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Culture and Education
Cultura y Educación
Volume 24, 2012 - Issue 3
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Original Articles

La aplicación del conocimiento contextualizado en la resolución de problemas matemáticos un estudio sobre las dificultades de los niños en la resolución de problemas no rutinarios

Applying contextualised knowledge to math problem solving: A study on children's difficulties in non-routine problem solving

Pages 351-362 | Received 15 Nov 2010, Accepted 20 Dec 2011, Published online: 23 Jan 2014

Referencias

  • Baruk, S. (1985). L'âge du capitaine. De l'erreur en mathématiques. París: Seuil.
  • Brousseau, G. (1984). The IREM's role in helping elementary-school teachers. En R. Morris (Ed.), Studies in mathematics education. The mathematical education of primary-school teachers (Vol. 3, pp. 235–251). París: UNESCO.
  • Cai, J. & Silver, E. A. (1995). Solution processes and interpretations of solutions in solving a division with remainder story problems: Do Chinese and U.S. students have similar difficulties? Journal for Research in Mathematics Education, 26, 491–497.
  • Caldwell, L. (1995). Contextual considerations in the solution of children's multiplication and division word problems. Tesis doctoral no publicada, Belfast: Queen's University.
  • Carpenter, T. P., Hiebert, J. & Moser, J. M. (1983). The effect of instruction on children's solutions of addition and subtraction word problems. Educational Studies in Mathematics, 14, 55–72.
  • Carpenter, T. P., Lindquist, M. M., Matthews, W. & Silver, E. A. (1983). Results of the third NAEP mathematics assessment: Secondary school. Mathematics Teacher, 76, 652–659.
  • Cooper, B. (1992). Testing National Curriculum Mathematics: Some critical comments on the treatment of ‘real’ contexts for mathematics. The Curriculum Journal, 3, 231–243.
  • Cooper, B. (1994). Authentic testing in mathematics? The boundary between everyday and mathematical knowledge in National Curriculum testing in English schools. Assessment in Education: Principles, Policy and Practice, 1 (2), 143–166.
  • De corte, E. & Verschaffel, L. (1985). Beginning first graders' initial representation of arithmetic word problems. Journal of Mathematical Behaviour, 4, 3–21.
  • Fuson, K. C. (1992). Research on whole number addition and subtraction. En D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). Nueva York: MacMillan.
  • Greer, B. (1993). The mathematical modeling perspective on wor(l)d problems. Journal of Mathematical Behaviour, 12 (3), 239–250.
  • Greer, B. (1997). Modeling reality in mathematics classrooms: the case of word problems. Learning & Instruction, 7 (4), 293–307.
  • Hatano, G. (1997). Cost and benefit of modeling activity. Commentary. Learning & Instruction, 7 (4), 383–387.
  • Hegarty, M., Mayer, R. E. & Monk, C. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87, 18–32.
  • Hernández, M. L. (2004). Libros de texto, algoritmos y problemas verbales: ¿cuál es el resultado de mezclar estos ingredientes? UNO, Revista de Didáctica de las Matemáticas, 35, 66–73.
  • Hidalgo, M. C. (1997). L'activation des connaissances à propos du monde réel dans la résolution de problèmes verbaux en arithmétique. Tesis doctoral no publicada, Québec, Canada: Université Laval.
  • Inoue, N. (2005). The realistic reasons behind unrealistic solutions: the role of interpretive activity in word problem solving. Learning & Instruction, 15, 69–83.
  • INSTITUT DE RECHERCHE SUR L'ENSEIGNEMENT DES MATHÉMATIQUES (IREM) DE GRENOBLE (1980). Bulletin de l'Association des Professeurs de Mathématique de l'Enseignement Public, 323, 235–243.
  • Lago, M. O, Rodríguez, P., Enesco, I., Jiménez, L. & Dopico, C. (2008). “Me sobran cuatro y no sé qué hacer con ellos”: un estudio sobre los problemas de división con resto en alumnos de 1° de ESO. Anales de Psicología, 24 (2), 201–212.
  • Li, Y. & Silver, E. A. (2000). Can younger students succeed where older students fail? An examination of third graders' solutions of a division-with-remainder (DWR) problem. Journal of Mathematical Behavior, 19, 233–246.
  • LITTLEFIELD, J. & RIESER, J. J. (1993). Semantic features of similarity and children's strategies for identification of relevant information in Mathematical Story Problems. Cognition & Instruction, 11 (2), 133–188.
  • Mayer, R. (2003). Mathematical problem solving. En J. Royer (Ed.), Mathematical Cognition (pp. 69–92). Greenwich, CO: Information Age Publishing.
