Exploring students' creative thinking processes in solving non-routine mathematical problems
DOI:
https://doi.org/10.35719/educare.v6i2.384Keywords:
Creative Thinking, Non-routine Mathematical Problems, Problem SolvingAbstract
Creative thinking is an essential 21st-century skill that plays a significant role in mathematics learning, especially when students encounter non-routine problems. Unfortunately, learning practices still predominantly use routine questions that emphasize algorithmic procedures, limiting students’ opportunities to develop their creative potential. This study aims to analyze the types of creative thinking students employ when solving non-routine mathematical problems and to describe their cognitive characteristics. Using an exploratory qualitative approach and a case study design, the research involved 108 eighth-grade students, with three representative subjects selected for analysis through written tests and in-depth interviews. The findings reveal variations in students’ creative thinking in solving non-routine math problems. Most (48.15%) are replicative, imitating solutions with limited flexibility; 37.96% are adaptive, adjusting strategies to context; and 13.89% are constructive, creating original solutions independently. This highlights the need for non-routine problems, creativity-based learning, and STEM integration to enhance flexibility, advanced creativity, and contextual analytical skills. The study contributes by demonstrating how non-routine problems and creativity-focused, STEM-integrated learning can cultivate diverse creative thinking types, enhance cognitive flexibility, and foster students’ ability to generate original, contextually informed solutions in mathematics education.
References
Ammar, M., Al-Thani, N. J., & Ahmad, Z. (2024). Role of pedagogical approaches in fostering innovation among K-12 students in STEM education. Social Sciences & Humanities Open, 9, 100839. https://doi.org/10.1016/j.ssaho.2024.100839
Bicer, A., Lee, Y., Perihan, C., Capraro, M. M., & Capraro, R. M. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics, 105(3), 457–485. https://doi.org/10.1007/s10649-020-09995-8
Borg Preca, C., Baldacchino, L., Briguglio, M., & Mangion, M. (2023). Are STEM students creative thinkers? Journal of Intelligence, 11(6), 1. https://doi.org/10.3390/jintelligence11060106
Brennen, B. S. (2025). Qualitative research methods for media studies (4th ed.). Routledge. https://doi.org/10.4324/9781003457411
Cerdán, R., Vidal-Abarca, E., Martínez, T., Gilabert, R., & Gil, L. (2009). Impact of question-answering tasks on search processes and reading comprehension. Learning and Instruction, 19(1), 13–27. https://doi.org/10.1016/j.learninstruc.2007.12.003
Chan, C. K. Y., & Lee, K. K. W. (2021). Reflection literacy: A multilevel perspective on the challenges of using reflections in higher education through a comprehensive literature review. Educational Research Review, 32, 100376. https://doi.org/10.1016/j.edurev.2020.100376
Chen, S.-J., Chen, C.-Q., & Shan, X.-F. (2024). The Effects of an Immersive Virtual-Reality-Based 3D Modeling Approach on the Creativity and Problem-Solving Tendency of Elementary School Students. Sustainability, 16(10), 4092. https://doi.org/10.3390/su16104092
Creswell, J. W., & Creswell, J. D. (2023). Research design: Qualitative, quantitative, and mixed methods approaches (6th ed.). SAGE Publications.
Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry & research design: Choosing among five approaches (4th ed.). SAGE Publications.
