Enhancing geometry problem-solving through visualization for multilingual learners

Phumlani Hlongwana; Vimolan Mudaly; Mzwandile Wiseman Zulu

doi:10.29333/ejmste/16564

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Phumlani Hlongwana ¹ ^* , Vimolan Mudaly ¹ , Mzwandile Wiseman Zulu ¹

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¹ University of KwaZulu-Natal, Durban, SOUTH AFRICA^* Corresponding Author

Abstract

Visualization is key in developing learners’ problem-solving skills and mathematical reasoning, yet many South African Grade 11 multilingual learners (MLs) struggle with geometry. This qualitative study, informed by the commognitive framework, explores how visual aids and language influence their understanding. Eighteen MLs participated in task-based interviews and focus group discussions. Findings revealed two main challenges: limited understanding of geometry terms like “arc,” “bisect,” and “subtend,” and difficulty visualizing concepts without a clear vocabulary. However, when visual representations supported instruction, learners showed improved comprehension, identified misconceptions, and communicated their reasoning more effectively. The study concludes that combining visual aids with explicit language support enhances MLs’ geometry learning. Multilingual classrooms should incorporate annotated diagrams, drawing tasks, and vocabulary-focused prompts to strengthen visualization and conceptual understanding.

Keywords

mathematics problem-solving
visualization in geometry
multilingual learning in mathematics education
commognition in geometry thinking

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 21, Issue 7, July 2025, Article No: em2662

