Main Article Content

Abstract

Despite extensive research indicating that students often fail to apply real-world knowledge and common sense when solving word problems, the underlying causes remain underexplored. Teacher behavior and instructional methods are potential factors contributing to students' tendency to provide unrealistic answers to such problems. The current study aims to address this gap by examining the cognitive processes and perspectives of pre-service teachers when solving problematic word problems. A group of 146 pre-service teachers (97 females, 49 males) in Iran participated in the study, which consisted of two phases. In the first phase, participants were given three problematic word problems to solve and were subsequently asked to evaluate four different student responses. A significant correlation was found between the participants' responses in the initial test and their evaluations in the second phase. In the second phase, the study employed a phenomenographic approach to explore the thinking processes and perspectives of the pre-service teachers while solving the problems. The analysis of interview data led to the identification of two primary categories of unrealistic problem-solving: "inattention" and "ignoring." In the "inattention" category, the problem solver fails to recognize the relevance of real-world knowledge, while in the "ignoring" category, the solver acknowledges real-world factors but deliberately chooses not to integrate them into the solution. In the end, a model of unrealistic problem-solving is proposed and discussed, with implications for teacher training and pedagogical practices.

Keywords

Common Sense Mathematics Phenomenography Pre-Service Teacher Problematic Word Problems

Article Details

How to Cite
Rafiepour, A., Khazaie, Z., & Verschaffel, L. (2025). Pre-service teachers’ perspective toward problematic word problems. Journal on Mathematics Education, 16(1), 255–274. https://doi.org/10.22342/jme.v16i1.pp255-274

