Exploring students’ metacognitive processes in scaffolded integration problem solving

Siti Maslihah; Kartono; Wardono; Kharisudin

doi:10.58524/jasme.v6i3.1505

Authors

Siti Maslihah Universitas Islam Negeri Walisongo, Indonesia
Kartono Universiats Negeri Semarang, Indonesia
Wardono Universitas Negeri Semarang, Indonesia
Kharisudin Universitas Negeri Semarang, Indonesia

DOI:

https://doi.org/10.58524/jasme.v6i3.1505

Keywords:

Integration Problem Solving, Mathematics Education, Metacognitive Processes, Metacognitive Regulation, Scaffolding

Abstract

Background: Integration techniques are fundamental to advanced mathematics, yet students frequently encounter difficulties in recognizing problem structures, selecting appropriate integration methods, and regulating their problem-solving processes. Scaffolding may facilitate these processes by supporting students’ metacognitive awareness, monitoring, and evaluation.

Aim: This study aimed to explore students’ metacognitive processes during scaffolded integration problem solving.

Method: A qualitative case study was conducted with three Mathematics Education students enrolled in an Integral Calculus course at UIN Walisongo. Participants represented different performance levels and were examined through open-ended integration problems and follow-up interviews. Their problem-solving processes were analyzed according to three metacognitive dimensions: awareness, monitoring, and evaluation.

Results: The findings revealed varying levels of metacognitive engagement across participants. Awareness and monitoring were more evident among higher-performing students, particularly in recognizing problem characteristics, selecting appropriate integration strategies, and controlling procedural steps. In contrast, evaluation remained consistently underdeveloped, as students rarely verified their answers or reflected on the effectiveness of their strategies.

Conclusion: Scaffolded integration problem solving can facilitate the emergence of metacognitive awareness and monitoring; however, explicit evaluative prompts are needed to strengthen verification and reflection during mathematical problem solving.

References

Azizah, R., Tahmir, S., Asdar, A., Nurhasanah, N., & Hirpan, H. (2025). Scaffolding metakognitif dalam pemecahan masalah geometri ditinjau dari gaya belajar auditorial. Issues in Mathematics Education (IMED), 9(1), 72–83. https://doi.org/10.35580/imed.v9i1.4619

Braithwaite, D. W., & Sprague, L. (2021). Conceptual knowledge, procedural knowledge, and metacognition in routine and nonroutine problem solving. Cognitive Science, 45(10), e13048. https://doi.org/10.1111/cogs.13048

Cervantes-Barraza, J. A., Rodríguez-Nieto, C. A., Damian-Mojica, A., & Morales-Carballo, A. (2025). Promoting the use of the Python programming language to analyze contextualized situations on derivatives and integrals considering the fundamental theorem of calculus. Eurasia Journal of Mathematics, Science and Technology Education, 21(9), em2705. https://doi.org/10.29333/ejmste/16885

Ferreira, P. D. C., Ferreira, A. I., Simão, A. M. V. D. V., Prada, R., Paulino, A. P., & Rodrigues, R. (2022). Self-regulated learning and working memory determine problem-solving accuracy in math. The Spanish Journal of Psychology, 25, e23. https://doi.org/10.1017/SJP.2022.19

Gao, Z., Yan, H., Liu, J., Cui, C., Wang, J., Zhang, X., Sun, X., & Feng, J. (n.d.). Untangling complexity of competency evolution: Multi-channel learning trajectories of score, engagement and problem-solving efficiency. British Journal of Educational Technology, .. https://doi.org/10.1111/bjet.70017

Garte, S., Marshall, P., & Kauffman, S. (2025). The reasonable ineffectiveness of mathematics in the biological sciences. Entropy, 27(3).. https://doi.org/10.3390/e27030280

Greengrass, C. J. (2026). Transforming clinical reasoning—The role of AI in supporting human cognitive limitations. Frontiers in Digital Health, 7.. https://doi.org/10.3389/fdgth.2025.1715440

Hegedus, S. J., & Otálora, Y. (2023). Mathematical strategies and emergence of socially mediated metacognition within a multi-touch Dynamic Geometry Environment. Educational Studies in Mathematics, 112(2), 289–307. https://doi.org/10.1007/s10649–022–10170–4

Hidayat, R., Mohd Saad, M. R., & Wewe, M. (2025). A meta-analysis of the effect of metacognitive instruction on mathematics achievement. Cogent Education, 12(1), 2517510. https://doi.org/10.1080/2331186X.2025.2517510

Im, Y., Choe, J., & Shin, Y. (2026). Capturing the temporal interplay of knowledge construction and group-level regulation in collaborative problem solving. Metacognition and Learning, 21(1), 29. https://doi.org/10.1007/s11409–026–09473–1

