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Artículos

Vol. 17 No. 1 (2014): Marzo

ECOCAM, A CONTEXT SENSITIVE COMPUTATIONAL SYSTEM TO PROMOTE MENTALCALCULATION STRATEGIES: DESIGN CHARACTERISTICS AND PRELIMINARY RESULTS

DOI
https://doi.org/10.12802/relime.13.1712
Submitted
July 12, 2023
Published
2023-07-13

Abstract

Based on our previous work on cognitive strategies for mental calculation, we present the design of a context sensitive computational system called ECOCAM, which aims to promote strategies for mental calculation in primary school students. We carry out a first test of our proposal through a specific implementation of the ECOCAM for an addition strategy task, that is to say the “transfer” strategy, in a pilot experiment and study case with boys and girls from different grades in basic education. We discussed the results and its implications for a future development and implementation of the ECOCAM.

 

References

  1. Abowd, G. (1999). Classroom 2000: An experiment with the instrumentation of a living educational environment. IBM Systems Journal, 38(4), 508-530.
  2. Allan, C., Avgustinov, P., Christensen, A. S., Hendren, L., Kuzins, S., Lhoták, O., Moor, O, Sereni, G., Sittampalam G., & Tibble, J. (2005). Adding trace matching with free variables to AspectJ. ACM SIGPLAN Notices, 40(10), 345-364.
  3. Anselmo, B,. Evesque-Sagnard, S., Fenoy, K., Planchette, P., & Zuchetta, H. (2008). Calcul mental au collège: Nostalgie ou innovation? Lyon, France: IREM de Lyon.
  4. Askew, M. (2004). El CM, piedra angular del aprendizaje matemático inicial (entrevista). Revista de Educación, Ministerio de Educación de Chile, 310-311, 23-25.
  5. Askew, M., Ebbutt, S., & Mosley, F. (2006). Enseñanza de Estrategias de CM. 3° y 4° de Enseñanza Básica. Santiago, Chile: Galileo Libros.
  6. Baroody, A. J. (1987). The development of counting strategies for single-digit addition. Journal for Research in Mathematics Education, 18(2), 141-157.
  7. Beishuizen, M. (1993). Mental Strategies and Materials or Models for Addition and Subtraction up to 100 in Dutch Second Grades. Journal for Research in Mathematics Education, 24(4), 294-323.
  8. Braten, I. (1998). Cognitive strategies in mathematics, Part I: on children’s strategies for solving simple addition problems. Scandinavian Journal of Educational Research, 42(1), 5-24.
  9. Brissiaud, R. (2003). Comment les enfants apprennent à calculer. Paris, France: Retz.
  10. Bruner, J. (1996). The Culture of Education. Cambridge, EEUU: Harvard University Press.
  11. Butlen, D. & Pezard, M. (1992). Calcul mental et résolution de problèmes multiplicatifs. Recherche en Didactique des Mathématiques, 12(2/3), 319-368.
  12. Butlen, D. (2007). Le calcul mental entre sens et technique: recherches sur l’enseignement des mathématiques aux élèves en difficulté, du calcul mental à la résolution des problèmes numériques. Besançon, France: Presses de l’Université du Franche-Comté.
  13. Carpenter, T. P. & Moser, J. M. (1982). The development of addition and subtraction problem-solving skills. In T. P. Carpenter, J. M. Moser & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 9-24). Hillsdale, EEUU: Lawrence Erlbaum Associates.
  14. Christensen, C. A. & Cooper, T. J. (1991). Children’s solution strategies to single-digit addition problems: Some Australian data. Educational Research and Perspectives, 18(2), 62-70.
  15. Cook, D. (2006). Health Monitoring and Assistance to Support Aging in Place. Journal of Universal Computer Science, 12(1), 15-29. doi: 10.3217/jucs-012-01-0015
  16. Duval, R. (1995). Sémiosis et pensée humaine. Berna, Suiza: Peter Lang AG.
  17. Ebbutt, S., Mosley, F., & Skinner, C. (2005). Enseñanza de Estrategias de CM 1º y 2º Enseñanza Básica, Santiago, Chile: Galileo Libros.
  18. Ecocam (2010). http://www.pleger.cl/research/ecocam2. Recuperado el 20 de Septiembre del 2010, de http://pleger.cl/research/ecocam2
