Advertisement

PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS

  • Dominic Voyer
Article

Abstract

Many factors influence a student’s performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils’ real-world knowledge, which support the construction of a ‘situation model’. In this study, we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process, and we assess the effects of the situation model on pupils’ problem solving performance. The sample is composed of 750 pupils of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec, Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem. Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem. The situation model influences pupils’ problem solving performance, but this influence depends on the type of information included in the problem statement, as well as on the arithmetic skills of each individual pupil.

Key words

arithmetic comprehension mathematics problem solving teaching word problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barnett, J. (1979). The study of syntax variables. In G. A. Goldin & C. E. McClintock (Eds.), Task variables in mathematical problem solving (pp. 23–68). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  2. Bélanger, N., Gauthier, C. & Tardif, M. (1993). Évolution des programmes de mathématiques: de 1861 à nos jours. Sainte-Foy, Quebec, Canada: Université Laval.Google Scholar
  3. Caldwell, J. H. & Goldin, G. A. (1979). Variables affecting word problem difficulty in elementary school mathematics. Journal for Research in Mathematics Education, 10(5), 323–336.CrossRefGoogle Scholar
  4. Coquin-Viennot, D. & Moreau, S. (2003). Highlighting the role of the episodic situation model in the solving of arithmetical problems. European Journal of Psychology of Education, 18(3), 267–279.CrossRefGoogle Scholar
  5. Coquin-Viennot, D. & Moreau, S. (2007). Arithmetic problems at school: When there is an apparent contradiction between the situation model and the problem model. The British Journal of Educational Psychology, 77(1), 69–80.CrossRefGoogle Scholar
  6. Cummins, D. D., Kintsch, W., Reusser, K. & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology, 20(4), 405–438.CrossRefGoogle Scholar
  7. El Boudali, A. (1984). L'influence de la familiarité du contexte sur la résolution de problèmes verbaux en mathématiques, au niveau du secondaire au Maroc. Unpublished M.A., Sainte-Foy: Université Laval.Google Scholar
  8. Hembree, R. (1992). Experiments and relational studies in problem-solving: A meta-analysis. Journal for Research in Mathematics Education, 23, 242–273.CrossRefGoogle Scholar
  9. Kintsch, W. (1998). Comprehension: A paradigm for cognition. Cambridge, MA: Cambridge University Press.Google Scholar
  10. Kintsch, W. & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92(1), 109–129.CrossRefGoogle Scholar
  11. Kintsch, W. & van Dijk, T. A. (1978). Toward a model of text comprehension and production. Psychological Review, 85(5), 363–394.CrossRefGoogle Scholar
  12. Kulm, G. (1984). The classification of problem-solving research variables. In G. A. Goldin & C. E. McClintock (Eds.), Task variables in mathematical problem solving (pp. 1–21). Philadelphia: The Franklin Institute Press.Google Scholar
  13. Moreau, S. & Coquin-Viennot, D. (2003). Comprehension of arithmetic word problems by fifth-grade pupils: Representations and selection of information. The British Journal of Educational Psychology, 73(1), 109–121.CrossRefGoogle Scholar
  14. Nasser, R. & Carifio, J. (1993). Key contextual features of algebra word problems: A theoretical model and review of the literature. Paper presented at the annual conference of the Eastern Educational Research Association (Clearwater, FL, February 17–22, 1993).Google Scholar
  15. National Council of Teachers of Mathematics (1980). An agenda for action: Recommendations for school mathematics of the 1980s. Reston, VA: NCTM.Google Scholar
  16. National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.Google Scholar
  17. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  18. Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.Google Scholar
  19. Reusser, K. (1990). From text to situation to equation: Cognitive simulation of understanding and solving mathematical word problems. In H. Mandl, E. De Corte, S. N. Bennett & H. F. Friedrich (Eds.), Learning & instruction: European research in an international context (Vol. 2, pp. 477–498). Oxford, England: Pergamon Press.Google Scholar
  20. Sovik, N., Frostrad, P. & Heggberget, M. (1999). The relation between reading comprehension and task-specific strategies used in arithmetical word problems. Scandinavian Journal of Educational Research, 43(4), 371–398.CrossRefGoogle Scholar
  21. Stern, E. & Lehrndorfer, A. (1992). The role of situational context in solving word problems. Cognitive Development, 7(1), 259–268.CrossRefGoogle Scholar
  22. van Dijk, T. A. (1977). Semantic macro-structures and knowledge frames in discourse comprehension. In M. A. Just & P. A. Carpenter (Eds.), Cognitive processes in comprehension (pp. 3–32). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar

Copyright information

© National Science Council, Taiwan 2010

Authors and Affiliations

  1. 1.Université du Québec à Rimouski—Campus de LévisLévisCanada

Personalised recommendations