https://doi.org/10.29333/ejmste/16564

Publication date: 04 Jul 2025

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References

Atebe, H. U., & Schäfer, M. (2010a). Beyond teaching language: Towards terminological primacy in learners’ geometric conceptualisation. Pythagoras, 2010(71), 53-64. https://doi.org/10.4102/pythagoras.v0i71.7
Atebe, H. U., & Schäfer, M. (2010b). Research evidence on geometric thinking level hierarchies and their relationships with students’ mathematical performance. Journal of the Science Teachers Association of Nigeria, 45(1-2), 76-84.
Bandalos, D. L., & Finney, S. J. (2018). Factor analysis: Exploratory and confirmatory. In G. R. Hancock, L. M. Stapleton, & R. O. Mueller (Eds.), The reviewer’s guide to quantitative methods in the social sciences (pp. 98-122). Routledge. https://doi.org/10.4324/9781315755649-8
Baroody, A. J. (1989). A guide to teaching mathematics in the primary grades. Allyn and Bacon.
Bartolini, M. G., & Martignone, F. (2020). Manipulatives in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 487-494). Springer. https://doi.org/10.1007/978-3-030-15789-0_93
Barwell, R. (2018). From language as a resource to sources of meaning in multilingual mathematics classrooms. The Journal of Mathematical Behavior, 50, 155-168. https://doi.org/10.1016/j.jmathb.2018.02.007
Barwell, R., Barton, B., & Setati, M. (2007). Multilingual issues in mathematics education: Introduction. Educational Studies in Mathematics, 64, 113-119. https://doi.org/10.1007/s10649-006-9065-x
Bautista, A., & Ortega-Ruiz, R. (2015). Teacher professional development: International perspectives and approaches. Psychology, Society & Education, 7(3), 240-251. https://doi.org/10.25115/psye.v7i3.1020
Braun, V., & Clarke, V. (2025). Reporting guidelines for qualitative research: A values-based approach. Qualitative Research in Psychology, 22(2), 399-438. https://doi.org/10.1080/14780887.2024.2382244
Bruner, J. (1985). Models of the learner. Educational Researcher, 14(6), 5-8. https://doi.org/10.3102/0013189X014006005
Carrier, K. A. (2005). Supporting science learning through science literacy objectives for English language learners. Science Activities, 42(2), 5-11. https://doi.org/10.3200/SATS.42.2.5-11
Chawla, N., & Mittal, A. K. (2013). Pedagogy of mathematics: Role of technology in teaching-learning mathematics. Journal of Indian Research, 1(1), 105-110.
Chu, M., & Kita, S. (2011). The nature of gestures’ beneficial role in spatial problem solving. Journal of Experimental Psychology: General, 140(1), Article 102. https://doi.org/10.1037/a0021790
Chval, K. B., Smith, E., Trigos-Carrillo, L., & Pinnow, R. J. (2020). Teaching math to multilingual students, grades K-8: Positioning English learners for success. Corwin.
Clarkson, P. (2016). Multilingual contexts overview: A new positioning for stem teaching /learning. In Proceedings of the ESERA 2015 (pp. 1838-1845).
DBE. (2014). Curriculum and assessment policy statement. Department of Basic Education.
Deliyianni, E., Monoyiou, A., Elia, I., Georgiou, C., & Zannettou, E. (2009). Pupils’ visual representations in standard and problematic problem solving in mathematics: Their role in the breach of the didactical contract. European Early Childhood Education Research Journal, 17(1), 95-110.
Duval, R. (2017). Understanding the mathematical way of thinking–The registers of semiotic representations. Springer. https://doi.org/10.1007/978-3-319-56910-9
Duvenhage, M. (2020). Grade 8 and 9 township learners’ response to a problem-based mathematics extension programme [M.Ed. thesis, University of the Free State].
Essien, A. A. (2013). Preparing pre-service mathematics teachers to teach in multilingual classrooms: A community of practice perspective [PhD dissertation, Wits University].
Fahy, P. J. (2013). Uses of published research: An exploratory case study. International Review of Research in Open and Distributed Learning, 14(1), 145-166. https://doi.org/10.19173/irrodl.v14i1.1382
Franceschini, R. (2009). The genesis and development of research in multilingualism: Perspectives for future research. In The exploration of multilingualism: Development of research on L3, multilingualism and multiple language acquisition (pp. 27-61). John Benjamins Publishing Company. https://doi.org/10.1075/aals.6.03ch3
Ge, L. W., Easterday, M., Kay, M., Dimara, E., Cheng, P., & Franconeri, S. L. (2024). V-FRAMER: Visualization framework for mitigating reasoning errors in public policy. In Proceedings of the 2024 CHI Conference on Human Factors in Computing Systems (pp. 1-15). https://doi.org/10.1145/3613904.3642750
González, A., Gallego-Sánchez, I., Gavilán-Izquierdo, J. M., & Puertas, M. L. (2021). Characterizing levels of reasoning in graph theory. Eurasia Journal of Mathematics, Science and Technology Education, 17(8), Article em1990. https://doi.org/10.29333/ejmste/11020
Harbi, A. G. (2024). Using visuals and manipulatives for supporting English language learners. The Peerian Journal, 27, 154-163. https://www.peerianjournal.com/index.php/tpj/article/view/767
Hasanah, S. I., Tafrilyanto, C. F., & Aini, Y. (2019). Mathematical reasoning: The characteristics of students’ mathematical abilities in problem solving. Journal of Physics: Conference Series, 1188(1), Article 012057. https://doi.org/10.1088/1742-6596/1188/1/012057
Jones, L. L. (2013). How multimedia-based learning and molecular visualization change the landscape of chemical education research. Journal of Chemical Education, 90(12), 1571-1576. https://doi.org/10.1021/ed4001206
