Pre-Service Teachers’ Level and Processes of Metacognition in Non-Routine Problem Solving

Metacognition is essential in mathematical problem-solving because it enables learners to plan, monitor, and evaluate their thinking while solving unfamiliar tasks. This study aimed to determine the level of metacognition of pre-service mathematics teachers and describe their metacognitive processes in terms of planning, monitoring, and evaluation while solving non-routine mathematical problems. A descriptive research design supported by qualitative data was employed. The participants were 27 third-year secondary mathematics pre-service teachers from the College of Education, Mindanao State University–Iligan Institute of Technology, selected through purposive sampling. Data were gathered using two non-routine mathematical problems, written solutions, reflective journals, and a validated metacognition scoring rubric. Quantitative data were analyzed using mean, standard deviation, frequency, and percentage, while qualitative data were analyzed deductively based on planning, monitoring, and evaluation. Results revealed that the pre-service teachers demonstrated a moderate level of metacognition (M = 6.15). Planning, monitoring, and evaluation were evident in their solutions; however, evaluation emerged as the least consistently demonstrated metacognitive process. Qualitative findings showed that high-level pre-service teachers demonstrated systematic planning, active monitoring, and careful evaluation, whereas moderate- and low-level pre-service teachers showed partial or developing metacognition, misunderstanding of problem conditions, and limited verification of answers. The findings suggest the need to strengthen metacognitive instruction to better prepare future mathematics teachers for reflective and effective problem-solving.

Pre-Service Teachers, Metacognition, Non-Routine Problem-Solving

1. Ajani, O. A. (2024). Enhancing problem-solving skills among pre-service teachers in higher education: A systematic literature review. Journal of Pedagogical Sociology and Psychology, 6(2), 98-113. [Google Scholar] [Crossref]

2. Akyüz, G. (2020). Non-routine problem solving performances of mathematics teacher candidates. Educational Research and Reviews, 15(5), 214-224. [Google Scholar] [Crossref]

3. Darr, C., & Fisher, J. (2005). Self-regulated learning in mathematics classes. Set: Research Information for Teachers, 2, 44-49. [Google Scholar] [Crossref]

4. Department of Education. (2017). National adoption and implementation of the Philippine Professional Standards for Teachers (DepEd Order No. 42, s. 2017). https://www.deped.gov.ph/wp-content/uploads/2017/08/DO_s2017_042-1.pdf [Google Scholar] [Crossref]

5. Desoete, A. (2007). Evaluating and improving the mathematics teaching-learning process through metacognition. Electronic Journal of Research in Educational Psychology, 5(3), 705–730. https://doi.org/10.25115/ejrep.v5i13.1243 [Google Scholar] [Crossref]

6. Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). McGraw-Hill. [Google Scholar] [Crossref]

7. Fono, D., & Zohar, A. (2024). Metacognitive instruction: central aspects of pre-service and novice in-service teachers’ knowledge and professional development. Professional Development in Education, 1-24. [Google Scholar] [Crossref]

8. Güner, P., & Erbay, H. N. (2021). Metacognitive skills and problem-solving. International Journal of Research in Education and Science, 7(3), 715-734. [Google Scholar] [Crossref]

9. Gurat, M., & Medula, C., Jr. (2016). Metacognitive strategy knowledge use through mathematical problem solving amongst pre-service teachers. American Journal of Educational Research, 4(2), 170–189. [Google Scholar] [Crossref]

10. Hallgren, K. A. (2012). Computing inter-rater reliability for observational data: An overview and tutorial. Tutorials in Quantitative Methods for Psychology, 8(1), 23-34. [Google Scholar] [Crossref]

11. Jiang, P., Zhang, Y., Jiang, Y., & Xiong, B. (2022). Preservice mathematics teachers' perceptions of mathematical problem solving and its teaching: A case from China. Frontiers in Psychology, 13, 998586. [Google Scholar] [Crossref]

12. Koo, T. K., & Li, M. Y. (2016). A guideline of selecting and reporting intraclass correlation coefficients for reliability research. Journal of Chiropractic Medicine, 15(2), 155-163. [Google Scholar] [Crossref]

13. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics. [Google Scholar] [Crossref]

14. OECD. (2006). PISA released items: Mathematics. https://www.acer.org/files/pisa_relitems_maths_2.pdf [Google Scholar] [Crossref]

15. 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]

16. Scribd. (n.d.). Non-routine problems. https://www.scribd.com/doc/49811009/non-routine-problems [Google Scholar] [Crossref]

17. Usta, N. (2020). Evaluation of preservice teachers' skills in solving non-routine mathematical problems through various strategies. Asian Journal of Education and Training, 6(3), 362-383. [Google Scholar] [Crossref]

18. Vadivu, P. P., Logeshwaran, S. V., Lakshmi, S. J., & V, S. (2025). Advancing mathematical problem solving through metacognitive learning strategies innovations and applications in medical and health sciences. International Journal for Multidisciplinary Research. [Google Scholar] [Crossref]

19. Wilkerson, T. L. (2022). Problem solving: An approach to understanding and critiquing our world. National Council of Teachers of Mathematics. https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Trena-Wilkerson/Problem-Solving_-An-Approach-to-Understanding-and-Critiquing-Our-World/ [Google Scholar] [Crossref]

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