  19. English, L. (Ed.) (1997). Mathematical reasoning: Analogies, metaphors, and images. London, UK: Lawrence Erlbaum.
  20. Fernández, A. (2005). Avatares y estereotipos sobre la enseñanza de los algoritmos en matemáticas. Revista de Iberoamericana de Educación Matemática, 4, 31-46.
  21. Gallese, V. & Lakoff, G. (2005). The Brain’s concepts: the role of the Sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22 (3), 455-479. doi: 10.1080/ 02643290442000310.
  22. Gálvez, G. (2009). CM: pensado, reflexionado, simplificado. Santiago, Chile: Fundación Arauco.
  23. Gálvez, G., Cubillos, L., Cosmelli, D., Léger, P., Mena, A., Tanter, É., Flores, X., Luci, G., Montoya, S., & Soto Andrade, J. (2011). Estrategias cognitivas para el Cálculo Mental. Revista Latinoamericana de Investigación en Matemática Educativa, 14(1), 9-40.
  24. Godino, J. D. (1993). Paradigmas, problemas y metodologías en didáctica de la matemática. Quadrante, 2(1), 9-22.
  25. Heirdsfield, A. (2000). Mental computation: Is it more than mental architecture? Annual Meeting of the Australian Association for Research in Education. Recuperado el 15 de Enero de 2010, de http://www.aare.edu.au/00pap/hei00259.htm
  26. Hirschfeld, R., Constanza, P., & Nierstrasz, O. (2008). Context-Oriented Programming. Journal of Object Technology, 7(3), 125-151.
  27. Houlihan, D. M. & Ginsburg, H. P. (1981). The addition methods of first and second-grade children. Journal for Research in Mathematics Education, 12(2), 95-106.
  28. Isoda, M., Arcavi, A. & Mena, A. (Eds) (2008). El Estudio de Clases japonés en Matemáticas (2da ed.). Valparaíso, Chile: Ediciones Universitarias de Valparaíso.
  29. Johnson, M. & Lakoff, G. (2003). Metaphors we live by. New York, EEUU: The University of Chicago Press.
  30. Kamii, C., Lewis, B. A., & Livingston, S. J. (1993). Primary arithmetic: Children inventing their own procedures. Arithmetic Teacher, 41(4), 200-203.
  31. Kamii, C. & Dominick, A. (1998). The harmful effects of algorithms in grades 1-4. In L.J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics, 1998 yearbook (pp. 130-140). Reston, EEUU: NCTM.
  32. Klein, T. & Beishuizen, M. (1994). Assessment of flexibility in mental arithmetic. In J.E.H. Van Luit (Ed.), Research on learning and instruction of mathematics in kindergarten and primary schools (pp. 125-152). Doetinchem, The Netherlands: Graviatt Publishing Company.
  33. Knops, A., Thirion, B., Hubbard, E., Michel, V., & Dehaene, S. (2009). Recruitment of an area involved in eye movements during mental arithmetic. Science 1, 324 (5934), 1583-1585. doi: 10.1126/science.1171599
  34. Lakoff, G. & Núñez, R. (2000). Where Mathematics comes from. New York, EEUU: Basic Books.
  35. Leger, P. & Tanter, É. (2010). An open trace-based mechanism. In J. Aldrich & R. Massa (Eds.), Proceedings of SBLP 2010: 14 th Brazilian Symposium on Programming Languages. (pp. 123-138). Salvador de Bahia, Brasil: Brazilian Conference on Software: Theory and Practice.
  36. Lethielleux, C. (2005), Le calcul mental au cycle des apprentissages fondamentaux (Vol. 1). Paris, France: Bordas/Séjer
  37. Masciotra, D., Roth, W. M., & Morel, D. (2007). Enaction: toward a Zen mind in learning and teaching. Twente, The Netherlands: Sense Publishers.
  38. Ortega, T. y Ortiz, M. (2002). Diseño de una intervención para la enseñanza-aprendizaje del CM en el aula. Revista Latinoamericana de Investigación en Matemática Educativa, 5(3), 271-291.
  39. Parra, C. (1993). CM en la escuela primaria. En C. Parra e I. Sáiz (Eds.), Didáctica de matemáticas. Aportes y reflexiones (pp. 219-272). Buenos Aires, Argentina: Paidós.
  40. Pochon, L-O. (1997). Regard sur le calcul mental. Math Ecole, 36(179), 19-27.
  41. Postlewait, K. B., Adams, M. R., & Shih, J. C. (2003). Promoting meaningful mastery of addition and subtraction. Teaching Children Mathematics, 9(6), 354-357.
  42. Presmeg, N. C.(1997). Reasoning with metaphors and metonymies in mathematics learning. In L. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images, (pp. 267-279). London,UK: Lawrence Erlbaum Associates.
