Identifying key factors influencing mathematical visual thinking among pre-service mathematics teachers
DOI:
https://doi.org/10.59672/ijed.v6i3.4620Keywords:
Cognitive factors, Mathematical visual thinking, Pre-service mathematics teachers, Quadratic functions, Technological toolAbstract
Mathematical visual thinking is essential for understanding complex mathematical concepts, as it enables learners to interpret and connect visual and symbolic representations. However, many pre-service mathematics teachers struggle to integrate visual representations with algebraic expressions, leading to conceptual misunderstandings. This study aims to identify the key factors influencing mathematical visual thinking among pre-service mathematics teachers. A mixed-methods descriptive study was conducted, involving 150 students for quantitative analysis and 15 selected participants for qualitative interviews. Data were collected through a mathematical visual thinking test, a visual thinking factors questionnaire, semi-structured interviews, and document analysis of students’ mathematical tasks. The results indicate that most students exhibit moderate visual thinking ability (50%), with challenges in linking graphical and algebraic representations. The key influencing factors include teaching approaches (4.3), concept understanding (4.1), motivation (4.0), and technology use (4.2), whereas anxiety plays a lesser role (2.9). Students relying heavily on technological tools tend to improve accuracy but struggle with independent visualization. These findings suggest that instructional strategies should integrate structured visual exercises, emphasize transformation understanding, and balance technological support with manual problem-solving. This study provides new insights into enhancing visual thinking in mathematics and offers pedagogical recommendations for pre-service teacher education.
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Abu, M., & Toyon, S. (2021). Explanatory sequential design of mixed methods research: Phases and challenges. International Journal of Research in Business and Social Science (2147- 4478), 10(5), 253–260. https://doi.org/10.20525/IJRBS.V10I5.1262
Agus, R. N., & Oktaviyanthi, R. (2023). Worksheet graphing quadratics berbantuan phet simulation untuk optimalisasi mathematical visual thinking mahasiswa. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(2), 2166–2180. https://doi.org/10.24127/AJPM.V12I2.6908
Alam, A., & Mohanty, A. (2024). Unveiling the complexities of ‘abstract algebra’ in university mathematics education (ume): Fostering ‘conceptualization and understanding’ through advanced pedagogical approaches. Cogent Education, 11(1). https://doi.org/10.1080/2331186X.2024.2355400
Albert, C. N., Mihai, M., & Mudure-Iacob, I. (2022). Visual thinking strategies theory and applied areas of insertion. Sustainability 2022, Vol. 14, Page 7195, 14(12), 7195. https://doi.org/10.3390/SU14127195
Arnheim, Rudolf. (2020). Visual thinking. https://www.ucpress.edu/books/visual-thinking/paper
Artasari, A., Oktaviyanthi, R., Zahwatuzzukhrufiah, & Delvianingsih, N. (2024). Optimizing algebraic thinking using the area model algebra worksheet based on phet interactive simulation. Plusminus: Jurnal Pendidikan Matematika, 4(2), 241–254. https://doi.org/10.31980/PLUSMINUS.V4I2.1465
Bernadetha Rizki Kaize, Ni Nyoman Rediani, & Syahfitriani Br Ginting. (2024). Optimizing students’ critical thinking and numeracy literacy skills through task-based learning: An experimental study. Indonesian Journal of Educational Development (IJED), 5(2), 183–193. https://doi.org/10.59672/ijed.v5i2.4049
Bronkhorst, H., Roorda, G., Suhre, C., & Goedhart, M. (2021). Student development in logical reasoning: results of an intervention guiding students through different modes of visual and formal representation. Canadian Journal of Science, Mathematics and Technology Education, 21(2), 378–399. https://doi.org/10.1007/S42330-021-00148-4/FIGURES/10
Clark, V. L. P., & Ivankova, N. V. (2016). Mixed methods research: A guide to the field. Mixed Methods Research: A Guide to the Field. https://doi.org/10.4135/9781483398341
Coessens, K., François, K., & Van Bendegem, J. P. (2021). Understanding without words: Visual representations in math, science and art. Production, Presentation, and Acceleration of Educational Research: Could Less Be More?, 141–156. https://doi.org/10.1007/978-981-16-3017-0_9
Creswell, W.John; Creswell, J. D. (2022). Research design : Qualitative, quantitative, and mixed methods approaches. SAGE Publications, 283.