Donzallaz, M. C., Haaf, J. M., & Stevenson, C. E. (2023). Creative or not? Hierarchical diffusion modeling of the creative evaluation process. Journal of Experimental Psychology: Learning, Memory, and Cognition, 49(6), 849–865. https://doi.org/10.1037/xlm0001177
Ďuriš, V., Vasileva, L. N., Chumarov, S. G., & Trofimova, I. G. (2023). Development of creative thinking skills of bachelor engineers based on STEM technology. TEM Journal, 12(2), 1211–1217. https://doi.org/10.18421/TEM122-67
English, L. D. (2023). Ways of thinking in STEM-based problem solving. ZDM – Mathematics Education, 55(7), 1219–1230. https://doi.org/10.1007/s11858-023-01474-7
Evans, T., Thomas, M. O. J., & Klymchuk, S. (2021). Non-routine problem solving through the lens of self-efficacy. Higher Education Research & Development, 40(7), 1403–1420. https://doi.org/10.1080/07294360.2020.1818061
Hayashi, P., Abib, G., & Hoppen, N. (2019). Validity in qualitative research: A processual approach. The Qualitative Report, 24(1), 98–112. https://doi.org/10.46743/2160-3715/2019.3443
Kablan, Z., & Uğur, S. S. (2021). The relationship between routine and non-routine problem solving and learning styles. Educational Studies, 47(3), 328–343. https://doi.org/10.1080/03055698.2019.1701993
Kholid, M. N., Mahmudah, M. H., Ishartono, N., Putra, F. G., & Forthmann, B. (2024). Classification of students’ creative thinking for non-routine mathematical problems. Cogent Education, 11(1), 1–16. https://doi.org/10.1080/2331186X.2024.2394738
Kholil, M. (2020). Students’ creative thinking skills in solving mathematical logic problems with open-ended approaches. Journal of Physics: Conference Series, 1465(1), 1–9. https://doi.org/10.1088/1742-6596/1465/1/012044
Kholil, M., Qohar, A., Subanji, & Rahardi, R. (2024). Student’s creativity in solving problems on number operations lesson. Gradiva, 63(01). https://doi.org/10.5281/zenodo.10570616
Komarova, S., Ndungu, F., Gavazzoli, A., & Mineo, R. (2023). Group dynamics and creativity: A research with young adults in Reggio Emilia, Italy. Creativity Studies, 16(1), 297–314. https://doi.org/10.3846/cs.2023.17564
Leavy, P. (2017). Research design: Quantitative, qualitative, mixed methods, arts-based, and community-based participatory research approaches. The Guilford Press.
Leibovitch, Y. M., Beencke, A., Ellerton, P. J., McBrien, C., Robinson-Taylor, C.-L., & Brown, D. J. (2025). Teachers’ (evolving) beliefs about critical thinking education during professional learning: A multi-case study. Thinking Skills and Creativity, 56, 101725. https://doi.org/10.1016/j.tsc.2024.101725
Leikin, R. (2011). Multiple-solution tasks: From a teacher education course to teacher practice. ZDM – International Journal on Mathematics Education, 43(6), 993–1006. https://doi.org/10.1007/s11858-011-0342-5
Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM, 45(2), 183–197. https://doi.org/10.1007/s11858-012-0460-8
Leikin, R., Subotnik, R., Pitta-Pantazi, D., Singer, F. M., & Pelczer, I. (2012). Teachers’ views on creativity in mathematics education: An international survey. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-012-0472-4
Lu, X., & Kaiser, G. (2021). Can mathematical modelling work as a creativity-demanding activity? An empirical study in China. ZDM – Mathematics Education, 54, 67–81. https://doi.org/10.1007/s11858-021-01316-4
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE Publications.
Newton, L. D., & Newton, D. P. (2014). Creativity in 21st-century education. Prospects, 44(4), 575–589. https://doi.org/10.1007/s11125-014-9322-1
Nufus, H., Muhandaz, R., Hasanuddin, Nurdin, E., Ariawan, R., Fineldi, R. J., Hayati, I. R., & Situmorang, D. D. B. (2024). Analyzing the students’ mathematical creative thinking ability in terms of self-regulated learning: How do we find what we are looking for? Heliyon, 10(3), e24871. https://doi.org/10.1016/j.heliyon.2024.e24871
Öztürk, M., Akkan, Y., & Kaplan, A. (2020). Reading comprehension, mathematics self-efficacy perception, and mathematics attitude as correlates of students’ non-routine mathematics problem-solving skills in Turkey. International Journal of Mathematical Education in Science and Technology, 51(7), 1042–1058. https://doi.org/10.1080/0020739X.2019.1648893
Panglipur, I. R., Lestari, N. D. S., Yudianto, E., & Susanto. (2025). Systematic literature review: The framework of creative thinking behavior. International Journal of Innovative Research and Scientific Studies, 8(2), 2516–2529. https://doi.org/10.53894/ijirss.v8i2.5729
Rahayuningsih, S., Sirajuddin, S., & Ikram, M. (2021). Using open-ended problem-solving tests to identify students’ mathematical creative thinking ability. Participatory Educational Research, 8(3), 285–299. https://doi.org/10.17275/per.21.66.8.3
