Students’ Mathematical Reasoning
A Systematic Literature Review with a Focus on Metaphorical Thinking-Based Learning Approaches
DOI:
https://doi.org/10.33830/ijrse.v8i1.14309Keywords:
mathematical reasoning, metaphorical thinking, mathematics education, instructional models, conceptual metaphorsAbstract
Mathematical reasoning is a fundamental component of meaningful mathematics learning; however, research on instructional approaches that systematically support its development remains fragmented. In particular, studies on mathematical reasoning and metaphorical thinking have largely evolved independently, resulting in limited integrative insights. This systematic literature review (SLR) aims to synthesize research trends on students’ mathematical reasoning over the past decade and to examine the role of metaphorical-thinking-based learning in supporting its development. Following the PRISMA 2020 framework, a systematic search of the Scopus and ERIC databases identified 36 peer-reviewed journal articles published between 2017 and 2025. These studies were analyzed using reflexive thematic analysis, focusing on research trends, instructional implementations, metaphor types, learning models, and reported effects on mathematical reasoning. The findings indicate a shift toward a multidimensional view of mathematical reasoning encompassing cognitive, representational, social, and contextual aspects. Metaphorical thinking predominantly functions as a cognitive–linguistic approach embedded within diverse instructional models. Conceptual and embodied metaphors are most prevalent, supporting reasoning through cognitive bridging, enriched mental representation, and increased engagement. Nevertheless, gaps remain regarding explicit interventions, longitudinal evidence, and comparative analyses of metaphor types.
References
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Alcaraz-Carrión, D., Alibali, M. W., & Valenzuela, J. (2022). Adding and subtracting by hand: Metaphorical representations of arithmetic in spontaneous co-speech gestures. Acta Psychologica, 228(April). https://doi.org/10.1016/j.actpsy.2022.103624
Bakar, M. T., Suryadi, D., Darhim, Tonra, W. S., & Noto, M. S. (2018). The association between conceptual understanding and reasoning ability in mathematics: An analysis of DNR-based instruction models. Journal of Physics: Conference Series, 1088, 0–5. https://doi.org/10.1088/1742-6596/1088/1/012107
Braun, V., & Clarke, V. (2022). Thematic analysis. APA Handbook of Research Methods in Psychology, Vol 2: Research Designs: Quantitative, Qualitative, Neuropsychological, and Biological., 2, 57–71. https://doi.org/10.1037/13620-004
Cervantes-Barraza, J. A., & Araujo, A. A. (2023). Design of interactive mathematical tasks that make up the reasoning and the Ethnomathematics program. Journal on Mathematics Education, 14(3), 469–482. https://doi.org/10.22342/jme.v14i3.pp469-482
Connett, D. F. (2018). A guide to qualitative meta-synthesis. New York, NY, USA:: Routledge.
Falani, I., Supriyati, Y., Marzal, J., Iriani, D., & Simatupang, G. M. (2023). Metaphor Studies Investigation in Mathematics Education: A Systematic Review. Indonesian Journal of Mathematics Education, 6(1), 40–62. https://doi.org/10.31002/ijome.v6i1.554
Fraihat, M. A. K., Khasawneh, A. A., & Al-Barakat, A. A. (2022). The effect of situated learning environment in enhancing mathematical reasoning and proof among tenth grade students. Eurasia Journal of Mathematics, Science and Technology Education, 18(6). https://doi.org/10.29333/ejmste/12088
Ghifari, M. (2025). Systematic Literature Review: The Metaphorical Thinking Approach in Mathematics in Indonesia from 2020 to 2025. Lambda: Jurnal Ilmiah Pendidikan MIPA Dan Aplikasinya, 5(2), 536–546. https://doi.org/10.58218/lambda.v5i2.1428
