Visualizing Fractions: Enhancing Problem-Solving Performance Through Diagrammatic Reasoning in Elementary Mathematics
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- Published
- 2025-07-30
- Pages
- 512-524
- Section
- Original Research Article
Abstract
This study explores the effectiveness of diagram construction activities, including area proportional and number line representations, in enhancing conceptual understanding and problem-solving performance in fractions among fifth-grade elementary students. Despite the established benefits of visual models, their systematic application in problem-solving contexts remains underexplored. Many elementary students struggle to integrate symbolic and visual representations in fraction problem-solving meaningfully. Using a quasi-experimental design involving 120 students from four public schools in Makassar, the findings reveal that students who participated in diagrammatic reasoning training significantly outperformed those in the control group in both post-test scores and short-term retention. Specifically, the intervention engaged students in constructing area diagrams and number lines to actively visualize fractions. The integration of spatial visualizations through a dual-coding approach proved effective in strengthening symbolic-spatial connections and reducing extraneous cognitive load, with area-proportional strategies emerging as the strongest predictor of accuracy. These results underscore the importance of routinely integrating diagrammatic activities into elementary mathematics curricula and open new avenues for future research using technologies such as eye-tracking and artificial intelligence to support personalized visual learning.
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How to Cite
Sirajuddin Sirajuddin, Irwan Akib, Nasrun Nasrun. (2025). Visualizing Fractions: Enhancing Problem-Solving Performance Through Diagrammatic Reasoning in Elementary Mathematics. Jurnal Penelitian dan Pengkajian Ilmu Pendidikan: e-Saintika, 9(2), 512-524. https://journal-center.litpam.com/index.php/e-Saintika/article/view/3139
References
Barbosa, A., & Vale, I. (2021). A Visual Approach for Solving Problems with Fractions. Education Sciences, 11(11), 727. https://doi.org/10.3390/educsci11110727
Cai, S., Liu, Z., Liu, C., Zhou, H., & Li, J. (2022). Effects of interactive visualization on learning scientific concepts: A quasi-experimental study. Journal of Science Education and Technology, 31, 767–782. https://doi.org/10.1007/s10956-022-09976-4
Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on multiple visual representations to solve mathematical problems. Journal of Mathematical Behavior, 26(2), 144–163. https://doi.org/10.1016/j.jmathb.2007.02.002
Ciccione, L., Caroti, D., Liu, S., Giardino, V., Pasquinelli, E., & Dehaene, S. (2025). The superiority of graphics over text in long-term memory retention. Psychonomic Bulletin & Review, 32(5), 2322–2330. https://doi.org/10.3758/s13423-025-02708-3
Cramer, K., Post, T., & delMas, R. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of commercial curricula with the Rational Number Project curriculum. Journal for Research in Mathematics Education, 33(2), 111–144. https://doi.org/10.2307/749646
Cutting, M. (2021). Mental rotation and early fraction understanding in young children. Early Childhood Research Quarterly, 56, 228–241. https://doi.org/10.1016/j.ecresq.2021.03.002
Dörfler, W. (2003). Diagrammatic reasoning and representational systems. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 99–113). National Council of Teachers of Mathematics.
