Abstract
Research on mathematical word problems suggests that differences in success are not only due to different levels of pupils’ cognitive abilities but that their motivation plays a role, too. Therefore, in this study, we focused on the context as a non-mathematical parameter of word problems and investigated its influence on pupils’ success in solving the problems. We focused on the potential attractiveness of the context and investigated whether pupils would be more successful in solving word problems with elements of fairy tale, science fiction or humour than in the case of similar problems with the same structure but with a neutral context. Pupils of the 5th and 6th grades of primary school (n5 = 623, n6 = 291) were divided into two groups of a comparable ability and each was presented with one of the variants – either attractive or neutral. To evaluate the results quantitatively, we used the Item Response Theory which allowed us to determine the difficulty of the task depending on the latent abilities of pupils and enabled us to assess the discriminating properties of the problems. In the qualitative part of the study, we investigated the differences between pupils in terms of their solving strategies and errors. It was established that the attractive context could, under certain conditions, stimulate the pupils’ efforts towards solving the problems and, in some cases, can slightly improve the success rate. The study also showed that when varying the context, it is difficult to keep the other parameters of the problem without changes, possibly influencing the complexity of the situational model, and pointed out inconsistencies in some research results.
References
Beswick, K. (2011). Putting context in context: An examination of the evidence for the benefits of ‘contextualised’ tasks. International Journal of Science and Mathematics Education, 9(2), 367–390. https://doi.org/10.1007/s10763-010-9270-z
Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more “real”? For the Learning of Mathematics, 13(2), 12–17. https://www.jstor.com/stable/40248079
Borasi, R. (1986). On the nature of problems. Educational Studies in Mathematics, 17(2), 125–141. https://doi.org/10.1007/BF00311517
Bottge, B.A. (1999). Effects of contextualized math instruction on problem solving of average and below-average achieving students. The Journal of Special Education, 33(2), 81–92. https://doi.org/10.1177/002246699903300202
Cooper, 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. https://doi.org/10.1023/A:1016013332659
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
De Bock, D., Verschaffel, L., Janssens, D., Van Dooren, W., & Claes, K. (2003). Do realistic contexts and graphic representations always have a beneficial impact on students’ performance? Negative evidence from a study on modelling non-linear geometry problems. Learning and Instruction, 13(4), 441–463. https://doi.org/10.1016/S0959-4752(02)00040-3
Gersten, R., Chard, D. J., Jayanthi, M., Baker, S.K., Morphy, P., & Flojo, J. (2008). Mathematics instruction for students with learning disabilities or difficulty learning mathematics: A synthesis of the intervention research. Center on Instruction. https://files.eric.ed.gov/fulltext/ED521890.pdf
Havlíčková, R. (2020). Vliv atraktivity kontextu slovní úlohy na úspěšnost a motivaci žáků. [Disertační práce, Pedagogická fakulta Univerzity Karlovy]. (v přípravě)
Hejný, M. (2003). Anatómia slovnej úlohy o veku. Disputationes scientificae Universitatis Catholicae in Ružomberok, 3(3), 21–32. http://math.ku.sk/data/konferenciasub/pdf2003/Hejny.pdf
Hejný, M. (2014). Vyučování matematice orientované na budování schémat: aritmetika 1. stupně. Univerzita Karlova v Praze, Pedagogická fakulta.
Hembree, R. (1992). Experiments and relational studies in problem solving: A meta-analysis. Journal for Research in Mathematics Education, 23(3), 242–273. https://doi.org/10.2307/749120
Kmínková, E., & Pavelková, I. (2011). Obtížnost a zaujetí úkolem v matematice. In T. Janík, P. Knecht, & S. Šebestová (Eds.), Smíšený design v pedagogickém výzkumu: Sborník příspěvků z 19. výroční konference České asociace pedagogického výzkumu (s. 434–438). Masarykova univerzita. http://www.ped.muni.cz/capv2011/sbornikprispevku/kminkovapavelkova.pdf
Lewis, A. B., & Mayer, R. E. (1987). Students’ miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79(4), 363–371. https://doi.org/10.1037/0022-0663.79.4.363
López, C. L., & Sullivan, H. J. (1992). Effect of personalization of instructional context on the achievement and attitudes of hispanic students. Educational Technology Research and Development, 40(4), 5–14. https://doi.org/10.1007/BF02296895
Lord, F.M. (1980). Applications of item response theory to practical testing problems. Lawrence Erlbaum Associates.