Giberti, C., Santi, G., & Spagnolo, C. (2023). The role of metaphors in interpreting students’ difficulties in operating with percentages: A mixed method study based on large scale assessment. European Journal of Science and Mathematics Education, 11(2), 297–321. https://doi.org/10.30935/scimath/12642
Hamidah, D., Susiswo, Susanto, H., Hakim, Z. A., & Osman, S. (2025). Exploring the Mathematical Reasoning Skills Across Different Levels of Prospective Mathematics Teachers: A Mixed-Methods Investigation. Mathematics Education Journal, 19(2), 389–412. https://doi.org/10.22342/mej.v19i2.pp389-412
Hansen, E. K. S., & Naalsund, M. (2025). Toward an analytical model for noticing interaction patterns in creative collaborative mathematical reasoning. Mathematical Thinking and Learning, 00(00), 1–19. https://doi.org/10.1080/10986065.2025.2452222
Hasanah, U., Putrawangsa, S., Purwanta, E., Setiawati, F. A., & Purnomo, Y. W. (2024). Primary Student Spatial Reasoning Abilities: Progression and Challenges. Mathematics Education Journal, 18(3), 329–348. https://doi.org/10.22342/jpm.v18i3.pp329-348
Hendriana, H., Eti Rohaeti, E., & Hidayat, W. (2017). Metaphorical thinking learning and junior high school teachers’ mathematical questioning ability. Journal on Mathematics Education, 8(1), 55–64. https://doi.org/10.22342/jme.8.1.3614.55-64
Hicks, M. D. (2024). “I’ll just try to mimic that”: an exploration of students’ analogical structure creation in abstract algebra. Educational Studies in Mathematics, 117(2), 303–327. https://doi.org/10.1007/s10649-024-10345-1
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/s10649-017-9761-8
Kertil, M. (2020). Covariational reasoning of prospective mathematics teachers: How do dynamic animations affect? Turkish Journal of Computer and Mathematics Education, 11(2), 312–342. https://doi.org/10.16949/turkbilmat.652481
Kursius, C. M., Muttaqien, A., & Istadi, I. (2025). Metaphorical Thinking CoRelEx Spatial Students on Trigonometry Word Problem Solving Ability. Jurnal Riset Pendidikan Matematika, 12(1), 53–66. https://doi.org/10.21831/jrpm.v12i1.83173
Martins, M., da Ponte, J. P., & Mata-Pereira, J. (2023). Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education. Eurasia Journal of Mathematics, Science and Technology Education, 19(5). https://doi.org/10.29333/EJMSTE/13127
Masfingatin, T., Murtafiah, W., & Maharani, S. (2020). Exploration of Creative Mathematical Reasoning in Solving Geometric Problems. Mathematics Education Journal, 14(2), 155–168. https://doi.org/10.22342/jpm.14.2.7654.155-168
Medová, J., Bulková, K. O., & Čeretková, S. (2020). Relations between generalization, reasoning and combinatorial thinking in solving mathematical open-ended problems within mathematical contest. Mathematics, 8(12), 1–20. https://doi.org/10.3390/math8122257
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics.
Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic Analysis: Striving to Meet the Trustworthiness Criteria. International Journal of Qualitative Methods, 16(1), 1–13. https://doi.org/10.1177/1609406917733847
Pantaleon, K. V., Tamur, M., & Men, F. E. (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
Pantsar, M. (2018). Early numerical cognition and mathematical processes. Theoria (Spain), 33(2), 285–304. https://doi.org/10.1387/theoria.17682
Purwasi, L. A., & Fitriyana, N. (2021). The enhancement of mathematical reasoning and problem solving ability through metaphorical thinking approach. Journal of Physics: Conference Series, 1731(1). https://doi.org/10.1088/1742-6596/1731/1/012040
Putri, B. N., Amirudin, & Pratiwi, D. D. (2022). Penerapan Methaporical Thinking : Kemampuan Matematis Peserta Didik. Jurnal Pendidikan Matematika Dan Sains, 10(1), 15–21.