  43. Radford, L. & André, M. (2009). Cerebro, cognición y matemáticas. Revista Latinoamericana de Investigación en Matemática Educativa, 12(2), 215-250.
  44. Reys, R. E., Reys, B. J., Nohda, N., & Emori, H. (1995). Mental computation performance and strategy use of Japanese students in grades 2, 4, 6, and 8. Journal for Research in Mathematics Education, 26(4), 304-326.
  45. Riveros, M., Gálvez, G., Navarro, S., & Zanocco, P. (1996). Tilín-Tilón. Actividades para el desarrollo de la capacidad de calcular. Programa de las 900 Escuelas. Santiago, Chile: MINEDUC.
  46. Sfard, A. (1994). Reification as the birth of metaphor. For the Learning of Mathematics, 14(1),44-55.
  47. Sfard, A. (1997). Commentary: On metaphorical roots of conceptual growth. In L. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 339-371). London, UK: Lawrence Erlbaum Associates.
  48. Shrager, J. & Siegler, R. S. (1998), SCADS: A model of children’s strategy choices and strategy discoveries. Psychological Science, 9(5), 405-410. doi: 10.1111/1467-9280.00076
  49. Siegler, R. S. & Campbell, J. (1989). Individual differences in children’s strategy choices. In P. L. Ackerman, R. J. Sternberg, & R. Glaser (Eds.), Learning and individual differences: Advances in theory and research (pp. 219-254). New York, EEUU: Freeman.
  50. Siegler, R. S. & Jenkins, E. (1989). How children discover new strategies. Hillsdale, EEUU: Lawrence Erlbaum Associates.
  51. Siegler, R. S. & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), The origins of cognitive skills (pp. 229-293). Hillsdale, EEUU: Lawrence Erlbaum Associates.
  52. Soto-Andrade, J. (2006). Un monde dans un grain de sable: Métaphores et analogies dans l’apprentissage des mathématiques. Annales de Didactique et de Sciences Cognitives, 11, 123-147.
  53. Soto-Andrade, J. (2007a). Metaphors and cognitive styles in the teaching-learning of mathematics. In D. Pitta-Pantazi, & J. Philippou (Eds.), Proceedings Congress of European Research in Mathematics Education 5 (pp. 191-200). Larnaca, Cyprus.
  54. Soto-Andrade, J. (2007a). Metaphors and cognitive styles in the teaching-learning of mathematics. In D. Pitta-Pantazi, & J. Philippou (Eds.), Proceedings Congress of European Research in Mathematics Education 5 (pp. 191-200). Recuperado de http://ermeweb.free.fr/CERME5b/
  55. Soto-Andrade, J. (2007b), La cognición hecha cuerpo florece en metáforas…. En A. Ibáñez & D. Cosmelli, (Eds.), Nuevos Enfoques de la Cognición : Redescubriendo la dinámica de la acción, la intención y la intersubjetividad (pp. 71-90). Santiago, Chile: Universidad Diego Portales.
  56. Soto-Andrade, J. (2008, July). Mathematics as the art of seeing the invisible…. Paper presented at 11th International Congress in Mathematics Education, Monterrey, México.
  57. Stewart, J. R., Gapenne, O., & Di Paolo, E. A. (2010). Enaction: Towards a New Paradigm for Cognitive Science. Cambridge, EEUU: MIT Press.
  58. Sun, H. (2008). Chinese young children’s strategies on basic addition facts. In M. Goos, R. Brown, K. Makar (Eds.), Proceedings of the 31th annual conference of the Mathematics Education Research Group of Australasia (pp. 499-505). Brisbane, Australia: MERGA
  59. Taton, R. (1953). Le calcul mental, Coll. Que sais-je, No 605. Paris, France: P.U.F.
  60. Varela, F. J., Thomson, E., & Rosch, E. (1991). The Embodied Mind: Cognitive Science and Human Experience. Cambridge, EEUU: MIT Press.
  61. Williamson, V. (2007). Mental Maths – Passive to Active. Mathematics Teaching, 201, 12-15.
  62. Yeap, B. H. (2005). Helping every student to develop the ability in mathematical problem solving: The Singapore experience. In S. Chaiyasang, P. Wongyai & R. Janjaruporn, (Eds.). The Proceedings of Symposium on Mathematics Education: Mathematical Problem Solving (pp. 3-12). Bangkok, Thailand: Srinakharinwirot University.

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