Ke, F., & Clark, K. M. (2020). Game-based multimodal representations and mathematical problem solving. International Journal of Science and Mathematics Education, 18(1), 103–122. https://doi.org/10.1007/s10763–018–9938–3

Khalid, M., Saad, S., Hamid, S. R. A., Abdullah, M. R., Ibrahim, H., & Shahrill, M. (2020). Enhancing creativity and problem solving skills through creative problem solving in teaching mathematics. Creativity Studies, 13(2), 270–291. https://doi.org/10.3846/cs.2020.11027

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), 2394738. https://doi.org/10.1080/2331186X.2024.2394738

Liu, J., Keane, T., Sun, D., Yang, Y., & Yang, Y. (2025). Design and evaluation of ChatGPT-MWPS: An AI-enhanced learning system for improving primary students' mathematical word problem solving. Smart Learning Environments, 12(1), 68. https://doi.org/10.1186/s40561–025–00419–9

Malenkov, Y., Kapustina, I., Kudryavtseva, G., Shishkin, V. V., & Shishkin, V. I. (2021). Digitalization and strategic transformation of retail chain stores: Trends, impacts, prospects. Journal of Open Innovation: Technology, Market, and Complexity, 7(2). https://doi.org/10.3390/joitmc7020108

Mannan, A. M. K., Bajuri, M. R., Abdul Rahim, S. S., & Abdullah, N. A. (2026). How do digital tools support metacognition in mathematics learning? A systematic review of research on GeoGebra and problem-solving. Educational Research Review, 52, 100827. https://doi.org/10.1016/j.edurev.2026.100827

Mannan, A. M. K., Bajuri, M. R., Abdullah, N. A., & Redzuan, R. S. (2025). Exploring metacognitive processes in calculus problem-solving: A case study using GeoGebra. Journal of Mathematics, Science and Technology Education, 2(2), 103–115. https://doi.org/10.12973/jmste.2.2.103

Maries, A., & Singh, C. (2023). Helping students become proficient problem solvers part I: A brief review. Education Sciences, 13(2).. https://doi.org/10.3390/educsci13020156

Mas', Badolo, U., Malik, M. A., Rafi', Nur, A., & Latifa, A. (2025). The impact of metacognitive strategy training on higher-order thinking skills (HOTS) in high school mathematics: A quasi-experimental study. International Journal of Environment, Engineering and Education, 7(2), 146–157. https://doi.org/10.55151/ijeedu.v7i2.302

McDonald, P. A., & Smith, J. M. (2020). Improving mathematical learning in Scotland's Curriculum for Excellence through problem posing: An integrative review. The Curriculum Journal, 31(3), 398–435. https://doi.org/10.1002/curj.15

Michalsky, T. (2024). Metacognitive scaffolding for preservice teachers' self-regulated design of higher order thinking tasks. Heliyon, 10(2).. https://doi.org/10.1016/j.heliyon.2024.e24280

Msomi, A. M., & Bansilal, S. (2022). Analysis of students' errors and misconceptions in solving linear ordinary differential equations using the method of Laplace transform. International Electronic Journal of Mathematics Education, 17(1).. https://doi.org/10.29333/iejme/11474

Ncube, M., & Luneta, K. (n.d.). Concept-based instruction: Improving learner performance in mathematics through conceptual understanding. Pythagoras, 46(1), 815. https://doi.org/10.4102/pythagoras.v46i1.815

Prastiti, T. D., Ahmadah, I. F., & Siswono, T. Y. E. (2026). Metacognitive regulation in collaborative math problem-solving among heterogeneous secondary students. Eurasia Journal of Mathematics, Science and Technology Education, 22(5), em2834. https://doi.org/10.29333/ejmste/18518

Riva, G. (2026). The architecture of cognitive amplification: Enhanced cognitive scaffolding as a resolution to the comfort-growth paradox in AI-supported learning. Cognitive Systems Research, 99, 101500. https://doi.org/10.1016/j.cogsys.2026.101500

Rivas, S. F., Saiz, C., & Ossa, C. (2022). Metacognitive strategies and development of critical thinking in higher education. Frontiers in Psychology, 13.. https://doi.org/10.3389/fpsyg.2022.913219

Rivers, M. L., Dunlosky, J., & Persky, A. M. (2020). Measuring metacognitive knowledge, monitoring, and control in the pharmacy classroom and experiential settings. American Journal of Pharmaceutical Education, 84(5), 7730. https://doi.org/10.5688/ajpe7730

