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Interval: Indonesian Journal of Mathematical Education

an Open Access Journal

Mathematics and Combinatorial Thinking: How Computational Ability Influences Problem-Solving in Number Patterns?

Khatriya Tiffani
State Islamic Junior High School 2 Bondowoso
Indonesia
khatriyatiffani@gmail.com
Mohammed Rizzman Manaf
Institut Pendidikan Guru Kampus Tun Hussein Onn
Malaysia
Riswan Efendi
Sultan Idris Education University ROR
Indonesia
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  • Purpose of the study: This study aims to analyze students' computational thinking abilities in solving combinatorial problems based on high, medium, and low ability categories.

    Methodology: This study uses a descriptive qualitative approach with subjects of 33 students of class VIII I State Islamic Junior High School 2 Bondowoso. Data were collected through written tests, semi-structured interviews, and documentation. Data analysis used the Miles and Huberman model (reduction, presentation, conclusion) with triangulation techniques for validation, comparing test results, interviews, and documentation.

    Main Findings: Students with high and medium computational abilities are able to meet all indicators of computational thinking, including identifying and understanding problems, and converting them into combinatorics. Meanwhile, students with low abilities have difficulty in re-understanding the problems found.

    Novelty/Originality of this study: This study provides new insights into how students' level of computational thinking ability influences their success in solving combinatorial problems, as well as offers perspectives in developing more effective learning strategies to enhance students' computational thinking ability.

  • How to cite

    Mathematics and Combinatorial Thinking: How Computational Ability Influences Problem-Solving in Number Patterns?. (2025). Interval: Indonesian Journal of Mathematical Education, 3(1), 13-25. https://doi.org/10.37251/ijome.v3i1.1616