Del Cerro Velázquez, F., & Méndez, G. M. (2021). Application in augmented reality for learning mathematical functions: A study for the development of spatial intelligence in secondary education students. Mathematics 2021, Vol. 9, Page 369, 9(4), 369. https://doi.org/10.3390/MATH9040369
Dorel, L. (2024). The relationship between visual and abstract comprehension in spatial geometry, and its importance to developing spatial perception and vision. International Journal for Technology in Mathematics Education, 30(4), 219–226. https://doi.org/10.1564/TME_V30.4.3
Downton, A., & Livy, S. (2022). Insights into students’ geometric reasoning relating to prisms. International Journal of Science and Mathematics Education, 20(7), 1543–1571. https://doi.org/10.1007/S10763-021-10219-5/TABLES/6
Dunstan, J., & Cole, S. (2021). Flexible mindsets in schools: Channelling brain power for critical thinking, complex problem-solving and creativity. Flexible Mindsets in Schools: Channelling Brain Power for Critical Thinking, Complex Problem-Solving and Creativity, 1–174. https://doi.org/10.4324/9781003204817/FLEXIBLE-MINDSETS-SCHOOLS-JULIE-DUNSTAN-SUSANNAH-COLE/RIGHTS-AND-PERMISSIONS
Dwikamayuda, D. M., Ari, I. A. N. M. D., Ekawati, N., Nitiasih, P. K., Riastini, P. N., & Sudatha, I. G. W. (2024). Empowering education: Integrating critical pedagogy into transformative teaching strategies. Indonesian Journal of Educational Development (IJED), 5(2), 230–242. https://doi.org/10.59672/ijed.v5i2.3823
Elsayed, S. A., & Al-Najrani, H. I. (2021). Effectiveness of the augmented reality on improving the visual thinking in mathematics and academic motivation for middle school students. Eurasia Journal of Mathematics, Science and Technology Education, 17(8), em1991. https://doi.org/10.29333/EJMSTE/11069
Flick, U. (2018). Doing triangulation and mixed methods. Doing Triangulation and Mixed Methods. https://doi.org/10.4135/9781529716634
García-García, J., & Dolores-Flores, C. (2021). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33(1), 1–22. https://doi.org/10.1007/S13394-019-00286-X/METRICS
Geçici, M. E., & Türnüklü, E. (2021). Visual reasoning in mathematics education: A conceptual framework proposal. Acta Didactica Napocensia, 14(1), 115–126. https://doi.org/10.24193/adn.14.1.9
Gligorea, I., Cioca, M., Oancea, R., Gorski, A. T., Gorski, H., & Tudorache, P. (2023). Adaptive learning using artificial intelligence in e-learning: A literature review. Education Sciences 2023, Vol. 13, Page 1216, 13(12), 1216. https://doi.org/10.3390/EDUCSCI13121216
González-Gómez, B., Colomé, À., & Núñez-Peña, M. I. (2024). Math anxiety and attention: Biased orienting to math symbols or less efficient attentional control? Current Psychology, 43(7), 6533–6548. https://doi.org/10.1007/S12144-023-04828-2/FIGURES/3
Gray, M. E., & Holyoak, K. J. (2021). Teaching by analogy: From theory to practice. Mind, Brain, and Education, 15(3), 250–263. https://doi.org/10.1111/MBE.12288
Halkiopoulos, C., & Gkintoni, E. (2024). Leveraging ai in e-learning: Personalized learning and adaptive assessment through cognitive neuropsychology a systematic analysis. Electronics 2024, Vol. 13, Page 3762, 13(18), 3762. https://doi.org/10.3390/ELECTRONICS13183762
Hussein, Y. F., & Csíkos, C. (2023). The effect of teaching conceptual knowledge on students’ achievement, anxiety about, and attitude toward mathematics. Eurasia Journal of Mathematics, Science and Technology Education, 19(2), em2226. https://doi.org/10.29333/EJMSTE/12938
Kim, Y. S., & Park, J. A. (2021). Design thinking in the framework of visual thinking and characterization of service design ideation methods using visual reasoning model. The Design Journal, 24(6), 1–23. https://doi.org/10.1080/14606925.2021.1977497