  • Orrantia, J. (2003). El rol del conocimiento conceptual en la resolución de problemas aritméticos con estructura aditiva. Infancia y Aprendizaje, 26 (4), 451–468.
  • Orrantia, J., González, L. B. & Vicente, S. (2005). Estudios del conocimiento numérico: Aprendizaje y enseñanza. Un análisis de los problemas aritméticos en los libros de texto de Educación Primaria. Infancia y Aprendizaje, 28 (4), 429–451.
  • Palm, T. (2006). Word problems as a simulations of real-world situation: A proposed framework. For the Learning of Mathematics, 26 (1), 42–47.
  • Palm, T. (2008). Impact of authenticity on sense-making in word problem solving. Educational Studies in Mathematics, 67 (1), 37–58.
  • Puchalska, E. & Semanemi, Z. (1987). Children's reactions to verbal arithmetical problems with missing, surplus or contradictory data. For the Learning of Mathematics, 7 (3), 9–16.
  • Raddatz, H. (1983). Untersuchungen zum Lö sen eingekleideter Aufgaben. Zeitschrift f¨r Mathematik Didaktik, 4, 205–217.
  • Renkl, A. (1999). The gap between school and everyday knowledge in mathematics. Comunicación presentada a la 8th European Conference for Research on Learning and Instruction, Gö teborg, Sweden.
  • Reusser, K. (1988). Problem solving beyond the logic of things: Contextual effects on understanding and solving word problems. Instructional Science, 17, 309–338.
  • Reusser, K. & Stebler, R. (1997). Every word problem has a solution: The suspension of reality and sense- making in the culture of school mathematics. Learning & Instruction, 7, 309–328.
  • Rodríguez, P., Lago, M. O., Hernández, M. L., Jiménez, L., Guerrero, S. & Caballero, S. (2009). How do secondary students approach different types of division with remainder situations? Some evidence from Spain. European Journal of Educational Psychology, 24 (4), 529–543.
  • Säljö, R. & Wyndhamn, J. (1987). The formal setting as context for cognitive activities. An empirical study of arithmetic operations under conflicting premises for communication. European Journal of Psychology of Education, 2 (3), 233–245.
  • Schoenfeld, A. H. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. En J. F. Voss, D. N. Perkins & J. W. Segal (Eds.), Informal reasoning and education (pp. 311–343). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • SEAC—SCHOOLS EXAMINATIONS AND ASSESSMENT COUNCIL (1992). Mathematics test 1992, Key Stage 3. Londres: SEAC/University of London.
  • Selter, C. (1994). How old is the captain? Strategies, J (1), 34–37.
  • Silver, E. A. (1986). Using conceptual and procedural knowledge: A focus on relationships. En J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 181–197). Hillsdale, NJ: Lawrence Erlbaum
  • Silver, E. A., Mukhopadhyay, S. & Gabriele, A. J. (1992). Referential mappings and the solution of division story problems involving remainders. Focus on Learning Problems in Mathematics, 14, 29–39.
  • Silver, E. A., Shapiro, L. J. & Deutsch, A. (1993). Sense making and the solution of division problem involving remainders: An examination of middle school students' solution processes and their interpretations of solutions. Journal for Research in Mathematics Education, 24, 117–135.
  • Verschaffel, L. & De corte, E. (1997). Word problems: A vehicle for promoting authentic mathematical understanding and problem solving in the primary school? En T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 69–97). Hove, East Sussex: Psychology Press Ltd.
  • Verschaffel, L., De corte, E. & Lasure, S. (1994). Realistic considerations in mathematical modelling of school arithmetic word problems. Learning & Instruction, 4, 273–294.
  • Verschaffel, L., De corte, E. & Lasure, S. (1999). Children's conceptions about the role of real-world knowledge in mathematical modelling of school word problems. En W. Schnotz, S. Vosniadou & M. Carretero (Eds.), New perspectives on conceptual change (pp. 175–189). Oxford: Elsevier.
  • Verschaffel, L., De corte, E. & Borghart, I. (1997). Pre-service teachers' conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning & Instruction, 4, 339–59.
  • Verschaffel, L., Greer B. & De corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger.
  • Vicente, S., Van dooren, W. V. & Verschaffel, L. (2008). Utilizar las matemáticas para resolver problemas reales. Cultura y Educación, 20 (4), 391–406.
  • Yoshida, H., Verschaffel, L. & De corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? Learning & Instruction, 7, 329–338.

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