Klerlein, J., & Hervey, S., (2020). Mathematics as a complex problem solving activity. https://www.generationready.com/white-papers/mathematics-as-acomplex-problem-solving-activity/
Lowrie, T., & Logan, T. (2023). Spatial visualization supports students’ math: Mechanisms for spatial transfer. Journal of Intelligence, 11(6), Article 127. https://doi.org/10.3390/jintelligence11060127
Maries, A., & Singh, C. (2013). Exploring one aspect of pedagogical content knowledge of teaching assistants using the test of understanding graphs in kinematics. Physical Review Special Topics–Physics Education Research, 9(2), Article 020120. https://doi.org/10.1103/PhysRevSTPER.9.020120
Mesaroš, M. (2012). Forms of visualization as a solving approach in teaching mathematics. In Proceedings of the 13^th International Scientific Conference of PhD Students and Young Scientists and Pedagogues (pp. 318-325).
Moleko, M. M. (2021). Teachers’ perspectives on addressing linguistic factors affecting visualization of mathematics word problems. Eurasia Journal of Mathematics, Science and Technology Education, 17(11), Article em2029. https://doi.org/10.29333/ejmste/11248
Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2-3), 189-212. https://doi.org/10.1207/S15327833MTL04023_5
Moschkovich, J. (2012). Mathematics, the common core, and language: Recommendations for mathematics instruction for ELs aligned with the common core. Common Core State Standards and Next Generation Science Standards, 94, Article 17.
Moschkovich, J. N. (2015). Academic literacy in mathematics for English learners. The Journal of Mathematical Behavior, 40, 43-62. https://doi.org/10.1016/j.jmathb.2015.01.005
Mudaly, V. (2012). Diagrams in mathematics: To draw or not to draw? Perspectives in Education, 30(2), 22-31.
Mudaly, V. (2016). Pre-service teachers’ understanding of the concept of proof. International Scientific Researches Journal, 72(5), 137-158. https://doi.org/10.21506/j.ponte.2016.5.15
Mudaly, V. (2021). Constructing mental diagrams during problem-solving in mathematics. Pythagoras, 42(1), Article 633. https://doi.org/10.4102/pythagoras.v42i1.633
Mudaly, V., & Naidoo, J. (2015). The concrete-representational-abstract sequence of instruction in mathematics classrooms. Perspectives in Education, 33(1), 42-56.
Mudaly, V., & Rampersad, R. (2010). The role of visualisation in learners’ conceptual understanding of graphical functional relationships. African Journal of Research in Mathematics, Science and Technology Education, 14(1), 36-48. https://doi.org/10.1080/10288457.2010.10740671
Mudaly, V., & Reddy, L. (2016). The role of visualisation in the proving process of Euclidean geometry problems. International Scientific Research Journal, 72(8), 178-204. https://doi.org/10.21506/j.ponte.2016.8.13
Mudhefi, F., Mabotja, K., & Muthelo, D. (2024). The use of Van Hiele’s geometric thinking model to interpret grade 12 learners’ learning difficulties in Euclidean geometry. Perspectives in Education, 42(2), 162-175. https://doi.org/10.38140/pie.v42i2.8350
Naicker, K. (2021). An exploration of the barriers to effective geometric thought in the further education and training phase of selected secondary schools in the Umlazi District [Doctoral dissertation, University of KwaZulu-Natal, Edgewood].
Naidoo, J. (2011). Exploring master teachers’ use of visuals as tools in mathematics classrooms [Doctoral dissertation, University of KwaZulu-Natal, Edgewood].
Naidoo, J., & Kapofu, W. (2020). Exploring female learners’ perceptions of learning geometry in mathematics. South African Journal of Education, 40(1), 1-11. https://doi.org/10.15700/saje.v40n1a1727
NCTM. (2022). Problem solving: An approach to understanding and critiquing our world. National Council of Teachers of Mathematics. https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Trena-Wilkerson/Problem-Solving_-An-Approach-to-Understanding-and-Critiquing-Our-World
Peng, A., Cao, L., & Yu, B. (2020). Reciprocal learning in mathematics problem posing and problem solving: An interactive study between Canadian and Chinese elementary school students. Eurasia Journal of Mathematics, Science and Technology Education, 16(12), Article em1913. https://doi.org/10.29333/ejmste/9130
Pi, Z., Guo, X., Liu, C., & Yang, J. (2023). Students with low prior knowledge learn more when explaining to a peer than to a teacher after viewing educational videos. Active Learning in Higher Education, 26(1), 91-107. https://doi.org/10.1177/14697874231212260
Planas, N., & Civil, M. (2013). Language-as-resource and language-as-political: Tensions in the bilingual mathematics classroom. Mathematics Education Research Journal, 25, 361-378. https://doi.org/10.1007/s13394-013-0075-6
Planas, N., Morgan, C., & Schütte, M. (2018). Mathematics education and language: Lessons and directions from two decades of research. In Developing research in mathematics education (pp. 196-210). https://doi.org/10.4324/9781315113562-15
Pólya, G. (1945). How to solve it: A new aspect of mathematics. Princeton University Press. https://doi.org/10.1515/9781400828678
Prediger, S., Erath, K., & Opitz, E. M. (2019). The language dimension of mathematical difficulties. In International handbook of mathematical learning difficulties: From the laboratory to the classroom (pp. 437-455). https://doi.org/10.1007/978-3-319-97148-3_27
Prediger, S., Wilhelm, N., Büchter, A., Gürsoy, E., & Benholz, C. (2018). Language proficiency and mathematics achievement: Empirical study of language-induced obstacles in a high stakes test, the central exam ZP10. Journal für Mathematik-Didaktik, 39(Suppl 1), 1-26. https://doi.org/10.1007/s13138-018-0126-3