Riling, M. (2020). Recognizing mathematics students as creative: Mathematical creativity as community-based and possibility-expanding. Journal of Humanistic Mathematics, 10(2), 6–39. https://doi.org/10.5642/jhummath.202002.04
Ruiz-del-Pino, B., Fernández-Martín, F. D., & Arco-Tirado, J. L. (2022). Creativity training programs in primary education: A systematic review and meta-analysis. Thinking Skills and Creativity, 46, 101172. https://doi.org/10.1016/j.tsc.2022.101172
Ruth, A., Wutich, A., & Bernard, H. R. (2024). The handbook of teaching qualitative and mixed research methods: A step-by-step guide for instructors. Routledge. https://doi.org/10.4324/9781003213277
Schoevers, E. M., Kroesbergen, E. H., & Kattou, M. (2020). Mathematical creativity: A combination of domain-general creative and domain-specific mathematical skills. Journal of Creative Behavior, 54(2), 242–252. https://doi.org/10.1002/jocb.361
Schoevers, E. M., Kroesbergen, E. H., Moerbeek, M., & Leseman, P. P. M. (2021). The relation between creativity and students’ performance on different types of geometrical problems in elementary education. ZDM – Mathematics Education, 54, 133–147. https://doi.org/10.1007/s11858-021-01315-5
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM – International Journal on Mathematics Education, 29(3), 75–80. https://doi.org/10.1007/s11858-997-0003-x
Sriraman, B. (2008). The characteristics of mathematical creativity. ZDM – International Journal on Mathematics Education, 14(1), 19–34. https://doi.org/10.1007/s11858-008-0114-z
Subanji, Nusantara, T., Rahmatina, D., & Purnomo, H. (2021). The statistical creative framework in descriptive statistics activities. International Journal of Instruction, 14(2), 591–608.
Subanji, Nusantara, T., Sukoriyanto, & Atmaja, S. A. A. (2023). Student’s creative model in solving mathematics controversial problems. Cakrawala Pendidikan, 42(2), 310–326.
Sundquist, D., & Lubart, T. (2022). Being intelligent with emotions to benefit creativity: Emotion across the seven Cs of creativity. Journal of Intelligence, 10(106). https://doi.org/10.3390/jintelligence10040106
Supena, I., Darmuki, A., & Hariyadi, A. (2021). The influence of 4C (constructive, critical, creativity, collaborative) learning model on students’ learning outcomes. International Journal of Instruction, 14(3), 873–892. https://doi.org/10.29333/iji.2021.14351a
Suryanto, H., Degeng, I. N. S., Djatmika, E. T., & Kuswandi, D. (2021). The effect of creative problem solving with the intervention social skills on the performance of creative tasks. Creativity Studies, 14(2), 323–335. https://doi.org/10.3846/cs.2021.12364
Suyitno, A. (2020). Growth of student mathematical creativity as part of 4C competence for entering the 21st century. Journal of Physics: Conference Series, 1567(2), 4–9. https://doi.org/10.1088/1742-6596/1567/2/022100
Szabo, Z. K., Körtesi, P., Guncaga, J., Szabo, D., & Neag, R. (2020). Examples of problem-solving strategies in mathematics education supporting the sustainability of 21st-century skills. Sustainability, 12(23), 1–28. https://doi.org/10.3390/su122310113
Titikusumawati, E., Sa’dijah, C., As’ari, A. R., & Susanto, H. (2019). An analysis of students’ creative thinking skill in creating open-ended mathematics problems through semi-structured problem posing. Journal of Physics: Conference Series, 1227, 012024. https://doi.org/10.1088/1742-6596/1227/1/012024
Ulger, K. (2018). The effect of problem-based learning on the creative thinking and critical thinking disposition of students in visual arts education. Interdisciplinary Journal of Problem-Based Learning, 12(1), 3–6. https://doi.org/10.7771/1541-5015.1649
Utami, S., Usodo, B., & Pramudya, I. (2019). Level of students’ creative thinking in solid geometry. Journal of Physics: Conference Series, 1227(1), 1–9. https://doi.org/10.1088/1742-6596/1227/1/012023
Villanova, A. L. I., & Cunha, M. P. E. (2020). Everyday creativity: A systematic literature review. Journal of Creative Behavior, 55(3), 673–695. https://doi.org/10.1002/jocb.481
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Mohammad Kholil, Nur Faizah, Anis Hidayati, Chanda Chansa Thelma

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Copyright Notice
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under an Attribution-Share-Alike (CC BY-SA) license. that allows others to Share — copy and redistribute the material in any medium or format, Adapt — remix, transform, and build upon the material for any purpose, even commercially.
![]()
This work is licensed under a Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).
EDUCARE: Journal of Primary Education
Published by Faculty of Tarbiyah and Teacher Training, Kiai Haji Achmad Siddiq State Islamic University of Jember, East Java, Indonesia


1.png)