Scheiner, T., Godino, J. D., Montes, M. A., Pino-Fan, L. R., & Climent, N. (2022). On metaphors in thinking about preparing mathematics for teaching: In memory of José (“Pepe”) Carrillo Yáñez (1959–2021). Educational Studies in Mathematics, 111(2), 253–270. https://doi.org/10.1007/s10649-022-10154-4
Schindler, M., Hußmann, S., Nilsson, P., & Bakker, A. (2017). Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Mathematics Education Research Journal, 29(4), 471–492. https://doi.org/10.1007/s13394-017-0202-x
Setiani, C., Waluya, S. B., & Wardono. (2018). Analysis of mathematical literacy ability based on self-efficacy in model eliciting activities using metaphorical thinking approach. Journal of Physics: Conference Series, 983(1). https://doi.org/10.1088/1742-6596/983/1/012139
Siregar, G. M. A., Wahyudin, & Herman, T. (2025). Case study in a grounded theory perspective: Students’ reasoning abilities in Lithner’s framework across self-regulated. Infinity Journal, 14(1), 259–282. https://doi.org/10.22460/infinity.v14i1.p259-282
Zhang, W., Li, L., & Disney, L. (2025). “Asking questions is the key”: Chinese kindergarten teachers support children’s mathematics concept learning and spatial reasoning through a Conceptual PlayWorld approach. Mathematics Education Research Journal, 0123456789. https://doi.org/10.1007/s13394-025-00530-7
Adelia, V., Putri, R. I. I., Zulkardi, & Doorman, M. (2025). The development of web-based learning environment to enhance students’ numeracy and reasoning. Journal on Mathematics Education, 16(2), 651–670. https://doi.org/10.22342/jme.v16i2.pp651-670
Alcaraz-Carrión, D., Alibali, M. W., & Valenzuela, J. (2022). Adding and subtracting by hand: Metaphorical representations of arithmetic in spontaneous co-speech gestures. Acta Psychologica, 228(April). https://doi.org/10.1016/j.actpsy.2022.103624
Bakar, M. T., Suryadi, D., Darhim, Tonra, W. S., & Noto, M. S. (2018). The association between conceptual understanding and reasoning ability in mathematics: An analysis of DNR-based instruction models. Journal of Physics: Conference Series, 1088, 0–5. https://doi.org/10.1088/1742-6596/1088/1/012107
Braun, V., & Clarke, V. (2022). Thematic analysis. APA Handbook of Research Methods in Psychology, Vol 2: Research Designs: Quantitative, Qualitative, Neuropsychological, and Biological., 2, 57–71. https://doi.org/10.1037/13620-004
Cervantes-Barraza, J. A., & Araujo, A. A. (2023). Design of interactive mathematical tasks that make up the reasoning and the Ethnomathematics program. Journal on Mathematics Education, 14(3), 469–482. https://doi.org/10.22342/jme.v14i3.pp469-482
Connett, D. F. (2018). A guide to qualitative meta-synthesis. New York, NY, USA:: Routledge.
Falani, I., Supriyati, Y., Marzal, J., Iriani, D., & Simatupang, G. M. (2023). Metaphor Studies Investigation in Mathematics Education: A Systematic Review. Indonesian Journal of Mathematics Education, 6(1), 40–62. https://doi.org/10.31002/ijome.v6i1.554
Fraihat, M. A. K., Khasawneh, A. A., & Al-Barakat, A. A. (2022). The effect of situated learning environment in enhancing mathematical reasoning and proof among tenth grade students. Eurasia Journal of Mathematics, Science and Technology Education, 18(6). https://doi.org/10.29333/ejmste/12088
Ghifari, M. (2025). Systematic Literature Review: The Metaphorical Thinking Approach in Mathematics in Indonesia from 2020 to 2025. Lambda: Jurnal Ilmiah Pendidikan MIPA Dan Aplikasinya, 5(2), 536–546. https://doi.org/10.58218/lambda.v5i2.1428
Giberti, C., Santi, G., & Spagnolo, C. (2023). The role of metaphors in interpreting students’ difficulties in operating with percentages: A mixed method study based on large scale assessment. European Journal of Science and Mathematics Education, 11(2), 297–321. https://doi.org/10.30935/scimath/12642
Hamidah, D., Susiswo, Susanto, H., Hakim, Z. A., & Osman, S. (2025). Exploring the Mathematical Reasoning Skills Across Different Levels of Prospective Mathematics Teachers: A Mixed-Methods Investigation. Mathematics Education Journal, 19(2), 389–412. https://doi.org/10.22342/mej.v19i2.pp389-412
Hansen, E. K. S., & Naalsund, M. (2025). Toward an analytical model for noticing interaction patterns in creative collaborative mathematical reasoning. Mathematical Thinking and Learning, 00(00), 1–19. https://doi.org/10.1080/10986065.2025.2452222
