Students’ Belief About Mathematics Through Metaphor
DOI:
https://doi.org/10.48017/dj.v11i1.3492Keywords:
phenomenological approach, epistemological beliefs, metaphor, qualitative studyAbstract
This study explored how junior high school students in Abra, Philippines, conceptualize mathematics through metaphors, revealing a developmental progression in their mathematical beliefs. Researchers employed a qualitative, phenomenological approach, analyzing visual and written metaphors from 20 students in Grade 7 to 10. Students were prompted to draw and reflect on what mathematics meant to them, generating a wide array of metaphors. Analysis revealed six thematic metaphor categories: mathematics as a journey, life, tool, value, history and tangible object. Younger students (Grade 7) commonly used playful and experiential metaphors such as game and adventure, indicating an identity-driven view of math. Grade 8 students introduced abstract and functional metaphors like dream and calculator reflecting transitional thinking. By Grade 9, students leaned toward concrete, object-based metaphor such as ruler and pyramid denoting applied understanding. Grade 10 students expressed more symbolic and reflective metaphors like river, trophy and ancient Greek suggesting deeper conceptual maturity and cultural awareness. The recurring metaphor of life across all grade levels signaled students’ perception of mathematics as essential and ever-present. These metaphor choices highlight how age, experience, and cognitive development shape students’ epistemological beliefs about mathematics. Findings suggest that metaphors are powerful cognitive tools, providing insight into learners’ mathematical identities and experiences. Educators can use these insights to inform more responsive, developmentally appropriate teaching strategies.
Metrics
References
Adeshola, I., & Adepoju, A. P. (2024). The opportunities and challenges of ChatGPT in education. Interactive Learning Environments, 32(10), 6159-6172. https://doi.org/10.1080/10494820.2023.2253858
Akpalu, R., Boateng, P. A., Ayisi, E., & Owusu, J. (2025). Students’ perceptions of mathematics and the impact on their achievement among senior high school students in Ghana. International Journal of Research and Innovation in Social Science, 9(1), 3829-3840. https://dx.doi.org/10.47772/IJRISS.2025.9010299
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), 2355400. https://doi.org/10.1080/2331186X.2024.2355400
Albay, E. M., & Aquino, R. L. (2024). Utilizing flipped classroom and the first principles of effective instruction in teaching finite geometry. International Journal of Instruction, 17(1), 177–192. https://doi.org/10.29333/iji.2024.17110a
Albay, E. M., Aquino, R. L., Alambra, R. V. E., Eisma, D. V., & Quiambao, R. D. (2024). Assessing graduates’ attributes and job performance for program curriculum enhancement. International Journal of Evaluation and Research in Education (IJERE), 13(4), 2689-2697. DOI: 10.11591/ijere.v13i4.27090
Albay, E. M., & Eisma, D. V. (2025). Using design thinking for developing pre-service teachers’ creativity in designing teaching plans to promote interactive learning in mathematics. Learning and Instruction, 96, 102070. https://doi.org/10.1016/j.learninstruc.2024.102070
Asenova, M. (2024). Is theoretical topic-specific research “old fashioned”? An epistemological inquiry about the ontological creativity of Mathematics Education Research. Mathematics Education Research Journal, 36(4), 849-870. https://doi.org/10.1007/s13394-023-00471-z
Atkins, K., Dougan, B. M., Dromgold-Sermen, M. S., Potter, H., Sathy, V., & Panter, A. T. (2020). “Looking at myself in the future”: how mentoring shapes scientific identity for STEM students from underrepresented groups. International Journal of STEM Education, 7, 1-15. https://doi.org/10.1186/s40594-020-00242-3
Barete, M. G., & Taja-on, E. P. (2024). Students’ perception in learning the course mathematics in the modern world: A qualitative study. East Asian Journal of Multidisciplinary Research, 3(7), 2977-2988. https://doi.org/10.55927/eajmr.v3i7.10071
Brandt, N. D., Lechner, C. M., Tetzner, J., & Rammstedt, B. (2020). Personality, cognitive ability, and academic performance: Differential associations across school subjects and school tracks. Journal of Personality, 88(2), 249-265. https://doi.org/10.1111/jopy.12482
Chan, K. K., & Reynolds, B. L. (2022). Metaphoric beliefs of students engaged in dynamic mathematics lessons. Eurasia Journal of Mathematics, Science and Technology Education, 18(10), em2169. https://doi.org/10.29333/ejmste/12463
Demirbilek, N., & Korkmaz, C. (2021). Study concept as a metaphor from the lenses of university students. African Educational Research Journal, 9(1), 227-236. http://www.netjournals.org/aer_index.html
Gadanidis, G., Hughes, J. M., Namukasa, I., & Scucuglia, R. (2024). Computer programming puzzles, mathematics education, and the culture of learning. In Ways of Thinking in STEM-based Problem Solving (pp. 218-234). Routledge. https://www.taylorfrancis.com/chapters/edit/10.4324/9781003404989-16
Gibbs Jr, R. W., & Siman, J. (2021). How we resist metaphors. Language and Cognition, 13(4), 670-692. https://doi.org/10.1017/langcog.2021.18
Harefa, D. (2023). The relationship between students' interest in learning and mathematics learning outcomes. Afore: Jurnal Pendidikan Matematika, 2(2), 1-11. https://doi.org/10.57094/afore.v2i2.1054
