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

Artículos

Vol. 20 No. 1 (2017): Marzo

THE FRAMES OF MEANING HYPOTHESIS : CHILDREN ’S MATHEMATICAL PROBLEM-SOLVING ABILITIES

DOI
https://doi.org/10.12802/relime.17.2012
Submitted
June 29, 2023
Published
2017-03-31

Abstract

This paper intends to describe a phenomenon observed when children aged 6 and 7 years old, who had not yet received formal  instruction about division, tried to solve a problem of distribution by means of drawings. The phenomenon called “frames of  meaning” attempts to explain why some children were successful in solving problems and others were not. We illustrate this  hypothesis empirically through a case study. This hypothesis is a powerful theoretical and methodological tool for understanding  the underlying mathematical thinking and arithmetic problem-solving abilities of children this age. However, it is necessary to  continue to expand our analysis and the application of this framework. This would lead to reconsider conventional educational and  evaluative practices. In this article we try to point the way by which these changes could be made.

References

  1. Adams, R. (2005). PISA 2003 Technical Report: Programme for International Student Assessment: OECD Publishing.
  2. Andrade Londoño, E., Andrade Lotero, L. A., y Lotero Botero, L. A. (en elaboración). Beyond the Times-Tables: Making Sense of Multiplication.
  3. Bell, P. (2001). Content analysis of visual images. En T. V. Leeuwen y C. Jewitt (Eds.), Handbook of visual analysis (pp. 10-34). Oaks, California: SAGE Publications.
  4. Bello, S. (2004). Ideas previas y cambio conceptual. Educación química, 15(3), 210-217. Obtenido de http://depa.fquim.unam.mx/sie/Documentos/153-bel.pdf.
  5. Bermejo, V. (2005). Microgénesis y cambio cognitivo: adquisición del cardinal numérico. Psicothema, 17(4), 559-562. Obtenido de http://www.psicothema.com/psicothema.asp?id=3145.
  6. Bodner, G. M., y Domin, D. S. (2000). Mental models: The role of representations in problem solving in chemistry. University Chemistry Education, 4(1), 24-30. Obtenido de http://1393- chemed.chem.purdue.edu/chemed/bodnergroup/PDF_2008/70%20Mental%20Models%20UCEd.pdf.
  7. Brown, J. S., Collins, A., y Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32. doi:10.3102/0013189x018001032
  8. Camacho, M., y Good, R. (1989). Problem solving and chemical equilibrium: Successful versus unsuccessful performance. Journal of Research in Science Teaching, 26(3), 251-272. doi:10.1002/tea.3660260306.
  9. Carolan, J., Prain, V., y Waldrip, B. (2008). Using representations for teaching and learning in science. The Journal of the Australian Science Teachers Association, 54(1), 18-23.
  10. Carraher, T. N., Carraher, D. W., y Schliemann, A. D. (1985). Mathematics in the streets and in schools. British journal of developmental psychology. doi:10.1111/j.2044-835x.1985.tb00951.x.
  11. Castillo Ballén, M., Triana, N., Duarte-Agudelo, P., Pérez-Abril, M., y Lemus-Espinosa, E. (2007). Sobre las pruebas saber y de Estado: una mirada a su fundamentación y orientación de los instrumentos en lenguaje. Bogotá: Instituto Colombiano para el Fomento de la Educación Superior, ICFES.
  12. Chi, M. T., Feltovich, P. J., y Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5(2), 121-152. doi:10.1207/s15516709cog0502_2.
  13. Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. En R. Lesh y A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 547-589). Hillsdale, NJ: Lawrence Erlbaum.
  14. Cobb, P., y McClain, K. (2002). Supporting students’ learning of significant mathematical ideas. En G. Wells y G. Claxton (Eds.), Learning for life in the 21st century: Sociocultural perspectives on the future of education (pp. 154-166). New York: Cambridge University Press.
  15. Conlin, L. D., Gupta, A., y Hammer, D. (2010). Framing and Resource Activation: Bridging the Cognitive-Situative Divide Using a Dynamic Unit of Cognitive Analysis. Paper presentado en CogSci, Portland, USA. http://dhammer.phy.tufts.edu/home/publications_files/conlin%20gupt
  16. a%20hammer%20cog%20sci%202010.pdf
  17. diSessa, A. (1993). Toward an epistemology of physics. Cognition and Instruction, 10(2-3), 105-225. doi:10.1080/07370008.1985.9649008.
