1989). Estimación en Cálculo y Medida. Madrid, España: Síntesis.
  36. Segovia, I., Rico, L. & Castro, E. (1996). Estrategias de estimación de cantidades discretas: estudio exploratorio de competencias. Granada, España: Universidad de Granada. Recuperado el 21 de octubre de 2013 de http://cumbia.ath.cx:591/pna/Archivos/SegoviaI96-149.PDF
  37. Schoenfeld, A. H. (2007). Problem solving in the United States, 1970-2008: research and theory, practice and politics. ZDM The International Journal on Mathematics Education, 39(5-6), 537-551. DOI: 10.1007/s11858-007-0038-z
  38. Sriraman, B., Knott, L. & Adrian, H. (2009). The mathematics of estimation: Possibilities for interdisciplinary pedagogy and social consciousness. INTERCHANGE: A Quarterly Review of Education, 40(2), 205–223. DOI: 10.1007/s10780-009-9090-7
  39. Sriraman, B. & Lesh, R. (2006). Modeling conceptions revisited. ZDM The International Journal on Mathematics Education, 38(3), 247–254. DOI: 10.1007/BF02652808
  40. Stocker, D. (2006). Re-thinking real-world mathematics. For the Learning of Mathematics, 26(2), 29–29.
  41. Taylor, A. R., Jones, M. G. & Broadwell, B. (2009). Estimating linear size and scale: Body rulers. International Journal of Science Education, 31(11), 1495–1509. DOI:10.1080/ 09500690802101976
  42. Van Den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2–10.
  43. Verschaffel, L. (2002). Taking the modeling perspective seriously at the elementary level: Promises and pitfalls. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference (Vol. 1, pp. 64–80). Norwich. United Kingdom: PME
  44. Winter, H. (1994). Modelle als konstrukte zwischen lebensweltlichen situationen undarithmetischen begriffen. Grundschule, 26(3), 10–13.

Téléchargements

Les données relatives au téléchargement ne sont pas encore disponibles.

Articles similaires

1 2 3 4 5 6 7 8 9 10 > >> 

Vous pouvez également Lancer une recherche avancée de similarité pour cet article.