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    1. M. Schnieder, S. Williams, and S. Ghosh, “Comparison of in-person and virtual labs/tutorials for engineering students using blended learning principles,” Educ. Sci., vol. 12, no. 3, 2022, doi: 10.3390/educsci12030153. DOI: https://doi.org/10.3390/educsci12030153
    2. Y. Zhao and J. Watterston, “The changes we need: education post COVID-19,” J. Educ. Chang., vol. 22, no. 1, pp. 3–12, 2021, doi: 10.1007/s10833-021-09417-3. DOI: https://doi.org/10.1007/s10833-021-09417-3
    3. K. K. Aggarwal and S. Agrawal, “Artificial intelligence and its role in financial market,” Glob. Financ. Anal. Bus. Forecast., pp. 67–82, 2024.
    4. H. Zhang, I. Lee, S. Ali, D. DiPaola, Y. Cheng, and C. Breazeal, “Integrating ethics and career futures with technical learning to promote ai literacy for middle school students: an exploratory study,” Int. J. Artif. Intell. Educ., vol. 33, no. 2, pp. 290–324, 2023, doi: 10.1007/s40593-022-00293-3. DOI: https://doi.org/10.1007/s40593-022-00293-3
    5. M. C. Borba, “The future of mathematics education since COVID-19: humans-with-media or humans-with-non-living-things,” Educ. Stud. Math., vol. 108, no. 1–2, pp. 385–400, 2021, doi: 10.1007/s10649-021-10043-2. DOI: https://doi.org/10.1007/s10649-021-10043-2
    6. T. Dame Adjin-Tettey, “Combating fake news, disinformation, and misinformation: Experimental evidence for media literacy education,” Cogent Arts Humanit., vol. 9, no. 1, 2022, doi: 10.1080/23311983.2022.2037229. DOI: https://doi.org/10.1080/23311983.2022.2037229
    7. M. W. Habibi, L. Jiyane, and Z. Özşen, “Learning revolution: the positive impact of computer simulations on science achievement in madrasah ibtidaiyah,” J. Educ. Technol. Learn. Creat., vol. 2, no. 1, pp. 13–19, 2024, doi: 10.37251/jetlc.v2i1.976. DOI: https://doi.org/10.37251/jetlc.v2i1.976
    8. S. O. Pela, N. N. Le, P. G. Kaboro, and A. Nurjamil, “Innovation of physics e-module : utilizing local wisdom of Lampung ’ s handwritten batik in teaching heat and temperature material to foster students ’ scientific attitude,” SchrödingerJournal Phys. Educ., vol. 4, no. 4, pp. 132–138, 2023, doi: 10.37251/sjpe.v4i4.924. DOI: https://doi.org/10.37251/sjpe.v4i4.924
    9. R. Sari, I. I. Omeiza, and M. A. Mwakifuna, “The influence of number dice games in improving early childhood mathematical logic in early childhood education,” Interval Indones. J. Math. Educ., vol. 1, no. 2, pp. 61–66, 2023, doi: 10.37251/ijome.v1i2.776. DOI: https://doi.org/10.37251/ijome.v1i2.776
    10. J. M. P. Sanchez, “Teaching motion concepts through pokémon unite : atudents ’ acceptance and experiences,” SchrödingerJournal Phys. Educ., vol. 5, no. 3, pp. 98–106, 2024, doi: 10.37251/sjpe.v5i3.1076. DOI: https://doi.org/10.37251/sjpe.v5i3.1076
    11. M. H. Khoiruddin, Z. Hazmi, Z. Baharin, M. S. Kaka, and S. Saenpich, “Development of visual novel games as learning media for the history of Indonesia ’ s independence,” J. Educ. Technol. Learn. Creat., vol. 1, no. 1, pp. 33–41, 2023, doi: 10.37251/jetlc.v1i1.622. DOI: https://doi.org/10.37251/jetlc.v1i1.622
    12. Y. Yusipa, “Comparative analysis of students’ biology learning outcomes: memory and understanding aspects,” J. Acad. Biol. Biol. Educ., vol. 1, no. 1, pp. 1–9, 2024, doi: 10.37251/jouabe.v1i1.1012. DOI: https://doi.org/10.37251/jouabe.v1i1.1012
    13. B. Chen, X. Zhu, and F. Díaz del Castillo H., “Integrating generative AI in knowledge building,” Comput. Educ. Artif. Intell., vol. 5, no. August, p. 100184, 2023, doi: 10.1016/j.caeai.2023.100184. DOI: https://doi.org/10.1016/j.caeai.2023.100184
    14. Y. Huang and S. Wang, “How to motivate student engagement in emergency online learning? Evidence from the COVID-19 situation,” High. Educ., vol. 85, no. 5, pp. 1101–1123, 2023, doi: 10.1007/s10734-022-00880-2. DOI: https://doi.org/10.1007/s10734-022-00880-2
    15. H. Goss, “Student learning outcomes assessment in higher education and in academic libraries: a review of the literature,” J. Acad. Librariansh., vol. 48, no. 2, p. 102485, 2022, doi: https://doi.org/10.1016/j.acalib.2021.102485. DOI: https://doi.org/10.1016/j.acalib.2021.102485
    16. C. O’Reilly, A. Devitt, and N. Hayes, “Critical thinking in the preschool classroom - A systematic literature review,” Think. Ski. Creat., vol. 46, no. August, 2022, doi: 10.1016/j.tsc.2022.101110. DOI: https://doi.org/10.1016/j.tsc.2022.101110