  18. diSessa, A. (2002). Why “conceptual ecology” is a good idea. Reconsidering conceptual change: Issues in theory and practice, 28-60. doi:10.1007/0-306-47637-1_2.
  19. diSessa, A. (2007). An interactional analysis of clinical interviewing. Cognition and Instruction, 25(4), 523-565. doi:10.1080/07370000701632413.
  20. diSessa, A., y Sherin, B. L. (2000). Meta-representation: An introduction. The Journal of Mathematical Behavior, 19(4), 385-398. doi:10.1016/s0732-3123(01)00051-7.
  21. Domin, D., y Bodner, G. (2012). Using students’ representations constructed during problem solving to infer conceptual understanding. Journal of Chemical Education, 89(7), 837-843. doi:10.1021/ed1006037.
  22. Flores, F. (2004). El cambio conceptual: interpretaciones, transformaciones y perspectivas. Educación química, 15(3), 256-269. Obtenido de https://eva.fing.edu.uy/pluginfile.php/68483/mod_resource/content/4/Flores_cambioconceptual_EdQuimica15%283%292004.pdf.
  23. Garcia-Mila, M., Gilabert, S., y Rojo, N. (2011). Strategy change in knowledge acquisition: The microgenetic methodology. Infancia y Aprendizaje, 34(2), 169-180. doi:10.1174/021037011795377566 Obtenido de http://dx.doi.org/10.1174/021037011795377566.
  24. Gobbo, C., y Chi, M. (1986). How knowledge is structured and used by expert and novice children. Cognitive development, 1(3), 221-237. doi:10.1016/s0885-2014(86)80002-8.
  25. Goodwin, C. (2003). The semiotic body in its environment. Discourses of the body, 19-42. Obtenido de https://www.researchgate.net/publication/228901991_The_semiotic_body_in_its_environment.
  26. Greeno, J. G., y Hall, R. P. (1997). Practicing representation: Learning with and about representational forms. Phi Delta Kappan, 78, 361-367. Obtenido de https://www.researchgate.net/publication/ 238695196_Practicing_Representation_Learning_with_and_about_Representational_Forms.
  27. Habermas, J. (1984). The theory of communicative action, Vol. I. Bostonm, Massachusetts: Beacon Press.
  28. Hackenberg, A. J. (2010). Students’ reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383-432. doi:10.1080/07370008.2010.511565.
  29. Hmelo-Silver, C. E., y Pfeffer, M. G. (2004). Comparing expert and novice understanding of a complex system from the perspective of structures, behaviors, and functions. Cognitive Science, 28(1), 127-138. doi:10.1016/s0364-0213(03)00065-x.
  30. Hull, G. A., y Nelson, M. E. (2005). Locating the semiotic power of multimodality. Written Communication, 22(2), 224-261. doi:10.1177/0741088304274170.
  31. Kaltenbacher, M. (2007). Perspectivas en el análisis de la multimodalidad: desde los inicios al estado del arte. Revista Latinoamericana de Estudios del Discurso, 7(1), 31-57. Obtenido de http://www.comunidadaled.org/descarga/7-1.pdf#page=33.
  32. Koedinger, K. R., y Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 13(2), 129-164. doi:10.1207/s15327809jls1302_1.
  33. Krippendorff, K. (2004). Content analysis: An introduction to its methodology (2nd ed.). Beverly Hills: Sage Publications.
  34. Kulm, G. (1990). New directions for mathematics assessment. En G. Kulm (Ed.), Assessing higher order thinking in mathematics (pp. 71-80). USA: AAAS.
  35. Lave, J., y Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York, NY: Cambridge University Press.
  36. Lesh, R., y Carmona, G. (2003). Piagetian Conceptual Systems and Models for Mathematizing Everyday Experiences. En R. Lesh y H. M. Doerr (Eds.), Beyond constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  37. Lesh, R., y Doerr, H. (2000). Symbolizing, communicating, and mathematizing: Key components of models and modeling. En P. Cobb, E. Yackel, y K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms (pp. 361-384). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  38. Lesh, R., y Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2-3), 109-129. doi:10.1080/10986065.2003.9679996.
  39. Lotero Botero, L. A., Andrade Londoño, E. A., y Andrade Lotero, L. A. (2011). La crisis de la multiplicación: una propuesta para la estructuración conceptual. Voces y Silencios: Revista Latinoamericana de Educación, 2(Número Especial), 27. Obtenido de dialnet.unirioja.es.prox
  40. yiub.uits.iu.edu/descarga/articulo/4058881.pdf.
  41. Lotero Botero, L. A., Andrade Londoño, E. A., y Andrade Lotero, L. A. (2012). Tangibles, Construction of Meaning and Math Problem Solving. Paper presentado en The Future of Education 2nd Edition, Florence, Italy. http://www.pixel-online.net/edu_future2012/common/download/Paper_pdf/548-ITL75-FP-Botero-FOE2012.pdf