Hasanah, U., Putrawangsa, S., Purwanta, E., Setiawati, F. A., & Purnomo, Y. W. (2024). Primary Student Spatial Reasoning Abilities: Progression and Challenges. Mathematics Education Journal, 18(3), 329–348. https://doi.org/10.22342/jpm.v18i3.pp329-348
Hendriana, H., Eti Rohaeti, E., & Hidayat, W. (2017). Metaphorical thinking learning and junior high school teachers’ mathematical questioning ability. Journal on Mathematics Education, 8(1), 55–64. https://doi.org/10.22342/jme.8.1.3614.55-64
Hicks, M. D. (2024). “I’ll just try to mimic that”: an exploration of students’ analogical structure creation in abstract algebra. Educational Studies in Mathematics, 117(2), 303–327. https://doi.org/10.1007/s10649-024-10345-1
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/s10649-017-9761-8
Kertil, M. (2020). Covariational reasoning of prospective mathematics teachers: How do dynamic animations affect? Turkish Journal of Computer and Mathematics Education, 11(2), 312–342. https://doi.org/10.16949/turkbilmat.652481
Kursius, C. M., Muttaqien, A., & Istadi, I. (2025). Metaphorical Thinking CoRelEx Spatial Students on Trigonometry Word Problem Solving Ability. Jurnal Riset Pendidikan Matematika, 12(1), 53–66. https://doi.org/10.21831/jrpm.v12i1.83173
Martins, M., da Ponte, J. P., & Mata-Pereira, J. (2023). Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education. Eurasia Journal of Mathematics, Science and Technology Education, 19(5). https://doi.org/10.29333/EJMSTE/13127
Masfingatin, T., Murtafiah, W., & Maharani, S. (2020). Exploration of Creative Mathematical Reasoning in Solving Geometric Problems. Mathematics Education Journal, 14(2), 155–168. https://doi.org/10.22342/jpm.14.2.7654.155-168
Medová, J., Bulková, K. O., & Čeretková, S. (2020). Relations between generalization, reasoning and combinatorial thinking in solving mathematical open-ended problems within mathematical contest. Mathematics, 8(12), 1–20. https://doi.org/10.3390/math8122257
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics.
Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic Analysis: Striving to Meet the Trustworthiness Criteria. International Journal of Qualitative Methods, 16(1), 1–13. https://doi.org/10.1177/1609406917733847
Pantaleon, K. V., Tamur, M., & Men, F. E. (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
Pantsar, M. (2018). Early numerical cognition and mathematical processes. Theoria (Spain), 33(2), 285–304. https://doi.org/10.1387/theoria.17682
Purwasi, L. A., & Fitriyana, N. (2021). The enhancement of mathematical reasoning and problem solving ability through metaphorical thinking approach. Journal of Physics: Conference Series, 1731(1). https://doi.org/10.1088/1742-6596/1731/1/012040
Putri, B. N., Amirudin, & Pratiwi, D. D. (2022). Penerapan Methaporical Thinking : Kemampuan Matematis Peserta Didik. Jurnal Pendidikan Matematika Dan Sains, 10(1), 15–21.
Scheiner, T., Godino, J. D., Montes, M. A., Pino-Fan, L. R., & Climent, N. (2022). On metaphors in thinking about preparing mathematics for teaching: In memory of José (“Pepe”) Carrillo Yáñez (1959–2021). Educational Studies in Mathematics, 111(2), 253–270. https://doi.org/10.1007/s10649-022-10154-4
Schindler, M., Hußmann, S., Nilsson, P., & Bakker, A. (2017). Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Mathematics Education Research Journal, 29(4), 471–492. https://doi.org/10.1007/s13394-017-0202-x
Setiani, C., Waluya, S. B., & Wardono. (2018). Analysis of mathematical literacy ability based on self-efficacy in model eliciting activities using metaphorical thinking approach. Journal of Physics: Conference Series, 983(1). https://doi.org/10.1088/1742-6596/983/1/012139
Siregar, G. M. A., Wahyudin, & Herman, T. (2025). Case study in a grounded theory perspective: Students’ reasoning abilities in Lithner’s framework across self-regulated. Infinity Journal, 14(1), 259–282. https://doi.org/10.22460/infinity.v14i1.p259-282
Zhang, W., Li, L., & Disney, L. (2025). “Asking questions is the key”: Chinese kindergarten teachers support children’s mathematics concept learning and spatial reasoning through a Conceptual PlayWorld approach. Mathematics Education Research Journal, 0123456789. https://doi.org/10.1007/s13394-025-00530-7
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