Mental Image and its Impact on Types of Errors in Mathematical Problem Solving: A Case Study

Zainul Munawwir 1 Indonesia , Susanto Susanto 1 Indonesia , Abi Suwito 1 Indonesia
1 Departement of Mathematics Education, Universitas Jember
Link Copied!
Published 2025-12-24
Vol. 5 No. 1 (2025) PAGES 513-524
DOI 10.51574/ijrer.v5i1.4269
Views / Downloads 205 358

Students' difficulties in visualizing geometric objects often trigger various errors in problem-solving. Although mental imagery has an important function in clarifying the shape, position, and relationships between geometric elements, research specifically examining its relationship with student error types is still limited. This study aims to describe the relationship between mental imagery and student error types in solving geometric problems. The research method used is a qualitative approach with a case study design. The research subjects consisted of three mathematics education students selected based on the variety of errors they made. Data was collected through geometry tests, observations, think-alouds, and in-depth interviews. The results showed that inaccurate or incomplete mental imagery led to the emergence of visual representation errors, conceptual errors, procedural errors, and calculation errors. Mental imagery that is not integrated with conceptual and procedural understanding causes students to misinterpret problems. The contribution of this study emphasizes the importance of strengthening visualization skills and integrating geometric concepts in learning to minimize students' cognitive errors.

Munawwir, Z., Susanto, S., & Suwito, A. (2025). Mental Image and its Impact on Types of Errors in Mathematical Problem Solving: A Case Study. ETDC: Indonesian Journal of Research and Educational Review , 5(1), 513–524. https://doi.org/10.51574/ijrer.v5i1.4269
More Citation Formats
Download Citation