    17. M. N. Kholid, M. H. Mahmudah, N. Ishartono, F. G. Putra, and B. Forthmann, “Classification of students’ creative thinking for non-routine mathematical problems,” Cogent Educ., vol. 11, no. 1, p., 2024, doi: 10.1080/2331186X.2024.2394738. DOI: https://doi.org/10.1080/2331186X.2024.2394738
    18. E. Tursynkulova, N. Madiyarov, T. Sultanbek, and P. Duysebayeva, “The effect of problem-based learning on cognitive skills in solving geometric construction problems: a case study in Kazakhstan,” Front. Educ., vol. 8, no. December, 2023, doi: 10.3389/feduc.2023.1284305. DOI: https://doi.org/10.3389/feduc.2023.1284305
    19. A. J. Franco-Mariscal, M. J. Cano-Iglesias, E. España-Ramos, and Á. Blanco-López, The ENCIC-CT Model for the Development of Critical Thinking, vol. 2. 2024. doi: 10.1007/978-3-031-78578-8_1. DOI: https://doi.org/10.1007/978-3-031-78578-8_1
    20. R. E. Anggraeni and Suratno, “The analysis of the development of the 5E-STEAM learning model to improve critical thinking skills in natural science lesson,” J. Phys. Conf. Ser., vol. 1832, no. 1, 2021, doi: 10.1088/1742-6596/1832/1/012050. DOI: https://doi.org/10.1088/1742-6596/1832/1/012050
    21. S. Dolapcioglu and A. Doğanay, “Development of critical thinking in mathematics classes via authentic learning: an action research,” Int. J. Math. Educ. Sci. Technol., vol. 53, no. 6, pp. 1363–1386, 2022, doi: 10.1080/0020739X.2020.1819573. DOI: https://doi.org/10.1080/0020739X.2020.1819573
    22. D. Gudeta, “Professional development through reflective practice: The case of Addis Ababa secondary school EFL in-service teachers,” Cogent Educ., vol. 9, no. 1, 2022, doi: 10.1080/2331186X.2022.2030076. DOI: https://doi.org/10.1080/2331186X.2022.2030076
    23. C. Foster, T. Francome, D. Hewitt, and C. Shore, “Principles for the design of a fully-resourced, coherent, research-informed school mathematics curriculum,” J. Curric. Stud., vol. 53, no. 5, pp. 621–641, 2021, doi: 10.1080/00220272.2021.1902569. DOI: https://doi.org/10.1080/00220272.2021.1902569
    24. G. Sala-Sebastià, A. Breda, M. J. Seckel, D. Farsani, and À. Alsina, “Didactic–Mathematical–Computational Knowledge of Future Teachers When Solving and Designing Robotics Problems,” Axioms, vol. 12, no. 2, pp. 1–24, 2023, doi: 10.3390/axioms12020119. DOI: https://doi.org/10.3390/axioms12020119
    25. R. Prentner, “Mathematized phenomenology and the science of consciousness,” PsyArXiv, 2024, doi: 10.1007/s11097-025-10060-z. DOI: https://doi.org/10.31234/osf.io/8d2mf
    26. L. Ke, T. D. Sadler, L. Zangori, and P. J. Friedrichsen, “Developing and using multiple models to promote scientific literacy in the context of socio-scientific issues,” Sci. Educ., vol. 30, no. 3, pp. 589–607, 2021, doi: 10.1007/s11191-021-00206-1. DOI: https://doi.org/10.1007/s11191-021-00206-1
    27. D. Fortus, J. Lin, K. Neumann, and T. D. Sadler, “The role of affect in science literacy for all,” Int. J. Sci. Educ., vol. 44, no. 4, pp. 535–555, 2022, doi: 10.1080/09500693.2022.2036384. DOI: https://doi.org/10.1080/09500693.2022.2036384
    28. J. Nilimaa, “New examination approach for real-world creativity and problem-solving skills in mathematics,” Trends High. Educ., vol. 2, no. 3, pp. 477–495, 2023, doi: 10.3390/higheredu2030028. DOI: https://doi.org/10.3390/higheredu2030028
    29. A. Bakker, J. Cai, and L. Zenger, “Future themes of mathematics education research: an international survey before and during the pandemic,” Educ. Mat., vol. 35, no. 2, pp. 9–46, 2023, doi: 10.24844/EM3502.01. DOI: https://doi.org/10.24844/EM3502.01
    30. Y. Popova, M. Abdualiyeva, Y. Torebek, N. Yelshibekov, and G. Omashova, “Improving the effectiveness of senior graders’ education based on the development of mathematical intuition and logic: Kazakhstan’s experience,” Front. Educ., vol. 7, no. August, pp. 1–13, 2022, doi: 10.3389/feduc.2022.986093. DOI: https://doi.org/10.3389/feduc.2022.986093
    31. M. Q. E. Alfayez, S. Q. A. Aladwan, and H. R. A. Shaheen, “The effect of a training program based on mathematical problem-solving strategies on critical thinking among seventh-grade students,” Front. Educ., vol. 7, no. April, pp. 1–9, 2022, doi: 10.3389/feduc.2022.870524. DOI: https://doi.org/10.3389/feduc.2022.870524