Liang, C. P., & She, H. C. (2023). Investigate the effectiveness of single and multiple representational scaffolds on mathematics problem solving: evidence from eye movements. Interactive Learning Environments, 31(6), 3882–3897. https://doi.org/10.1080/10494820.2021.1943692
Liben, L. S. (2022). Conceptual issues in the development of spatial cognition. Spatial Cognition, 167–194. https://doi.org/10.4324/9781315785462-10/CONCEPTUAL-ISSUES-DEVELOPMENT-SPATIAL-COGNITION-LYNN-LIBEN
Lochmiller, C. R. (2021). Conducting thematic analysis with qualitative data. The Qualitative Report, 26(6), 2029–2044. https://doi.org/10.46743/2160-3715/2021.5008
Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21. https://doi.org/10.46328/IJEMST.1111
Mainali, B. (2022). Investigating pre-service teachers’ beliefs towards mathematics: A case study. European Journal of Science and Mathematics Education, 10(4), 412–435. https://doi.org/10.30935/SCIMATH/12103
Medina Herrera, L. M., Juárez Ordóñez, S., & Ruiz-Loza, S. (2024). Enhancing mathematical education with spatial visualization tools. Frontiers in Education, 9, 1229126. https://doi.org/10.3389/FEDUC.2024.1229126/BIBTEX
Ng, D. T. K., Leung, J. K. L., Su, J., Ng, R. C. W., & Chu, S. K. W. (2023). Teachers’ AI digital competencies and twenty-first century skills in the post-pandemic world. Educational Technology Research and Development, 71(1), 137–161. https://doi.org/10.1007/S11423-023-10203-6/FIGURES/2
Nilimaa, J. (2023). New examination approach for real-world creativity and problem-solving skills in mathematics. Trends in Higher Education 2023, Vol. 2, Pages 477-495, 2(3), 477–495. https://doi.org/10.3390/HIGHEREDU2030028
Nutov, L. (2021). Integrating visual arts into the mathematics curriculum: The case of pre-service teachers. Teaching and Teacher Education, 97, 103218. https://doi.org/10.1016/J.TATE.2020.103218
Oktaviyanthi, R., & Agus, R. N. (2023). Evaluating graphing quadratic worksheet on visual thinking classification: A confirmatory analysis. Infinity Journal, 12(2), 207–224. https://doi.org/10.22460/INFINITY.V12I2.P207-224
Panduwinata, L. F., Wulandari, R. N. A., Puspasari, D., Puspasari, D., & Wati, A. P. (2025). Developing a case-based e-book for office communication: Enhancing critical thinking and practical skills. Indonesian Journal of Educational Development (IJED), 6(2), 561–574. https://doi.org/10.59672/ijed.v6i2.4724
Purnadewi, G. A. A., & Widana, I. W. (2023). Improving students’ science numeration capability through the implementation of the PBL model based on local wisdom. Indonesian Journal of Educational Development (IJED), 4(3), 307-317. https://doi.org/10.59672/ijed.v4i3.3252
Reed, S. K. (2021). Thinking visually. Thinking Visually. https://doi.org/10.4324/9781003213253
Sholahudin, U., & Oktaviyanthi, R. (2023). The trigonometric adaptive worksheet performance in optimizing trigonometric thinking of prospective mathematics teacher: Single subject research. Jurnal Didaktik Matematika, 10(2), 250–265. https://doi.org/10.24815/JDM.V10I2.33216
Siregar, R. S. D., & Amir, M. T. . (2025). Factors influencing low motivation of PKWU teachers and organizational climate in the participation of MGMP. Indonesian Journal of Educational Development (IJED), 6(1), 124-134. https://doi.org/10.59672/ijed.v6i1.4573
Squires, V. (2023). Thematic Analysis. In J. M. , T. S. , W. K. D. Okoko (Ed.), Varieties of qualitative research methods (pp. 463–468). Springer, Cham. https://doi.org/10.1007/978-3-031-04394-9_72
Sumanik, N. B., Arismunandar, A., Nurhikmah, N., & Indrawati, N. (2024). Green chemistry learning transformation: Youtube integrated interactive video to improve critical thinking skills. Indonesian Journal of Educational Development (IJED), 5(3), 346–357. https://doi.org/10.59672/ijed.v5i3.4218