Presmeg, N. (2006). Semiotics and the “connections” standard: Significance of semiotics for teachers of mathematics. Educational Studies in Mathematics, 61, 163-182. https://doi.org/10.1007/s10649-006-3365-z
Rellensmann, J., Schukajlow, S., & Leopold, C. (2017). Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance. Educational Studies in Mathematics, 95, 53-78. https://doi.org/10.1007/s10649-016-9736-1
Robertson, S.-A., & Graven, M. (2018). Using a transdisciplinary framework to examine mathematics classroom talk taking place in and through a second language. ZDM – Mathematics Education, 50(6), 1013-1027. https://doi.org/10.1007/s11858-018-0952-2
Robertson, S., & Graven, M. (2020). Language as an including or excluding factor in mathematics teaching and learning. Mathematics Education Research Journal, 32, 77-101. https://doi.org/10.1007/s13394-019-00302-0
Rösken, B., & Rolka, K. (2006, July). A picture is worth a 1000 words–The role of visualization in mathematics learning. In Proceedings 30^th Conference of the International Group for the Psychology of Mathematics Education (pp. 457-464). Charles University.
Ryan, U., & Parra, A. (2019). Epistemological aspects of multilingualism in mathematics education: An inferentialist approach. Research in Mathematics Education, 21(2), 152-167. https://doi.org/10.1080/14794802.2019.1608290
Samosa, R. C., Dominguez, J. M., Budaño, S. D., Ronquillo, C. J., & Yumul, R. E. (2021). Visualize, represent and solve problem technique as teaching strategy to improve the learner’s problem-solving skill in mathematics 2. International Journal of Academic Multidisciplinary Research, 5(12), 75-78. https://doi.org/10.13140/RG.2.2.28700.62083
Sao, L. Y. (2008). Barriers to learning mathematics in rural secondary schools [Doctoral dissertation, Stellenbosch University]. http://hdl.handle.net/10019.1/2459
Schenck, K. E., & Nathan, M. J. (2024). Navigating spatial ability for mathematics education: A review and roadmap. Educational Psychology Review, 36(3), Article 90. https://doi.org/10.1007/s10648-024-09935-5
Setati, M., & Barwell, R. (2006). Discursive practices in two multilingual mathematics classrooms: An international comparison. African Journal of Research in Mathematics, Science and Technology Education, 10(2), 27-38. https://doi.org/10.1080/10288457.2006.10740602
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. The Journal of the Learning Sciences, 16(4), 565-613. https://doi.org/10.1080/10508400701525253
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Shoba, J. (2020). Interactive simulations and multilingual learners: Bridging language and conceptual understanding in mathematics. International Journal of Multilingual Education, 8(1), 22-35.
Sintonen, S. (2024). Stones, situated writing and education. Educational Philosophy and Theory, 56(14), 1366-1377. https://doi.org/10.1080/00131857.2024.2393424
Supardi, L., Zayyadi, M., Lanya, H., Hasanah, S. I., & Hidayati, S. N. (2021). Commognitive analysis of students’ errors in solving high order thinking skills problems. Turkish Journal of Computer and Mathematics Education, 12(6), 950-961. https://doi.org/10.17762/turcomat.v12i6.2373
Suto, I., & Zanini, N. (2018). Developing problem-solving skills through mathematics education: International perspectives. Large-Scale Assessments in Education, 6(1), 1-17.
Tachie, S. A. (2020). The challenges of South African teachers in teaching Euclidean geometry. International Journal of Learning, Teaching and Educational Research, 19(8), 297-312. https://doi.org/10.26803/ijlter.19.8.16
Vale, I., & Barbosa, A. (2018). Mathematical problems: The advantages of visual strategies. Journal of the European Teacher Education Network, 13, 23-33  https://jeten-online.org/index.php/jeten/article/view/158/187
Vale, I., Pimentel, T., & Barbosa, A. (2018). The power of seeing in problem solving and creativity: An issue under discussion. In Broadening the scope of research on mathematical problem solving: A focus on technology, creativity and affect (pp. 243-272). https://doi.org/10.1007/978-3-319-99861-9_11
Van Hiele, P. M. (1957). De Problematick van het Inzicht Gedemonstreed van het Inzicht van Schodkindren in Meetkundeleerstof [The problem of insight demonstrated from Schodkindren’s insight in geometry]. University of Utrecht.
Wu, Y., Hellerstein, J. M., & Satyanarayan, A. (2020). B2: Bridging code and interactive visualization in computational notebooks. In Proceedings of the 33^rd Annual ACM Symposium on User Interface Software and Technology (pp. 152-165). ACM. https://doi.org/10.1145/3379337.3415851
Yahya, F. H., Kurniawan, H., Shamsuddin, N. R., & Zain, R. M. (2022). Effects of visual learning geometry kits (VLGeo-Kits) on students’ level of geometrical thinking. In Proceedings of the 2^nd International Conference on Education and Technology (pp. 1-6). Atlantis Press. https://doi.org/10.2991/assehr.k.220103.001
Yin, L. (2010). Integrating 3D visualization and GIS in planning education. Journal of Geography in Higher Education, 34(3), 419-438. https://doi.org/10.1080/03098260903556030
Zhang, W., & Creswell, J. (2013). The use of “mixing” procedure of mixed methods in health services research. Medical Care, 51(8), e51-e57. https://doi.org/10.1097/MLR.0b013e31824642fd
Zimmermann, W., & Cunningham, S. (1991). Visualization in teaching and learning mathematics. Mathematical Association of America.

