The role of essential illustrations in a design experiment
DOI:
https://doi.org/10.31074/gyntf.2025.1.5.19Keywords:
essential illustration, design experiment, word problem, problemsolving, elementary schoolAbstract
The study reports the results of a developmental experiment conducted in the third grade of a suburban primary school in Budapest. The aim of this research was to help students to with the text of mathematical problems involving essential (Berends & Van Lieshout, 2009) figures. Students had to carry out 12 pairs of tasks containing of which design is considered to be essential for successful problem solving. We hypothesized that pupils participating in the experiment would be better able to solve this type of mathematical problem and that there would be an increase in the percentage of realistic answers to realistic (Verschaffel, 2009) textual problems. Our results suggest a tendency for the test group to increase the percentage of realistic responses to realistic text tasks, and a significant improvement was also observed in a PISA task. The results of the study can be used as a resource for in-service teachers in the field of mathematics education and problem solving.
Downloads
References
Berends, I. E. & Van Lieshout, E. C. (2009). The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load. Learning and Instruction, 19(4), 345–353. https://doi.org/10.1016/j.learninstruc.2008.06.012 DOI: https://doi.org/10.1016/j.learninstruc.2008.06.012
Cummins, D. D. (1991). Children’s interpretations of arithmetic word problems. Cognition and instruction, 8(3), 261–289. https://doi.org/10.1207/s1532690xci0803_2 DOI: https://doi.org/10.1207/s1532690xci0803_2
Csapó, B. (2003). A képességek fejlődése és iskolai fejlesztése. Akadémiai Kiadó.
Csíkos, Cs. (2003). Matematikai szöveges feladatok megértésének problémái 10–11 éves tanulók körében. Magyar Pedagógia, 103(1), 35–55.
Csíkos, Cs. (2008). Mentális modellek és metareprezentációk matematikai szöveges feladatok megoldásában. Egy fejlesztőkísérlet elméleti alapjai. In Kozma, T. & Perjés, I. (Eds.), Új kutatások a neveléstudományokban (pp. 109–117). MTA Pedagógiai Bizottság.
Csíkos, Cs., Szitányi, J. & Kelemen, R. (2010). Vizuális reprezentációk szerepe a matematikai problémamegoldásban. Egy 3. osztályos tanulók körében végzett fejlesztő kísérlet eredményei. Magyar Pedagógia, 110(2), 149–166.
Csíkos, Cs. (2012). Pedagógiai kísérletek kutatásmódszertana. Gondolat.
Csíkos, C. & Szitányi, J. (2020). Teachers’ pedagogical content knowledge in teaching word problem solving strategies. ZDM, 52(1), 165–178. https://doi.org/10.1007/s11858-019-01115-y DOI: https://doi.org/10.1007/s11858-019-01115-y
Csíkos, C., Szitányi, J. & Kelemen, R. (2012). The effects of using drawings in developing young children’s mathematical word problem solving: A design experiment with third-grade Hungarian students. Educational Studies in Mathematics, 81, 47–65. https://doi.org/10.1007/s10649-011-9360-z DOI: https://doi.org/10.1007/s10649-011-9360-z
Csíkos, C. & Verschaffel, L. (2011). Mathematical literacy and the application of mathematical knowledge. Framework for diagnostic assessment of mathematics, 57–93.
De Corte, E., Verschaffel, L. & Op’t Eynde, P. (2000). Self-regulation: A characteristic and a goal of mathematics education. In Handbook of self-regulation (pp. 687–726). Academic Press. https://doi.org/10.1016/B978-012109890-2/50050-0 DOI: https://doi.org/10.1016/B978-012109890-2/50050-0
Dewolf, T., Van Dooren, W., Hermens, F. & Verschaffel, L. (2013, July). Do students attend to and profit from representational illustrations of non-standard mathematical word problems? In Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 217–224).
Elia, I. & Philippou, G. (2004). The Functions of Pictures in Problem Solving. International group for the psychology of mathematics education.
Hegarty, M. & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684. https://doi.org/10.1037/0022-0663.91.4.684 DOI: https://doi.org/10.1037//0022-0663.91.4.684
Hidayatullah, A. & Csíkos, C. (2023). Students’ responses to the realistic word problems and their mathematics-related beliefs in primary education. Pedagogika, 150(2), 21–37. https://doi.org/10.15823/p.2023.150.2 DOI: https://doi.org/10.15823/p.2023.150.2
Kelemen, R. (2004). Egyes háttérváltozók szerepe „szokatlan” matematikai szöveges feladatok megoldásában. Iskolakultúra, 14(11), 28–38.
Kelemen, R. (2006). Nemzetközi tendenciák a matematikai szöveges feladatok elméletében. Iskolakultúra, 16(1), 56–65.
Kelemen, R. (2007). Fejlesztő kísérletek a realisztikus matematikai problémák megoldásában. Iskolakultúra, 6, 7.
Mayer, R. E. & Hegarty, M. (2012). The process of understanding mathematical problems. In The nature of mathematical thinking (pp. 29–53). Routledge.
McNeil, N. M., Uttal, D. H., Jarvin, L. & Sternberg, R. J. (2009). Should you show me the money? Concrete objects both hurt and help performance on mathematics problems. Learning and Instruction, 19(2), 171–184. https://doi.org/10.1016/j.learninstruc.2008.03.005 DOI: https://doi.org/10.1016/j.learninstruc.2008.03.005
Morris, S. B. (2005). Effect size estimation from prestest–posttest–control designs with heterogeneous variances. Paper presented at the 20th Annual Conference of the Society for Industrial and Organizational Psychology, Los Angeles, CA.
OECD (2004). Learning for tomorrow’s world: First results from PISA 2003. https://doi.org/10.1787/9789264006416-en DOI: https://doi.org/10.1787/9789264006416-en
OECD (2006). PISA released items – Mathematics. https://www.oecd.org/pisa/38709418.pdf (2025. 01. 30.)
Schnotz, W. (2002). Commentary: Towards an integrated view of learning from text and visual displays. Educational Psychology Review, 14, 101–120. https://doi.org/10.1023/A:1013136727916 DOI: https://doi.org/10.1023/A:1013136727916
Turzó-Sovák, N., Berecki, I., Csíkos, Cs. & Hidayatullah, A. (2025). Cognitive metacognitive and affective factors behind performance on a PISA task; A Hungarian-Indonesian comparative study (submitted for publication).
Viitala, H. (2015). Two Finnish girls and mathematics: Similar achievement level, same core curriculum, different competences. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 137–150. https://doi.org/10.31129/lumat.v3i1.1056 DOI: https://doi.org/10.31129/lumat.v3i1.1056
Verschaffel, L. & De Corte, E. (1997). Word problems: A vehicle for promoting authentic mathematical understanding and problem solving in the primary school? In T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 69–97). Psychology Press.
Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H. & Ratinckx, E. (1999). Design and evaluation of a learning environment for mathematical modeling and problem solving in upper elementary school children. Mathematical Thinking and Learning, 1(3), 195–230. https://doi.org/10.1207/s15327833mtl0103_2 DOI: https://doi.org/10.1207/s15327833mtl0103_2
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Author

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.