References

  1. Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 222–231). Chichester: Horwood. https://doi.org/10.1533/9780857099419.5.221
  2. Caldwell, L. (1995). Contextual considerations in the solution of children's multiplication and division word problems. Unpublished Master's thesis. Queen's University, Belfast, Northern Ireland.
  3. DeFranco, T. C, & Curcio, F. R. (1997). A division problem with a remainder embedded across two contexts: Children's solutions in restrictive versus real-world settings. Focus on Learning Problems in Mathematics, 19(2), 58-72.
  4. Dewolf, T., Van Dooren, W., Hermens, F., & Verschaffel, L. (2015). Do students attend to representational illustrations of non-standard mathematical word problems, and, if so, how helpful are they?. Instructional Science, 43, 147–171. https://doi.org/10.1007/s11251-014-9332-7
  5. Doerr, H.M., Ärlebäck, J.B., & Misfeldt, M. (2017). Representations of Modelling in Mathematics Education. In: Stillman, G., Blum, W., Kaiser, G. (eds) Mathematical Modelling and Applications. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-62968-1_6
  6. Dorri, M., & Rafiepour, A. (2016). Suspension of Sense-Making in Solving Word Problem: The Role of Authenticity. In the national conference on Primary Education, pp: 575-586. Birjand, Iran. (in Persian).
  7. Fitzpatrick, C. L., Hallett, D., Morrissey, K. R., Yıldız, N. R, Wynes, R., & Ayesu, F. (2019). Response sentences, examples, and authenticity do not help children solve real wor(l) d problems. Learning and Instruction, 61, 111–125. https://doi.org/10.1016/j. learninstruc.2018.10.002.
  8. Gall, M., Gall, J., & Borg, W. (1942). Educational Research: An Introduction. Pearson.
  9. Greer, B. (1993). The mathematical modelling perspective on problems. Journal of Mathematical Behavior, 12, 239-250.
  10. Han, F., & Ellis, R. (2019). Using phenomenography to tackle key challenges in science education. Frontiers in Psychology, 10, 1414. https://doi.org/10.3389/fpsyg.2019.01414
  11. Hidalgo, M. C. (1997). L'activation des connaissances a propos du monde réel dans la résolution de problémes verbaux en arithmétique. Unpublished doctoral dissertation, Université Laval, Québec, Canada.
  12. Higginson, W. (1980). On the foundations of mathematics education. For the Learning of Mathematics, 1(2), 3–7. http://www.jstor.org/stable/40247706.
  13. Inoue, N. (2001). The role of personal interpretation in mathematical problem solving: Enhancing the relevance of mathematical learning to everyday experience (Internal report). Teachers College, Columbia University.
  14. IREM de Grenoble. (1980). Bulletin de l’Association des professours de Mathématiques de l’Enseignement Public, n. 323, 235-243.
  15. Jacobson, E., Lobato, J. & Orrill, C.H. (2018). Middle school teachers’ use of mathematics to make sense of student solutions to proportional reasoning problems. International Journal of Science and Mathematics Education, 16, 1541–1559. https://doi.org/10.1007/s10763-017-9845-z.
  16. Laine, A., Ahtee, M. & Näveri, L. (2020). Impact of teacher’s actions on emotional atmosphere in mathematics lessons in primary school. International Journal of Science and Mathematics Education, 18, 163–181. https://doi.org/10.1007/s10763-018-09948-x.
  17. McCosker, H., Barnard, A., & Gerber, R. (2004). Phenomenographic study of women’s experiences of domestic violence during the childbearing years. Online Journal of Issues in Nursing, 9(1), 1-16.
  18. Mellone, M., Verschaffel, L., & Van Dooren, V. (2017) The effect of rewording and dyadic interaction on realistic reasoning in solving word problems. Journal of Mathematical Behavior, 46,1-12. https://doi.org/10.1016/j.jmathb.2017.02.002
  19. Morrison, J., Frost, J., Gotch, C., McDuffie, A. R., Austin, B., & French, B. (2021). Teachers’ role in students’ learning at a project-based STEM high school: Implications for teacher education. International Journal of Science and Mathematics Education, 19, 1103–1123. https://doi.org/10.1007/s10763-020-10108-3
  20. National Curriculum Document. (2011). Organization for Research and Programing. Ministry of Education, Iran.
  21. Radatz, H. (1983). Untersuchungen zum Lösen eingekleideter Aufgaben. Journal für Mathematik Didaktik, 4(3), 205–217. https://doi.org/10.1007/BF03339231
  22. 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 and Instruction, 7, 309—328. https://doi.org/10.1016/S0959-4752(97)00014-5
  23. Sarkar Arani, M. R., Shibata, Y., Sakamoto, M., Iksan, Z., Amirullah, A. H., & Lander, B. (2017). How teachers respond to students’ mistakes in lessons: A cross-cultural analysis of a mathematics lesson. International Journal for Lesson and Learning Studies, 6(3), 249-267. https://doi.org/10.1108/IJLLS-12-2016-0058
  24. Schoenfeld, A. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J.F. Voss, D. N. pekins & j. w. Segal (Eds.), Informal reasoning and education (pp.311-343). Erlbaum.
  25. Selter, Ch. (2001). "1/2 Busse heißt: ein halbvoller Bus!" Zu Vorgehensweisen von Grundschülern bei einer Textaufgabe mit Rest ["1/2 bus means a bus half-full!"—Solution strategies of elementary school children for DWR problems]. In C. Selter, & G. Walther (Eds.), Mathematik lernen und gesunder Menschenverstand (pp. 162 173). Leipzig: Klett.
  26. Van Dooren, L., Lem, S., De Wortelaer, H., & Verschaffel, L (2019). Improving realistic word problem solving by using humor. Journal of Mathematical Behavior, 53, 96-104. https://doi.org/10.1016/j.jmathb.2018.06.008.
  27. Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modeling of school word problems. Learning and Instruction, 4, 339–359. https://doi.org/10.1016/S0959-4752(97)00008-X
  28. Verschaffel, L., De Corte, B., & Greer, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger.
  29. Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4, 273–294. https://doi.org/10.1016/0959-4752(94)90002-7
  30. Verschaffel, L., Lehtinen, E., & Van Dooren, W. (2016). Neuroscientific studies of mathematical thinking and learning: A critical look from a mathematics education viewpoint. ZDM, 48, 385-391. https://doi.org/10.1007/s11858-016-0781-0
  31. Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM, 52, 1–16 (2020). https://doi.org/10.1007/s11858-020-01130-4
  32. Verschaffel, L., Van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problems as exercises in mathematical modelling. Journal für Mathematik-Didaktik, 31, 9-29. https://doi.org/10.1007/s13138-010-0007-x
  33. Vos, P. (2011). What is ‘authentic’ in the teaching and learning of mathematical modelling? Trends in teaching and learning of mathematical modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer. https://doi.org/10.1007/978-94-007-0910-2_68
  34. Xin, Z., Lin, C., Zhang, L., & Yan, R. (2007). The performance of Chinese primary school students on realistic arithmetic word problems. Educational Psychology in Practice, 23, 145–159. https://doi.org/10.1080/02667360701320853
  35. 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 and Instruction, 7, 329–338. https://doi.org/10.1016/S0959-4752(97)00007-8