Supriadi, N., Jamaluddin Z, W., & Suherman, S. (2024). The role of learning anxiety and mathematical reasoning as predictor of promoting learning motivation: The mediating role of mathematical problem solving. Thinking Skills and Creativity, 52, 101497. https://doi.org/10.1016/J.TSC.2024.101497
Svitek, S., Annuš, N., & Filip, F. (2022). Math can be visual teaching and understanding arithmetical functions through visualization. Mathematics 2022, Vol. 10, Page 2656, 10(15), 2656. https://doi.org/10.3390/MATH10152656
Swift, A. (2022). Being creative with resources in qualitative research. The SAGE Handbook of Qualitative Research Design, 290–306. https://doi.org/10.4135/9781529770278.N19
Thornberg, R., Forsberg, C., Hammar Chiriac, E., & Bjereld, Y. (2022). Teacher student relationship quality and student engagement: A sequential explanatory mixed-methods study. Research Papers in Education, 37(6), 840–859. https://doi.org/10.1080/02671522.2020.1864772
Ünal, Z. E., Ala, A. M., Kartal, G., Özel, S., & Geary, D. C. (2023). Visual and symbolic representations as components of algebraic reasoning. Journal of Numerical Cognition, 9(2), 327–345. https://doi.org/10.5964/JNC.11151
Uttal, D. H., McKee, K., Simms, N., Hegarty, M., & Newcombe, N. S. (2024). How can we best assess spatial skills? practical and conceptual challenges. Journal of Intelligence 2024, Vol. 12, Page 8, 12(1), 8. https://doi.org/10.3390/JINTELLIGENCE12010008
Vale, I., & Barbosa, A. (2023). Visualization: A pathway to mathematical challenging tasks. 283–306. https://doi.org/10.1007/978-3-031-18868-8_15
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/SUPPL_FILE/SJ-DOCX-3-TES-10.1177_0888406421996070.DOCX
Weingarden, M., & Heyd-Metzuyanim, E. (2024). Fostering pre-service teachers’ attention to mathematical objects: The realization tree mediator as a teaching representation. Journal of Mathematics Teacher Education, 1–27. https://doi.org/10.1007/S10857-024-09622-W/METRICS
Widana, I. W. & Ratnaya, I. G. (2021). Relationship between divergent thinking and digital literacy on teacher ability to develop HOTS assessment. Journal of Educational Research and Evaluation, 5(4), 516-524. https://doi.org/10.23887/jere.v5i4.35128
Widana, I. W., & Laksitasari, B. D. (2023). Improving students' learning outcomes on circle equation material using GeoGebra software. Indonesian Journal of Educational Development (IJED), 4(1), 32-39. https://doi.org/10.59672/ijed.v4i1.2792
Wilkie, K. J. (2021). Seeing quadratics in a new light: Secondary mathematics pre-service teachers’ creation of figural growing patterns. Educational Studies in Mathematics, 106(1), 91–116. https://doi.org/10.1007/S10649-020-09997-6/METRICS
Yao, Y., Hwang, S., & Cai, J. (2021). Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving. ZDM - Mathematics Education, 53(4), 937–949. https://doi.org/10.1007/S11858-021-01277-8/METRICS
Yeh, Y. C., Chiang, J. L., Chang, S. L., Ting, Y. S., Wang, C. M., & Peng, Y. Y. (2024). Integrating visible thinking and design thinking strategies to improve creativity and growth mindsets. Educational Technology Research and Development, 1–23. https://doi.org/10.1007/S11423-024-10429-Y/METRICS
Žakelj, A., & Klančar, A. (2022). The role of visual representations in geometry learning. European Journal of Educational Research, 11(3), 1393–1411. https://doi.org/10.12973/EU-JER.11.3.1393
Zulu, M. W., & Mudaly, V. (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), em2299. https://doi.org/10.29333/EJMSTE/13344
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