Su, C.-Y. (2026). Integrating metacognitive scaffolding into a physics simulation for elementary school students' conceptual understanding of force and motion. Journal of Science Education and Technology, 35(4), 917–932. https://doi.org/10.1007/s10956–025–10288-z

Susanna, T., Lasse, E., Henrik, N. J., & Sari, H.-N. (2026). From problem-solving to reflection: Activating diverse metacognitive skills in mathematics. International Journal of Science and Mathematics Education, 24(2), 10. https://doi.org/10.1007/s10763–025–10643-x

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).. https://doi.org/10.3390/su122310113

Tanreso, N. F., Irmawati, I., Musliha, M., Aldasafitri, J., Ain, N., Yusuf, M., & Hijra, H. (2025). Analisis literatur: Peran metakognisi dalam pemecahan masalah matematika siswa. Pedagogy: Jurnal Pendidikan Matematika, 10(3), 1287–1295. https://doi.org/10.30605/pedagogy.v10i3.6992

Toikka, S., Eronen, L., Atjonen, P., & Havu-Nuutinen, S. (2024). Combined conceptualisations of metacognitive knowledge to understand students' mathematical problem-solving. Cogent Education, 11(1), 2357901. https://doi.org/10.1080/2331186X.2024.2357901

Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM, 52(1), 1–16. https://doi.org/10.1007/s11858–020–01130–4

Vo, K., Sarkar, M., White, P. J., & Yuriev, E. (2024). Development of problem-solving skills supported by metacognitive scaffolding: Insights from students' written work. Chemistry Education Research and Practice, 25(4), 1197–1209. https://doi.org/10.1039/D3RP00284E

Wakhata, R., Mutarutinya, V., & Balimuttajjo, S. (2023). Exploring the impact of Stein et al.'s levels of cognitive demand in supporting students' mathematics heuristic problem-solving abilities. Frontiers in Education, 8.. https://doi.org/10.3389/feduc.2023.949988

Wang, C.-Y., & Huang, M.-Y. (2026). Strengthening novice diagnostic problem solving through explicit metacognitive scaffolding in emergency medicine education. Medical Education Online, 31(1), 2662714. https://doi.org/10.1080/10872981.2026.2662714

Wang, W.-S., Lin, C.-J., Lee, H.-Y., Huang, Y.-M., & Wu, T.-T. (2025). Enhancing self-regulated learning and higher-order thinking skills in virtual reality: The impact of ChatGPT-integrated feedback aids. Education and Information Technologies, 30(14), 19419–19445. https://doi.org/10.1007/s10639–025–13557-x

Weldeana, H. N., Sbhatu, D. B., & Berhe, G. T. (2023). Freshman STEM students' misconceptions in a basic limit theorem of lim x → 0 ( sin x / x ). Heliyon, 9(12).. https://doi.org/10.1016/j.heliyon.2023.e22359Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25–48. https://doi.org/10.1007/BF03217394

Wu, J., Wang, J., Lei, S., Wu, F., & Gao, X. (2025). The impact of metacognitive scaffolding on deep learning in a GenAI-supported learning environment. Interactive Learning Environments, 33(9), 5166–5183. https://doi.org/10.1080/10494820.2025.2479162

Zepeda, C. D., & Nokes-Malach, T. J. (2023). Assessing metacognitive regulation during problem solving: A comparison of three measures. Journal of Intelligence, 11(1).. https://doi.org/10.3390/jintelligence11010016

Zhang, J., Yin, J., & Wang, R. (2020). Basic framework and main methods of uncertainty quantification. Mathematical Problems in Engineering, 2020(1), 6068203. https://doi.org/10.1155/2020/6068203

Zhang, W., & Lian, R. (2024). The impact of reading metacognitive strategies on mathematics learning efficiency and performance: An analysis using PISA 2018 data in China. Acta Psychologica, 246, 104247. https://doi.org/10.1016/j.actpsy.2024.104247

Zhao, Y., & Saleh, S. (2025). Metacognition and mathematical problem-solving: An empirical investigation into series problems with junior high school students. Mathematics Education Journal, 9(1), 90–101. https://doi.org/10.22219/mej.v9i1.39924

Zhong, X., & Zhan, Z. (2024). An intelligent tutoring system for programming education based on informative tutoring feedback: System development, algorithm design, and empirical study. Interactive Technology and Smart Education, 22(1), 3–24. https://doi.org/10.1108/ITSE-09–2023–0182

Özgeldi, M., & Aydın, U. (2021). Identifying competency demands in calculus textbook examples: The case of integrals. International Journal of Science and Mathematics Education, 19(1), 171–191. https://doi.org/10.1007/s10763–019–10046–9