Metacognitive Regulation in Probability and Statistics Problem-Solving: A Phenomenological Study of Distance Mathematics Education Students

This study investigated how Ghanaian distance education students use metacognitive strategies in solving probability and statistics problems. Using a phenomenological qualitative design, 11 first-year Bachelor of Science in Mathematics Education students from three public universities were purposively selected across modular, online, and blended learning modes. Semi-structured online interviews captured experiences of planning, monitoring, and evaluating during problem-solving. Findings showed that students engaged in metacognitive regulation, though unevenly. Planning was dominant, especially in interpreting problems and recalling prior knowledge. Monitoring was selective, influenced by confidence and cognitive load, while evaluation involved checking plausibility and relevance of solutions. Learning modality shaped engagement: modular learning encouraged careful planning, online learning heightened self-checking, and blended learning supported balanced regulation through feedback. Structural and emotional constraints, including limited feedback, connectivity issues, and anxiety, reduced effective engagement. The study proposes a contextualised model linking learning modality and structural factors to self-regulated learning theory.

Distance learning, Metacognition, Phenomenology, Probability and statistics, Undergraduate mathematics education

1. Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review, 14(2), 243–248. https://doi.org/10.3758/BF03194059 [Google Scholar] [Crossref]

2. Azevedo, R., Taub, M., & Mudrick, N. V. (2018). Using multi-channel trace data to infer and foster self-regulated learning between humans and advanced learning technologies. In D. H. Schunk & J. A. Greene (Eds.), Handbook of Self-Regulation of Learning and Performance (2nd ed., pp. 254–270). Routledge. [Google Scholar] [Crossref]

3. Bol, L., & Garner, J. K. (2011). Challenges in supporting self-regulation in distance education environments. Journal of Computing in Higher Education, 23(2), 104–123. https://doi.org/10.1007/s12528-011-9046-7 [Google Scholar] [Crossref]

4. Creswell, J. W. (2007). Qualitative inquiry and research design (2nd ed.) Sage Publications, Inc. [Google Scholar] [Crossref]

5. Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry and research design: Choosing among five approaches (4th ed.). SAGE Publications. [Google Scholar] [Crossref]

6. Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34(10), 906–911. https://doi.org/10.1037/0003-066X.34.10.906 [Google Scholar] [Crossref]

7. Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer. [Google Scholar] [Crossref]

8. Ghana Tertiary Education Commission. (2023). Distance education policy audit (Phase 1). GTEC, Ghana. [Google Scholar] [Crossref]

9. Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving. Educational Studies in Mathematics, 49(2), 193–223. https://doi.org/10.1023/A:1016209010120 [Google Scholar] [Crossref]

10. Graphic Online. (2025, September 10). GTEC launches distance learning policy to improve standards. https://www.graphic.com.gh/ [Google Scholar] [Crossref]

11. Halmo, S. M., Yamini, K. A., & Stanton, J. D. (2024). Metacognition and self-efficacy in action: How first-year students monitor and use self-coaching to move past metacognitive discomfort during problem solving. CBE—Life Sciences Education, 23(2), ar13. https://doi.org/10.1187/cbe.23-08-0158 [Google Scholar] [Crossref]

12. Hanifa, M., Nursalam, N., Kusumayanti, A., & Suharti, S. (2025). Understanding the influence of metacognition on mathematical literacy: A literature review. Pedagonal: Jurnal Ilmiah Pendidikan, 9(2), 188-200. https://doi.org/10.55215/pedagonal.v9i2.42 [Google Scholar] [Crossref]

13. 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 [Google Scholar] [Crossref]

14. Kammer, J., Atiso, K., & Borteye, E. (2025). Internet policy and connectivity challenges for students in a Ghanaian university. Portal: Libraries and the Academy, 25(1), 55-65. [Google Scholar] [Crossref]

15. Kayi, E. A., & Van Wyk, M. M. (2025). Exploring Ghanaian distance learners’ views of self-regulated learning strategies and academic performance. Open Praxis, 17(2), 376-393. https://doi.org/10.55982/openpraxis.17.2.783 [Google Scholar] [Crossref]

16. Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. SAGE Publications. [Google Scholar] [Crossref]

17. Moustakas, C. (1994). Phenomenological research methods. SAGE Publications. [Google Scholar] [Crossref]

18. National Council for Curriculum and Assessment (NaCCA). (2023). Mathematics common core programme (CCP). NaCCA. [Google Scholar] [Crossref]

19. National Council for Curriculum and Assessment. (2024). Mathematics curriculum for secondary education (SHS 1). NaCCA. [Google Scholar] [Crossref]

20. Österholm, E., Iiskala, T., Mustonen, R., & Murtonen, M. (2025). Metacognitive regulation: emergence, focus, and function in interprofessional collaborative learning. Advances in Health Sciences Education, 31, 1-20. https://doi.org/10.1007/s10459-025-10458-z [Google Scholar] [Crossref]

21. Polya, G. (1973). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton University Press. Sarpong, R. A. (2023, November). Digitalisation of education in Ghana: An overview. WATHI. https://www.wathi.org/situation-education-ghana-2024/digitalisation-of-education-in-ghana-an-overview-november-2023/ [Google Scholar] [Crossref]

22. Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Journal of Education, 196(2), 1-38. https://doi.org/10.1177/002205741619600202 [Google Scholar] [Crossref]

23. Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26(1/2), 113-125. https://doi.org/10.1023/A:1003044231033 [Google Scholar] [Crossref]

24. Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary educational psychology, 19(4), 460-475. https://doi.org/10.1006/ceps.1994.1033 [Google Scholar] [Crossref]

25. Supratman., Budayasa, I. K., & Rahaju, E. B. (2025). Probabilistic thinking process in probability problem-solving prospective mathematics teacher with field independent based on Polya’s three stages. Educational Process: International Journal, 17, e2025333. https://doi.org/10.22521/edupij.2025.17.333 [Google Scholar] [Crossref]

26. Sweller, J., Van Merriënboer, J. J., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational psychology review, 31(2), 261-292. https://doi.org/10.1007/s10648-019-09465-5 [Google Scholar] [Crossref]

27. 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 [Google Scholar] [Crossref]

28. van Manen, M. (2016). Researching lived experience: Human science for an action sensitive pedagogy (2nd ed.). Routledge. [Google Scholar] [Crossref]

29. Veenman, M.V.J., Van Hout-Wolters, B.H.A.M. & Afflerbach, P. (2006). Metacognition and learning: conceptual and methodological considerations. Metacognition Learning, 1, 3-14. https://doi.org/10.1007/s11409-006-6893-0 [Google Scholar] [Crossref]

30. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Pressz [Google Scholar] [Crossref]

31. 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 [Google Scholar] [Crossref]

32. Zimmerman, B. J. (2002). Becoming a self-regulated learner: An overview. Theory Into Practice, 41(2), 64-70. https://doi.org/10.1207/s15430421tip4102_2 [Google Scholar] [Crossref]

• Interplay of Students’ Emotional Intelligence and Attitude toward Mathematics on Performance in Grade 10 Algebra
• Numerical Simulation of Fitzhugh-Nagumo Dynamics Using a Finite Difference-Based Method of Lines
• Fixed Point Theorem in Controlled Metric Spaces
• Usage of Moving Average to Heart Rate, Blood Pressure and Blood Sugar
• Exploring Algebraic Topology and Homotopy Theory: Methods, Empirical Data, and Numerical Examples