    32. L. I. González‐pérez and M. S. Ramírez‐montoya, “Components of education 4.0 in 21st century skills frameworks: systematic review,” Sustain., vol. 14, no. 3, pp. 1–31, 2022, doi: 10.3390/su14031493. DOI: https://doi.org/10.3390/su14031493
    33. M. Javaid, A. Haleem, R. Pratap Singh, R. Suman, and S. Rab, “Significance of machine learning in healthcare: Features, pillars and applications,” Int. J. Intell. Networks, vol. 3, no. May, pp. 58–73, 2022, doi: 10.1016/j.ijin.2022.05.002. DOI: https://doi.org/10.1016/j.ijin.2022.05.002
    34. T. Feraco, D. Resnati, D. Fregonese, A. Spoto, and C. Meneghetti, “An integrated model of school students’ academic achievement and life satisfaction. Linking soft skills, extracurricular activities, self-regulated learning, motivation, and emotions,” Eur. J. Psychol. Educ., vol. 38, no. 1, pp. 109–130, 2023, doi: 10.1007/s10212-022-00601-4. DOI: https://doi.org/10.1007/s10212-022-00601-4
    35. M. Karimi-Mamaghan, M. Mohammadi, P. Meyer, A. M. Karimi-Mamaghan, and E. G. Talbi, “Machine learning at the service of meta-heuristics for solving combinatorial optimization problems: A state-of-the-art,” Eur. J. Oper. Res., vol. 296, no. 2, pp. 393–422, 2022, doi: 10.1016/j.ejor.2021.04.032. DOI: https://doi.org/10.1016/j.ejor.2021.04.032
    36. F. Peres and M. Castelli, “Combinatorial optimization problems and metaheuristics: review, challenges, design, and development,” Appl. Sci., vol. 11, no. 6449, 2021. DOI: https://doi.org/10.3390/app11146449
    37. K. Suresh, C. Severn, and D. Ghosh, “Survival prediction models: an introduction to discrete-time modeling,” BMC Med. Res. Methodol., vol. 22, no. 1, pp. 1–18, 2022, doi: 10.1186/s12874-022-01679-6. DOI: https://doi.org/10.1186/s12874-022-01679-6
    38. F. Rodrigues and A. Agra, “Berth allocation and quay crane assignment/scheduling problem under uncertainty: A survey,” Eur. J. Oper. Res., vol. 303, no. 2, pp. 501–524, 2022, doi: https://doi.org/10.1016/j.ejor.2021.12.040. DOI: https://doi.org/10.1016/j.ejor.2021.12.040
    39. M. O. Aziza, Dafik, and A. I. Kristiana, “The analysis of the implementation of research-based learning on the students combinatorial thinking skills in solving a resolving perfect dominating set problem,” in Journal of Physics: Conference Series, 2021. doi: 10.1088/1742-6596/1836/1/012057. DOI: https://doi.org/10.1088/1742-6596/1836/1/012057
    40. V. Ďuriš, G. Pavlovičová, D. Gonda, and A. Tirpáková, “Teaching combinatorial principles using relations through the placemat method,” Mathematics, vol. 9, no. 15, pp. 1–13, 2021, doi: 10.3390/math9151825. DOI: https://doi.org/10.3390/math9151825
    41. C. Zhang et al., “A review on learning to solve combinatorial optimisation problems in manufacturing,” IET Collab. Intell. Manuf., vol. 5, no. 1, 2023, doi: 10.1049/cim2.12072. DOI: https://doi.org/10.1049/cim2.12072
    42. H. Ye, B. Liang, O. L. Ng, and C. S. Chai, “Integration of computational thinking in K-12 mathematics education: a systematic review on CT-based mathematics instruction and student learning,” Int. J. STEM Educ., vol. 10, no. 1, 2023, doi: 10.1186/s40594-023-00396-w. DOI: https://doi.org/10.1186/s40594-023-00396-w
    43. M. Kallia, van B. Sylvia Patricia, D. Paul, B. Erik, and J. and Tolboom, “Characterising computational thinking in mathematics education: a literature-informed Delphi study,” Res. Math. Educ., vol. 23, no. 2, pp. 159–187, May 2021, doi: 10.1080/14794802.2020.1852104. DOI: https://doi.org/10.1080/14794802.2020.1852104
    44. Y. Qian and I. Choi, “Tracing the essence: ways to develop abstraction in computational thinking,” Educ. Technol. Res. Dev., vol. 71, no. 3, pp. 1055–1078, 2023, doi: 10.1007/s11423-022-10182-0. DOI: https://doi.org/10.1007/s11423-022-10182-0
    45. S. W. Chan, C. K. Looi, W. K. Ho, W. Huang, P. Seow, and L. Wu, “Learning number patterns through computational thinking activities: A Rasch model analysis,” Heliyon, vol. 7, no. 9, p. e07922, 2021, doi: 10.1016/j.heliyon.2021.e07922. DOI: https://doi.org/10.1016/j.heliyon.2021.e07922
    46. H. Belmar, “Review on the teaching of programming and computational thinking in the world,” Front. Comput. Sci., vol. 4, 2022, doi: 10.3389/fcomp.2022.997222. DOI: https://doi.org/10.3389/fcomp.2022.997222