Resolución de problemas aritméticosconocimiento conceptual y nivel de competencia en matemáticas

  1. José Orrantia Rodríguez
  2. David Múñez Méndez
  3. María Fernández Sánchez
  4. Laura Matilla Cordero
Aula abierta

ISSN: 0210-2773

Year of publication: 2012

Volume: 40

Issue: 3

Pages: 23-32

Type: Article

More publications in: Aula abierta


Cited by

  • Dialnet Métricas Cited by: 3 (18-02-2024)


  • Social Sciences: B


Before formal schooling, children solve word problems with informal strategies modeling directly the situation described in the text of the problem. When problems do not allow to use such strategies, children need to apply the conceptual knowledge (commutativity, inversion...) needed to solve the problem. In the current study, students of secondary education (12 to 13 years old) with/without mathematical difficulties and undergraduate students (19 to 21 years old) solved word problems in two versions involving the same wording. The first version could be solved by modeling the situation described (SI problems), and in the second version children needed to use their conceptual knowledge (CC problems). Results indicated that, despite the reduced difficulty of the problems, SI problems were easier to solve than CC problems for all the participants. Furthermore, this effect was even much more pronounced for secondary education students with mathematical difficulties. These findings suggest two conclusions. First, after years of experience solving problems, students (even adults) avoid using their conceptual knowledge if they can use a strategy that models directly the situation. Secondly, less proficient students show a rigid and inefficient use of the conceptual knowledge needed to solve arithmetic problems even when procedural knowledge is available.

Bibliographic References

  • Brissiaud, R., y Sander, E. (2005). Arithmetic word problem solving : a Situation Strategy First framework. Developmental Science, 13, 92-107.
  • Carpenter, T. P., y Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 13, 179–202.
  • Kintsch, W., y Greeno, J. (1985). Undertanding and solving word arirmetic problem. Psychological Rewiev, 92, 109-129.
  • Orrantia, J. (2003). El rol del conocimiento conceptual en la resolución de problemas aritméticos con estructura aritmética. Infancia y Aprendizaje, 26, 451-468.
  • Orrantia, J., Rodríguez, L., Múñez, D., y Vicente, S. (2012). Inversereference in subtraction performance : An analysis from arithmetic word problems. The Quarterly Journal of Experimental Psychology, 65, 725-738.
  • Riley, M. S., Greeno, J. G., y Heller, J. I. (1983). Development of children’s problem solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153–196). New York : Academic Press.
  • Thevenot, C., Devidal, M., Barrouillet, P., y Fayol, M. (2007). Why does placing the question before an arithmetic Word problem improve performance? A situation model account. Quarterly Journal of Experimental Psychology, 60, 43–56.