Advertisement

ZDM

pp 1–15 | Cite as

The influence of situational information on pupils’ achievement in additive word problems with several states and transformations

  • Naďa Vondrová
  • Jarmila NovotnáEmail author
  • Radka Havlíčková
Original Article
  • 43 Downloads

Abstract

Research has shown that word problem difficulty is influenced by various linguistic, numerical and general variables, but results in this area are inconsistent. This paper focuses on the question of how the order of numerical data, the context, the position of the unknown transformation, and the length of the statement in an additive word problem, influence the achievement and reasoning of primary pupils. These variables were varied in two word problems requiring additive reasoning and these variants were solved by pupils in Grades 4 and 5 from four Prague primary schools. Item Response Theory was used both for the division of the pupils into four equally able groups each solving a different variant of the word problem, and for the quantitative interpretation of data. The pupils’ solutions were also analysed in a qualitative way. For a complex additive problem with several states and transformations, we noticed a significant influence of the order of data and the position of the unknown transformation on the pupils’ achievement and types of mistakes. No such influence of context (with which the pupils do not have immediate experience) or the length of the text (prolonged by superfluous information) was found. Some implications for teaching mathematics and preparing tests are given.

Keywords

Word problems Additive reasoning Order of data Transformation problems Context of word problems Mistakes 

Notes

Acknowledgements

The research was financially supported by GA ČR 16-06134S Context problems as a key to the application and understanding of mathematical concepts. We thank Martin Chvál from the Institute of Research and Development of Education, Faculty of Education, for the statistical evaluation of the data.

