The influence of situational information on pupils’ achievement in additive word problems with several states and transformations
- 43 Downloads
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.
KeywordsWord problems Additive reasoning Order of data Transformation problems Context of word problems Mistakes
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.
- 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
- Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale: Lawrence Erlbaum Associates.Google Scholar
- 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
- 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
- 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.
- 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
- 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
- Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger Publishers.Google Scholar
- 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
- Vlahovic-Štetič, V., Rovan, D., & Mendek, Ž (2004). Solving mathematical word problems. Review of Psychology, 11(1–2), 25–33.Google Scholar