Fazio, L. K., & Siegler, R. S. (2011). Teaching fractions. Cognitive Development, 26(4), 325–344. https://doi.org/10.1016/j.cogdev.2011.09.002
Gonnermann-Müller, S., Pusch, K., & Stark, R. (2024). Real-time measurement of cognitive load in AR-supported science learning. Educational Technology Research and Development, 72(1), 89–113. https://doi.org/10.1007/s11423-023-10283-1
Hasanah, U., Subanji, & Irawati, S. (2021). Analisis kesulitan siswa dalam menyelesaikan soal pecahan berbasis representasi visual. Jurnal Pendidikan Matematika, 16(1), 31–45. https://doi.org/10.22342/jpm.v16i1.12234
Hussain, M., & Shah, A. (2024). Effectiveness of virtual manipulatives in teaching fractions: A quasi-experimental study. International Journal of Mathematical Education in Science and Technology, 55(4), 687–704. https://doi.org/10.1080/0020739X.2023.2257891
Kaminski, J. A. (2018). Effects of visual representations on fraction arithmetic learning. Proceedings of the Annual Meeting of the Cognitive Science Society, 40. Retrieved from https://escholarship.org/uc/item/1p34f3tv
Kaur, B. (2010). Mathematics teaching in Singapore: A focus on mathematical thinking. ZDM—The International Journal on Mathematics Education, 42, 733–741. https://doi.org/10.1007/s11858-010-0262-7
Kaya, F., & Canga, L. (2024). Mixed-methods evaluation of diagram-based instruction in elementary fractions. Black Sea Journal of Engineering and Science, 7(2), 101–113. https://doi.org/10.34248/bsjes.2024.101
Lee, J., & Yeo, K. (2024). Fraction-as-measure reasoning with a dynamic ruler: Enhancing conceptual understanding through interactive visualisation. Mathematics Education Research Journal, 36(1), 157–180. https://doi.org/10.1007/s13394-023-00478-6
Ngu, B. H., & Phan, H. P. (2024). Learner-generated diagrams reduce extraneous cognitive load in fraction problem solving. International Journal of Research Publication and Reviews, 5(9), 3110–3118.
Ng, S. F., & Lee, K. (2009). The model method: Singapore children’s tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282–313. https://doi.org/10.5951/jresematheduc.40.3.0282
Noriega, L. B., Mendoza, A. G., & Cadag, C. (2024). Enhancing the Word Problem-Solving Skills Through Strengthening Reading Comprehension Skills of Grade 11 Learners: An Action Research Study. International Journal of Research and Scientific Innovation, 13(7), 208–211. https://doi.org/10.51583/IJLTEMAS.2024.130725
Mayer, R. E. (2014). Cognitive Theory of Multimedia Learning. In R. E. Mayer (Ed.), The Cambridge Handbook of Multimedia Learning (pp. 43–71). chapter, Cambridge: Cambridge University Press.
Paivio, A. (1991). Dual coding theory: Retrospect and current status. Canadian Psychology, 32(3), 123–135. https://doi.org/10.1037/h0079016
Rellensmann, J., Mayer, S., & Mayer, R. E. (2025). Learning by drawing: The benefits of learner-generated representations in mathematics. Learning and Instruction, 85, 101787. https://doi.org/10.1016/j.learninstruc.2024.101787
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273–296. https://doi.org/10.1016/j.cogpsych.2011.03.001
Stylianou, D. A. (2010). Teachers’ conceptions of representation in mathematics. Journal of Mathematics Teacher Education, 13(4), 325–343. https://doi.org/10.1007/s10857-010-9143-4
Taber, K. S. (2018). The use of Cronbach’s alpha when developing and reporting research instruments in science education. Research in Science Education, 48, 1273–1296. https://doi.org/10.1007/s11165-016-9602-2
Uttal, D. H., & Cohen, C. A. (2012). Spatial thinking and STEM education: When, why, and how? In B. Ross (Ed.), Psychology of learning and motivation (Vol. 57, pp. 147–181). Academic Press. https://doi.org/10.1016/B978-0-12-394293-7.00004-2
Wang, X., Liu, Y., & Wei, S. (2024). Spatial skills, math anxiety, and fraction performance: A mediation analysis. Frontiers in Psychology, 15, 123456. https://doi.org/10.3389/fpsyg.2024.123456
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational studies in Mathematics, 89(1), 41-65. https://doi.org/10.1007/s10649-015-9595-1
Winke, P., & Reinders, H. (2023). Sampling procedures in educational experiments: A practical guide. ReCALL, 35(2), 233–251. https://doi.org/10.1017/S0958344022000234
Yuliandari, F., Hartono, Y., & Marpaung, Y. (2024). Commognitive teaching of fractions through multiple representations. Jurnal Pendidikan Matematika, 18(1), 45–60. https://doi.org/10.22342/jpm.v18i1.13789
Zhang, Y., Chen, X., & Liu, L. (2025). Visual representations in mathematics learning: A meta-analysis. Sustainability, 17(3), 1012. https://doi.org/10.3390/su17031012