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APA

Hlongwana, P., Mudaly, V., & Zulu, M. W. (2025). Enhancing geometry problem-solving through visualization for multilingual learners. Eurasia Journal of Mathematics, Science and Technology Education, 21(7), em2662. https://doi.org/10.29333/ejmste/16564

Vancouver

Hlongwana P, Mudaly V, Zulu MW. Enhancing geometry problem-solving through visualization for multilingual learners. EURASIA J Math Sci Tech Ed. 2025;21(7):em2662. https://doi.org/10.29333/ejmste/16564

AMA

Hlongwana P, Mudaly V, Zulu MW. Enhancing geometry problem-solving through visualization for multilingual learners. EURASIA J Math Sci Tech Ed. 2025;21(7), em2662. https://doi.org/10.29333/ejmste/16564

Chicago

Hlongwana, Phumlani, Vimolan Mudaly, and Mzwandile Wiseman Zulu. "Enhancing geometry problem-solving through visualization for multilingual learners". Eurasia Journal of Mathematics, Science and Technology Education 2025 21 no. 7 (2025): em2662. https://doi.org/10.29333/ejmste/16564

Harvard

Hlongwana, P., Mudaly, V., and Zulu, M. W. (2025). Enhancing geometry problem-solving through visualization for multilingual learners. Eurasia Journal of Mathematics, Science and Technology Education, 21(7), em2662. https://doi.org/10.29333/ejmste/16564

MLA

Hlongwana, Phumlani et al. "Enhancing geometry problem-solving through visualization for multilingual learners". Eurasia Journal of Mathematics, Science and Technology Education, vol. 21, no. 7, 2025, em2662. https://doi.org/10.29333/ejmste/16564