Haser, Ç., Arslan, O., & Çelikdemir, K. (2024). Who is a mathematics teacher and what does a mathematics teacher do?. International Journal of Science and Mathematics Education, 22(2), 283-305. https://doi.org/10.1007/s10763-023-10378-7
Hill, J. L., Kern, M. L., Seah, W. T., & van Driel, J. (2020). Feeling good and functioning well in mathematics education: Exploring students’ conceptions of mathematical well-being and values. ECNU Review of Education, 4(2), 349-375. https://doi.org/10.1177/2096531120928084
Ingram, N., & Meaney, T. (2021). “My parents are pretty pleased with my math’s”: students’ navigation of identity stories about mathematics. Research in Mathematics Education, 24(1), 51-68. https://doi.org/10.1080/14794802.2021.1938190
Kaphesi, E. (2014). Third-year university mathematics education students’ metaphorical understanding of mathematics teaching and learning. African Journal of Research in Mathematics, Science and Technology Education, 18(3), 276-286. https://doi.org/10.1080/10288457.2014.962729
Katranci, Y., Kiral, B., & Kedikli, D. (2021). Pre-service high school mathematics teachers’ perceptions about mathematics and mathematics teachers: A metaphorical approach. In W. B. James, C. Cobanoglu, & M. Cavusoglu (Eds.), Advances in global education and research (Vol. 4, pp. 1–14). USF M3 Publishing. https://www.doi.org/10.5038/9781955833042
Khadpe, P., Krishna, R., Fei-Fei, L., Hancock, J. T., & Bernstein, M. S. (2020). Conceptual metaphors impact perceptions of human-AI collaboration. Proceedings of the ACM on Human-Computer Interaction, 4(CSCW2), 1-26. https://doi.org/10.1145/341523
Lutovac, S. (2020). How failure shapes teacher identities: Pre-service elementary school and mathematics teachers narrated possible selves. Teaching and Teacher education, 94, 103120. https://doi.org/10.1016/j.tate.2020.103120
Men, F. E., Pantaleon, K. V., & Tamur, M. (2024). Metaphorical thinking intervention in learning and its impact on mathematical reasoning ability. Mosharafa: Jurnal Pendidikan Matematika, 13(1), 29–38. https://doi.org/10.31980/mosharafa.v13i1.1973
Presto, A. C., & Menorca, E. (2023). Students metacognitive strategies in solving mathematics problems in distance learning: A phenomenological study. International Journal of Multidisciplinary: Applied Business and Education Research, 4(4), 1259-1269. http://dx.doi.org/10.11594/ijmaber.04.04.21
Russell, B. (2025). The study of mathematics. In Mysticism and logic (pp. 54-68). Routledge. https://doi.org/10.4324/9781003604990-4
Savas, G., Danisman, S., & Kacar, S. N. (2024). Metaphorical perceptions of secondary school students on new generation mathematics questions. Kulliye, 5(2), 332-346. https://doi.org/10.48139/aybukulliye.1358322
Shone, E. T., Weldemeskel, F. M., & Worku, B. N. (2023). Strategies of enhancing students’ mathematics perception and self-efficacy to improve their mathematics achievement. Cogent Education, 10(2), 2285642. https://doi.org/10.1080/2331186X.2023.2285642
Teke, B. (2023). Pre-service mathematics teachers and undergraduate mathematics students’ metaphorical perceptions of the concept of mathematics. International Journal of Scholars in Education, 6(2), 181-203. https://doi.org/10.52134/euader.1347872
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM Mathematics Education, 52, 1–16. https://doi.org/10.1007/s11858-020-01130-4 Note: I added an author to Verschaffel et al. as it was incomplete.
Vimbelo, S., & Bayaga, A. (2024). Transforming mathematics education in TVET Colleges through humanising pedagogy: An exploration of teaching approaches, student engagement, and real-life examples. IETE Journal of Education, 65(2), 139-154. https://doi.org/10.1080/09747338.2024.2324808
Walfurqan. (2022). Investigating of students’ metaphorical thinking in solving algebra problems. Journal of Mathematics Pedadogy, 1(2), 54-61. https://doi.org/10.26740/jomp.v1n2.p54-61 Note: I added volume, issue, and page numbers for Walfurqan based on the DOI provided.
Wang, Y. (2024). Examining the role of sense of belonging and formative assessment in reducing the negative impact of learning anxiety in mathematics. European Journal of Psychology of Education, 39, 431–453. https://doi.org/10.1007/s10212-023-00701-9 Note: I expanded the abbreviated journal name for Wang.
Winter, B., & Yoshimi, J. (2020). Metaphor and the philosophical implications of embodied mathematics. Frontiers in Psychology, 11, 569487. https://doi.org/10.3389/fpsyg.2020.569487
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Roselyn Villa
This work is licensed under a Creative Commons Attribution 4.0 International License.
The Diversitas Journal expresses that the articles are the sole responsibility of the Authors, who are familiar with Brazilian and international legislation.
Articles are peer-reviewed and care should be taken to warn of the possible incidence of plagiarism. However, plagiarism is an indisputable action by the authors.
The violation of copyright is a crime, provided for in article 184 of the Brazilian Penal Code: “Art. 184 Violating copyright and related rights: Penalty - detention, from 3 (three) months to 1 (one) year, or fine. § 1 If the violation consists of total or partial reproduction, for the purpose of direct or indirect profit, by any means or process, of intellectual work, interpretation, performance or phonogram, without the express authorization of the author, the performer, the producer , as the case may be, or whoever represents them: Penalty - imprisonment, from 2 (two) to 4 (four) years, and a fine. ”