References

  1. Busse, A. (2005). Individual ways of dealing with the context of realistic tasks—First steps towards a typology. ZDM, 37(5), 354–360.Google Scholar
  2. Carpenter, T. P., Hiebert, J., & Moser, J. M. (1981). Problem structure and first grade children’s initial solution processes for simple addition and subtraction problems. Journal for Research in Mathematics Education, 12, 27–39.CrossRefGoogle Scholar
  3. Cooper, B., Harris, B., & Harries, T. (2002). Children’s responses to contrasting “realistic” mathematics problems: Just how realistic are children ready to be? Educational Studies in Mathematics, 49(1), 1–23.CrossRefGoogle Scholar
  4. Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H. C. (2015). Word problems: a review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6(348), 22–34.  https://doi.org/10.3389/fpsyg.2015.00348.Google Scholar
  5. De Corte, E., & Verschaffel, L. (1987). The effect of semantic structure on first graders’ solution strategies of elementary addition and subtraction word problems. Journal for Research in Mathematics Education, 18(5), 363–381.CrossRefGoogle Scholar
  6. Englert, C. S., Culatta, B. E., & Horn, D. G. (1987). Influence of irrelevant information in addition word problems on problem solving. Learning Disability Quarterly, 10(1), 29–36.  https://doi.org/10.2307/1510752.CrossRefGoogle Scholar
  7. Hembree, R. (1992). Experiments and relational studies in problem solving: A meta-analysis. Journal for Research in Mathematics Education, 23, 242–273.CrossRefGoogle Scholar
  8. Jerman, M. (1973). Problem length as a structural variable in verbal arithmetic problems. Educational Studies in Mathematics, 5, 109–123.CrossRefGoogle Scholar
  9. Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92(1), 109–129.  https://doi.org/10.1037/0033-295X.92.1.109.CrossRefGoogle Scholar
  10. Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale: Lawrence Erlbaum Associates.Google Scholar
  11. Mason, J. (2018). Structuring structural awareness: A commentary. In M. G. Bartolini Bussi & X. H. Sun (Eds.), Building the foundation: Whole Numbers in the Primary Grades (pp. 323–340). Cham: Springer International Publishing.Google Scholar
  12. Moreau, S., & Coquin-Viennot, D. (2003). Comprehension of arithmetic word problems by fifth-grade pupils: Representations and selection of information. British Journal of Educational Psychology, 73(1), 109–121.CrossRefGoogle Scholar
  13. Nesher, P. (1976). Three determinants of difficulty in verbal arithmetic problems. Educational Studies in Mathematics, 7, 369–388.CrossRefGoogle Scholar
  14. Nesher, P., Hershkovitz, S., & Novotná, J. (2003). Situation model, text base and what else? Factors affecting problem solving. Educational Studies in Mathematics, 52(2), 151–176.CrossRefGoogle Scholar
  15. Nesher, P., & Teubal, E. (1975). Verbal cues as an interfering factor in verbal problem solving. Educational Studies in Mathematics, 6, 41–51.CrossRefGoogle Scholar
  16. Novotná, J., Kaur, B., Gervasoni, A., Askew, M., Veldhuis, M., Pearn, C., & Sun, X. H. (2018). How to teach and assess whole number arithmetic: Some international perspectives. In M. G. Bartolini Bussi & X. H. Sun (Eds.), Building the foundation: Whole Numbers in the Primary Grades (pp. 249–284). Cham: Springer International Publishing.Google Scholar
  17. Nunes, T., Dorneles, B. V., Lin, P. J., & Rathgeb-Schnierer, E. (2016). Teaching and learning about whole numbers in primary school. ICME-13 Topical Surveys. Cham: Springer International Publishing.CrossRefGoogle Scholar
  18. Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67(1), 37–58.  https://doi.org/10.1007/s10649-007-9083-3.CrossRefGoogle Scholar
  19. Polotskaia, E., Savard, A., & Freiman, V. (2015). Investigating a case of hidden misinterpretations of an additive word problem: Structural substitution. European Journal of Psychology of Education, 31(2), 135–153.  https://doi.org/10.1007/s10212-015-0257-6.CrossRefGoogle Scholar
  20. Reusser, K. (1990). Understanding word arithmetic problem. Linguistic and situational factors. Paper presented at the Annual Meeting of the American Educational Research Association. Boston, MA (April 16–20, 1990). Retrieved from https://files.eric.ed.gov/fulltext/ED326391.pdf
  21. Sarrazy, B. (1996). La sensibilité au contrat didactique: Rôle des Arrière-plans dans la résolution de problèmes d’arithmétique au cycle trois. Thèse pour le doctorat de l’Université de Bordeaux 2—Mention Sciences de l’Education, pp. 775.Google Scholar
  22. Searle, B. W., Lorton, P. Jr., & Suppes, P. (1974). Structural variables affecting CAI performance on arithmetic word problems of disadvantaged and deaf students. Educational Studies in Mathematics, 5, 371–384.  https://doi.org/10.1007/BF01424555.CrossRefGoogle Scholar
  23. Vergnaud, G. (1982). Cognitive and developmental psychology and research in mathematics education: Some theoretical and methodological issues. For the Learning of Mathematics, 3(2), 31–41.Google Scholar
  24. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger Publishers.Google Scholar
  25. Vicente, S., & Manchado, E. (2016). Arithmetic word problem solving. Are authentic word problems easier to solve than standard ones? Infancia y Aprendizaje, 39(2), 349–379.  https://doi.org/10.1080/02103702.2016.1138717.CrossRefGoogle Scholar
  26. Vicente, S., Orrantia, J., & Verschaffel, L. (2008). Influence of situational and mathematical information on situationally difficult word problems. Studia Psychologica, 50(4), 337–356.Google Scholar
  27. Vlahovic-Štetič, V., Rovan, D., & Mendek, Ž (2004). Solving mathematical word problems. Review of Psychology, 11(1–2), 25–33.Google Scholar
  28. Voyer, D. (2011). Performance in mathematical problem solving as a function of comprehension and arithmetic skills. International Journal of Science and Mathematics Education, 9(5), 1073–1092.  https://doi.org/10.1007/s10763-010-9239-y.CrossRefGoogle Scholar
  29. Wiest, L. R. (2001). The role of fantasy contexts in word problems. Mathematics Education Research Journal, 13(2), 74–90.CrossRefGoogle Scholar
  30. Zohar, A., & Gershikov, A. (2008). Gender and performance in mathematical tasks: Does the context make a difference? International Journal of Science and Mathematics Education, 6, 677–693.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  • Naďa Vondrová
    • 1
  • Jarmila Novotná
    • 1
    Email author
  • Radka Havlíčková
    • 1
  1. 1.Univerzita Karlova, Pedagogická fakultaPraha 1Czech Republic

Personalised recommendations