Playing with half a balloon? How different considerations and problem characteristics affect problematic word problem solving

Andrea Wisenöcker; Marcel Mayr; Cornelia S. Große

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Playing with half a balloon? How different considerations and problem characteristics affect problematic word problem solving

Andrea S. Wisenöcker ^[1] ; Marcel Mayr ^[1] ; Cornelia S. Große ^[1]
1. [1] Johannes Kepler University of Linz
  
  Johannes Kepler University of Linz
  
  Linz, Austria
Localización: European Journal of Psychology of Education, ISSN-e 1878-5174, ISSN 0256-2928, Vol. 40, Nº 3, 2025
Idioma: inglés
DOI: 10.1007/s10212-025-01008-7
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Resumen
- Providing realistic solutions for word problems proves to be challenging. A possible explanation is the influence of individual’s expectations and beliefs about word problems. This explanation was tested in the present study in an out-of-school context. Specifically, the study assessed effects of (1) prompting participants to make realistic considerations, (2) activating individual’s expectations and beliefs about mathematical problems by prompting participants to consider mathematical operations, and (3) problems where the exact mathematical result had varying degrees of applicability in reality, on the number of realistic responses in division-with-remainder problems. An experiment was conducted (N = 131, 14–61 years), factor 1 “realistic considerations” (with vs. without), factor 2 “mathematical operations” (with vs. without), and factor 3 “problem characteristics” (exact result pointless vs. exact result impractical). There was no significant main effect “realistic considerations,” F(1, 119) = 0.06, p = .801, and ηp2 = .001. Addressing mathematical operations significantly reduced realistic solutions (main effect “mathematical operations”: F(1, 119) = 4.20, p = .043, and ηp2 = .034). Realistic solutions occurred significantly more often with problems where the application of the exact mathematical result would be pointless in reality (main effect “problem characteristics”: F(1, 119) = 4.73, p = .032, and ηp2 = .038). The main effect “age” was significant; F(1, 119) = 3.94, p = .049, and ηp2 = .032. All two-way interactions and the three-way interaction between the three factors were not significant. The results indicate that activating individual’s expectations and beliefs about word problems and problem characteristics significantly influence the generation of realistic solutions.
Referencias bibliográficas
- Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application,...
- Blum, W., & Leiss, D. (2007). How do students and teachers deal with modelling problems. Mathematical modelling (ICTMA 12): Education,...
- Bonotto, C., & Wilczewski, E. (2007). I problem di matematica nella scuola primaria: sull’attivazione o meno di conoscenze di tipo realistico...
- Cialdini, R. B., Kallgren, C. A., & Reno, R. R. (1991). A focus theory of normative conduct: A theoretical refinement and reevaluation...
- Cooper, B., & Harries, T. (2002). Children’s responses to contrasting realistic mathematics problems: Just how realistic are children...
- Cruz-Márquez, E., Díaz-Espinoza, I. A., & Juárez-López, J. A. (2024). Exploring the primary school teachers’ reasoning and individuals...
- Csíkos, C., Kelemen, R., & Verschaffel, L. (2011). Fifth-grade students’ approaches to and beliefs of mathematics word problem solving:...
- Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers’ approaches towards word problem solving: Elaborating or restricting the...
- Dewolf, T., Van Dooren, W., & Verschaffel, L. (2017). Can visual aids in representational illustrations help pupils to solve mathematical...
- Dewolf, T., Van Dooren, W., Cimen, Ev. E., & Verschaffel, L. (2014). The impact of illustrations and warnings on solving mathematical...
- Dewolf, T., Van Dooren, W., Hermens, F., & Verschaffel, L. (2015). Do students attend to representational illustrations of non-standard...
- Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2009). Statistical power analyses using G*Power 3.1: Tests for correlation and regression...
- Fitzpatrick, C. L., Hallett, D., Morrissey, K. R., Yıldız, N. R., Wynes, R., & Ayesu, F. (2019). Response sentences, examples, and authenticity...
- Gravemeijer, K. (1997). Solving word problems: A case of modelling? Learning and Instruction, 7(4), 389–397. https://doi.org/10.1016/S0959-4752(97)00011-X
- Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293–307. https://doi.org/10.1016/S0959-4752(97)00006-6
- Große, C. S. (2014). Learning to solve story problems—Supporting transitions between reality and mathematics. European Journal of Psychology...
- Große, C. S. (2015). Fostering modeling competencies: Benefits of worked examples, problems to be solved, and fading procedures. European...
- Große, C. S. (2017). Effects of multiple choice options in mathematics learning. European Journal of Science and Mathematics Education, 5(2),...
- Große, C. S. (2018). “Copying allowed – But be careful, errors included!” – Effects of copying correct and incorrect solutions on learning...
- Große, C. S. (2022). Multiple solutions in dyads or alone – Fostering the acquisition of modeling competencies in mathematics. Learning and...
- Jiménez, L., & Verschaffel, L. (2014). El desarrollo de las soluciones infantiles en la resolución de problemas aritméticos no estándar...
- Kinda, S. (2012). Generating multiple answers for a word problem with insufficient information. Instructional Science, 40(6), 1021–1031. https://doi.org/10.1007/s11251-011-9200-7
- Krawitz, J., Chang, Y. P., Yang, K. L., & Schukajlow, S. (2022). The role of reading comprehension in mathematical modelling: Improving...
- Lee, J., & Yi, G. (2021). Pre-service teachers’ conceptions about considering the realistic contexts in the word problems. The Mathematical...
- Mayr, M. (2023). Learning for life: investigating the role of socio-mathematical norms and standards for realistic word problems [Master thesis,...
- Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and...
- 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
- Reusser, K., & Stebler, R. (1997). Every word problem has a solution—The social rationality of mathematical modeling in schools. Learning...
- Samuelsson, M., & Samuelsson, J. (2016). Gender differences in boys’ and girls’ perception of teaching and learning mathematics. Open...
- Schukajlow, S., Kaiser, G., & Stillman, G. (2018). Empirical research on teaching and learning of mathematical modelling: A survey on...
- Schukajlow, S., Kolter, J., & Blum, W. (2015). Scaffolding mathematical modelling with a solution plan. ZDM, 47, 1241–1254.
- Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance....
- Stadler, M., Sailer, M., & Fischer, F. (2021). Knowledge as a formative construct: A good alpha is not always better. New Ideas in Psychology,...
- Van Dooren, W., Lem, S., De Wortelaer, H., & Verschaffel, L. (2019). Improving p-problem solving by using humor. The Journal of Mathematical...
- Verschaffel, L., Corte, E. D., & Vierstraete, H. (1999). Upper elementary school pupils’ difficulties in modeling and solving nonstandard...
- Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge...
- Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems....
- Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM, 52(1), 1–16....
- Weyns, A., Van Dooren, W., Dewolf, T., & Verschaffel, L. (2017). The effect of emphasising the realistic modelling complexity in the text...
- Wisenöcker, A. S., Binder, S., Holzer, M., Valentic, A., Wally, C., & Große, C. S. (2024). Mathematical problems in and out of school:...
- Xin, Z., Lin, C., Zhang, L., & Yan, R. (2007). The performance of Chinese primary school students on realistic arithmetic word problems....
- Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian...
- Zhu, Z. (2007). Gender differences in mathematical problem solving patterns: A review of literature. International Education Journal, 8(2),...