  42. MEN. (2003). Estándares Básicos de Competencias en Matemáticas. http://www.eduteka.org/pdfdir/MENEstandaresMatematicas2003.pdf.
  43. Mulligan, J. T. (1992). Children’s solutions to multiplication and division word problems: a longitudinal study. Mathematics Education Research Journal, 4(1), 24-41. doi:10.1007/bf03217230.
  44. Mulligan, J. T., y Mitchelmore, M. C. (1997). Young children’s intuitive models of multiplication and division. Journal for Research in Mathematics Education, 309-330. doi:10.2307/749783.
  45. Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., y Chrostowski, S. J. (2004). TIMSS 2003 International Mathematics Report: Findings from IEA’s Trends in International Mathematics and Science Study at the Fourth and Eighth Grades: ERIC.
  46. Nehm, R. H., y Ridgway, J. (2011). What do experts and novices “see” in evolutionary problems? Evolution: Education and Outreach, 4(4), 666-679. doi:10.1007/s12052-011-0369-7.
  47. Nunes, T., y Bryant, P. (2005). Las Matemáticas y su Aplicación: La Perspectiva del Niño. Buenos Aires: Siglo XXI Editores.
  48. Penn, G. (2000). Semiotic analysis of still images. En M. W. Bauer y G. Gaskell (Eds.), Qualitative research with text, image and sound: A practical handbook (pp. 227-245). Thousand Oaks, California: SAGE Publications Ltd.
  49. Piaget, J., y García, R. (1997). Hacia una lógica de significaciones. Barcelona: Gedisa.
  50. Piaget, J., y Inhelder, B. (2007). Psicología del niño. Madrid: Ediciones Morata.
  51. Resnick, L. B., Bill, V., y Lesgold, S. (1992). Developing thinking abilities in arithmetic class. En A. Demetriou y A. Efklides (Eds.), Neo-Piagetian theories of cognitive development: Implications and applications for education (pp. 210-230). New York: Routledge.
  52. Romberg, T. A., Zarinnia, E. A., y Collis, K. F. (1990). A new world view of assessment in mathematics. Assessing higher order thinking in mathematics, 89, 21. doi:10.5860/choice.28-2839.
  53. Roth, W. M., y Bowen, G. M. (1994). Mathematization of experience in a grade 8 open-inquiry environment: An introduction to the representational practices of science. Journal of Research in Science Teaching, 31(3), 293-318. doi:10.1002/tea.3660310308.
  54. Sarama, J., y Clements, D. H. (2004). Building Blocks for early childhood mathematics. Early Childhood Research Quarterly, 19(1), 181-189. doi:10.1016/j.ecresq.2004.01.014.
  55. Scherr, R. E., y Hammer, D. (2009). Student behavior and epistemological framing: Examples from collaborative active-learning activities in physics. Cognition and Instruction, 27(2), 147-174. doi:10.1080/07370000902797379.
  56. Silver, W. S., Mitchell, T. R., y Gist, M. E. (1995). Responses to successful and unsuccessful performance: The moderating effect of self-efficacy on the relationship between performance and attributions. Organizational Behavior and Human Decision Processes, 62(3), 286-299. doi:10.1006/obhd.1995.1051.
  57. Smith, J. P., diSessa, A., y Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2), 115-163. doi:10.1207/s15327809jls0302_1.
  58. Verschaffel, L., De Corte, E., y Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4(4), 273-294. doi:10.1016/0959-4752(94)90002-7.
  59. Verschaffel, L., Greer, B., y de Corte, E. (2000). Making Sense of Word Problems (Vol. 42). Lisse, Netherlands.
  60. Von Glasersfeld, E. (1997). Anticipation in the constructivist theory of cognition. Paper presentado en CASYS’97 - International Conference on Computing Anticipatory Systems, Liege.
  61. Xin, Y. P., Wiles, B., y Lin, Y.-Y. (2008). Teaching conceptual Model–Based word problem story Grammar to Enhance Mathematics problem solving. The Journal of Special Education. doi:10.1177/0022466907312895.
  62. Yañez, C. J., y Chávez, R. M. (2009). Semiótica del dibujo infantil: una aproximación latinoamericana sobre la influencia de la televisión en los niños: casos de estudios en ciudades de Chile, El Salvador y México. Arte, individuo y sociedad, 21, 151-164. Obtenido de revistas.ucm.es.proxyiub.uits.iu.edu/index.php/ARIS/article/download/ARIS0909110151A/5765.

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

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