Downloads

Download data is not yet available.
  1. Bates, K. E., Gilligan‐Lee, K., & Farran, E. K. (2021). Reimagining mathematics: The role of mental imagery in explaining mathematical calculation skills in childhood. Mind, Brain, and Education, 15(2), 189-198. https://doi.org/10.1111/mbe.12281
  2. Blackwell, S. E. (2021). Mental imagery in the science and practice of cognitive behaviour therapy: Past, present, and future perspectives. International Journal of Cognitive Therapy, 14(1), 160-181. https://doi.org/10.1007/s41811-021-00102-0
  3. Çakır, M. P., & Stahl, G. (2012). The integration of mathematics discourse, graphical reasoning and symbolic expression by a virtual math team. In Visual mathematics and cyberlearning (pp. 49-96). Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-007-2321-4_3
  4. Commodari, E., Sole, J., Guarnera, M., & La Rosa, V. L. (2024). Mental imagery in education: What impact on the relationships with visuospatial processing and school performance in junior high school students?. Thinking Skills and Creativity, 54, 101667. https://doi.org/10.1016/j.tsc.2024.101667
  5. Douville, P., & Pugalee, D. K. (2003). Investigating the relationship between mental imaging and mathematical problem solving. In Proceedings of the international conference of Mathematics Education into the 21stcentury project, September 2003 (pp. 62-67).
  6. Esterlina, Dahlan, J. A., & Martadipura, B. A. P. (2023). Analysis Of Students’ Errors In Mathematical Problem Solving Based On Kastolan Error Analysis. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(1), 1505–1514. https://doi.org/10.24127/ajpm.v12i1.7224
  7. Fastame, M. C. (2021). Visuo-spatial mental imagery and geometry skills in school-aged children. School Psychology International, 42(3), 324-337. https://doi.org/10.1177/0143034321992458
  8. Guarnera, M., Pellerone, M., Commodari, E., Valenti, G. D., & Buccheri, S. L. (2019). Mental images and school learning: A longitudinal study on children. Frontiers in Psychology, 10, 2034. https://doi.org/10.3389/fpsyg.2019.02034
  9. Inganah, S., Nabila, A. I., & Putri, O. R. U. (2021). Kesalahan Konstruksi Konsep Matematis Dalam Proses Representasi Visual Mahasiswa. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(3), 1776–1786. https://doi.org/10.24127/ajpm.v10i3.3993
  10. Kirmac, B. K., & Bulut, S. (2013). A Case Study on the Ways How Engagement with Spatial Visualization Problem Solving Activities Helps Pre-Service Mathematics Teachers in Solving Mental Rotation Problems. Bartin University Journal of Faculty of Education, 2(2), 18–46. https://doi.org/10.14686/201321979
  11. Macchitella, L., Tosi, G., Romano, D. L., Iaia, M., Vizzi, F., Mammarella, I. C., & Angelelli, P. (2023). behavioral sciences Visuo-Spatial Working Memory and Mathematical Skills in Children : A Network Analysis Study. MDPI Behavioral Sciences, 13(294). https://doi.org/ 10.3390/bs13040294
  12. Mudaly, V. (2021). Constructing mental diagrams during problem-solving in mathematics. Pythagoras, 42(1), 633. https://doi.org/10.4102/pythagoras. v42i1.633
  13. Murphy, C. (2019). Exploring the Role of Visual Imagery in Learning Mathematics. Mathematics Education Research Group of Australasia.
  14. Naeem, M., Ozuem, W., Howell, K., & Ranfagni, S. (2024). A Step-by-Step Process of Thematic Analysis to Develop a Conceptual Model in Qualitative Research. International Journal of Qualitative Methods, 22(October), 1–18. https://doi.org/10.1177/16094069231205789
  15. Nuovo, S. Di, Angelica, A., Santoro, G., & Platania, S. (2018). Intelligence and Mental Imagery in ID. Mediterranean Journal of Clinical Psychology MJCP, 6(2), 1–17.
  16. Park, M., & Yoo, J. (2020). Effects of perceived interactivity of augmented reality on consumer responses: A mental imagery perspective. Journal of Retailing and Consumer Services, 52, 101912. https://doi.org/10.1016/j.jretconser.2019.101912
  17. Pearson, J., Naselaris, T., Holmes, E. A., & Kosslyn, S. M. (2015). Mental Imagery : Functional Mechanisms and Clinical Applications. Trends in Cognitive Sciences, 19(10), 590–602. https://doi.org/10.1016/j.tics.2015.08.003
  18. Permatasari, P. I., Sa’dijah, C., & Chandra, T. D. (2021). Analisis Kesalahan Representasi Matematis Siswa dalam Menyelesaikan Masalah Open-Ended Materi SMP Aritmetika Sosial 1. BRILIANT: Jurnal Riset Dan Konseptual, 6(3), 527–538. http://dx.doi.org/10.28926/briliant
  19. Pongsakdi, N., Kajamies, A., Veermans, K., Lertola, K., Vauras, M., & Lehtinen, E. (2020). What makes mathematical word problem solving challenging? Exploring the roles of word problem characteristics, text comprehension, and arithmetic skills. Zdm, 52(1), 33-44. https://doi.org/10.1007/s11858-019-01118-9
  20. Prayekti, N., Nusantara, T., Susanto, H., Rofiki, I., & Malang, U. N. (2020). Students ’ Mental Models In Mathematics Problem -Solving. Journal of Critical Reviews, 7(12), 468–470. http://dx.doi.org/10.31838/jcr.07.12.83
  21. Rif’at, M. (2018). The Exploring of Visual Imagery : In Their Relation to the Students ’ Mathematical Identity. Higher Education Research, 3(5), 75–91. https://doi.org/10.11648/j.her.20180305.11
  22. Schoenherr, J., & Schukajlow, S. (2024). Characterizing external visualization in mathematics education research: a scoping review. ZDM–Mathematics Education, 56(1), 73-85. https://doi.org/10.1007/s11858-023-01494-3
  23. Sitasari, N. W., Psikologi, F., & Esa, U. (2022). Mengenal Analisa Konten Dan Analisa Tematik. Forum Ilmiah, 19(1), 77–84. https://digilib.esaunggul.ac.id/public/UEU-Journal-23188-11_2248.pdf
  24. Van Garderen, D. (2006). Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. Journal of learning disabilities, 39(6), 496-506. https://doi.org/10.1177/00222194060390060201
  25. Van Garderen, D., Scheuermann, A., Poch, A., & Murray, M. M. (2018). Visual representation in mathematics: Special education teachers’ knowledge and emphasis for instruction. Teacher Education and Special Education, 41(1), 7-23. https://doi.org/10.1177/0888406416665448
  26. van Garderen, D., Scheuermann, A., Sadler, K., Hopkins, S., & Hirt, S. M. (2021). Preparing pre-service teachers to use visual representations as strategy to solve mathematics problems: What did they learn?. Teacher Education and Special Education, 44(4), 319-339. https://doi.org/10.1177/0888406421996070
  27. Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. Zdm, 52(1), 1-16. https://doi.org/10.1007/s11858-020-01130-4
  28. Zakaria, E., Ibrahim, & Maat, S. M. (2010). Analysis of Students ’ Error in Learning of Quadratic Equations. International Education Studies, 3(3), 105–110. https://eric.ed.gov/?id=EJ1065893
  29. Zaleskiewicz, T., Traczyk, J., & Sobkow, A. (2023). Decision making and mental imagery: A conceptual synthesis and new research directions. Journal of Cognitive Psychology, 35(5), 603-633. https://doi.org/10.1080/20445911.2023.2198066
  30. Zulu, M. W. (2023). Unveiling problem-solving strategies of pre-service mathematics teachers : A visual and discursive exploration. EURASIA Journal of Mathematics, Science and Technology Education, 19(7). https://doi.org/10.29333/ejmste/13344

Copyright (c) 2025 Zainul Munawwir, Susanto Susanto, Abi Suwito

Creative Commons License

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

Similar Articles

<< < 1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.

Dimensions Badge

Downloads

Downloads
Crossmark Badge
Crossmark Badge
Section
Articles
Keywords
Geometry Errors Mental Imagery Problem Solving Visualization
Crossref
Scopus
Google Scholar
Europe PMC