Man, F., & Mareš, J. (2005). Výkonová motivace a prožitek typu flow. Pedagogika, 55(2), 151–171. https://pages.pedf.cuni.cz/pedagogika/?p=1668&lang=cs
Meyer, M.R., Dekker, T., & Querelle, N. (2001). Context in mathematics curricula. Mathematics Teaching in the Middle School, 6(9), 522–527.
Murphy, L.O., & Ross, S. M. (1990). Protagonist gender as a design variable in adapting mathematics story problems to learner interests. Educational Technology Research and Development, 38(3), 27–37. https://doi.org/10.1007/bf02298179
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. https://doi.org/10.1023/A:1024028430965
Nesher, P., & Teubal, E. (1975). Verbal cues as an interfering factor in verbal problem solving. Educational Studies in Mathematics, 6(1), 41–51. https://doi.org/10.1007/BF00590023
Novotná, J. (2000). Analýza řešení slovních úloh. Univerzita Karlova v Praze, Pedagogická fakulta.
Organisation for Economic Co-operation and Development. (2010). Learning mathematics for life: A perspective from PISA. OECD Publishing. https://doi.org/10.1787/9789264075009-en
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
Rendl, M., Vondrová, N., Hříbková, L., Jirotková, D., Kloboučková, J., Kvasz, L., Páchová, A., Pavelková, I., Smetáčková, I., Tauchmanová, E., & Žalská, J. (2013). Kritická místa matematiky na základní škole očima učitelů. Pedagogická fakulta, Univerzita Karlova.
Reusser, K. (1990). Understanding word arithmetic problems. Linguistic and situational factors [Paper presentation]. Annual Meeting of the American Educational Research Association, Boston, MA. https://eric.ed.gov/?id=ED326391
Rheinberg, F., Man, F., & Mareš, J. (2001). Ovlivňování učební motivace. Pedagogika, 51(2), 155–184. https://pages.pedf.cuni.cz/pedagogika/?p=2165&lang=cs
Sweller, J. (2010). Element interactivity and intrinsic, extraneous, and germane cognitive load. Educational Psychology Review, 22(2), 123–138. https://doi.org/10.1007/s10648-010-9128-5
Šrut, P., & Miklínová, G. (2008). Lichožrouti. Paseka.
Tzohar-Rozen, M., & Kramarski, B. (2014). Metacognition, motivation and emotions: Contribution of self-regulated learning to solving mathematical problems. Global Education Review, 1(4), 76–95. https://files.eric.ed.gov/fulltext/EJ1055263.pdf
Verschaffel, L., & De Corte, E. (1993). A decade of research on word problem solving in Leuven: Theoretical, methodological, and practical outcomes. Educational Psychology Review [online], 5(3), 239–256. https://doi.org/10.1007/BF01323046
Verschaffel, L., De Corte, E., & Pauwels, A. (1992). Solving compare problems: An eye movement test of Lewis and Mayer’s consistency hypothesis. Journal of Educational Psychology, 84(1), 85–94. https://doi.org/10.1037/0022-0663.84.1.85
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets & Zeitlinger Publishers.
Ulovec, A. (2018). Reality? An analysis of text books’ “real life” tasks. [Přednáška]. Didakticko-matematický seminář KMDM PedF UK.
Vondrová, N. (2020). Příčiny používání povrchových strategií řešení slovních úloh a jak jim předcházet. Učitel matematiky, 28(2), 66–93.
Vondrová, N., Havlíčková, R., Hirschová, M., Chvál, M., Novotná, J., Páchová, A., Smetáčková, I., Šmejkalová, M., & Tůmová, V. (2019). Matematická slovní úloha: mezi matematikou, jazykem a psychologií. Nakladatelství Karolinum.
Vondrová, N., & Novotná, J. (2017). The influence of context and order of numerical data on the difficulty of word problems for grade 6 pupils. In J. Novotná, & H. Moraová (Eds.), Proceedings of SEMT ’17 (pp. 440–449). Charles University, Faculty of Education.
Wiest, L.R. (1998). The role of fantasy and real-world problem contexts in fourth-and sixth-grade students’ mathematical problem solving. Paper presented at the Annual Meeting of the American Educational Research Association (San Diego, CA, April 13–17, 1998). https://eric.ed.gov/?id=ED425910
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(4), 677–693. https://doi.org/10.1007/s10763-007-9086-7