Main Article Content
Abstract
Metacognitive skills are widely recognized as a critical foundation for mathematical competence, supporting students’ ability to organize, monitor, and evaluate their problem-solving processes. Despite this importance, limited research has addressed how these skills manifest among junior high school students with low self-efficacy (LSE), a group often at risk of underachievement in mathematics. This study contributes to filling this gap by examining the specific characteristics of metacognitive functioning in LSE students when engaging with problem-solving tasks. The research aimed to describe the metacognitive skills of LSE students in solving problems involving the Pythagorean Theorem and to analyze their strategies and thinking processes. Adopting a descriptive qualitative design, the study involved students identified as having low self-efficacy through questionnaires. Data were collected via self-efficacy questionnaires, problem-solving tasks, and semi-structured interviews, and analyzed using metacognitive indicators within Polya’s problem-solving framework. The results revealed that LSE students consistently demonstrated awareness and evaluation but applied regulation less effectively, particularly during the reviewing stage. Although they were able to plan and assess their solution strategies, errors frequently occurred, requiring repeated adjustments before arriving at correct answers. These findings underscore the need for instructional approaches that explicitly integrate the development of self-efficacy with metacognitive skill training, offering practical implications for mathematics teaching and advancing research on learners with diverse affective-motivational profiles.
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References
- Abdelshiheed, M., Zhou, G., Maniktala, M., Barnes, T., & Chi, M. (2023). Metacognition and Motivation: The Role of Time-Awareness in Preparation for Future Learning. Department of Computer Science. http://arxiv.org/abs/2303.13541
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- Agbata, B. C., Obeng-Denteh, W., Kwabi, P. A., Abraham, S., Okpako, S. O., Arivi, S. S., Asante-Mensa, F., & Adu, G. W. K. (2024). Everyday uses of mathematics and the roles of a mathematics teacher. Science World Journal, 19(3), 819–827. https://doi.org/10.4314/swj.v19i3.29
- Anggraini, E., Subanji, S., & Rahardjo, S. (2024). The Role of Self-Efficacy in Enhance Metacognitive and Academic Performance Through Problem-Solving. PRISMA, 13(2), 259. https://doi.org/10.35194/jp.v13i2.4382
- Bandura, A. (1977). Self-efficacy: Toward a Unifying Theory of Behavioral Change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
- Birt, L., Scott, S., Cavers, D., Campbell, C., & Walter, F. (2022). Member checking: a tool to enhance trustworthiness or merely a nod to validation? Corresponding author (present address). King’s Research Portal. https://doi.org/10.1177/1049732316654870
- Bozgün, K., & Pekdoğan, S. (2018). The Self-Efficacy as Predictors of the Metacognition Awareness in Children. In Journal of Education and Future year (Issue 14). https://doi.org/10.30786/jef.390814
- Callan, G. L., Marchant, G. J., Finch, W. H., & German, R. L. (2016). Metacognition, strategies, achievement, and demographics: Relationships across countries. Kuram ve Uygulamada Egitim Bilimleri, 16(5), 1485–1502. https://doi.org/10.12738/estp.2016.5.0137
- Clivaz, S., & Miyakawa, T. (2020). Cultural effects on mathematics lessons: through the international collaborative development of a lesson in two countries. HAL Open Science. https://hal.science/hal-02459223v1
- Duratun, A. D., & Maryani, I. (2023). The Influence of Self-Efficacy on Metacognition Skills of High Grade Students. International Journal of Elementary Education, 7(3), 403–409. https://doi.org/10.23887/ijee.v7i3.62125
- Gjone, G. (1998). Programs For the Education of Researchers in Mathematics Education. In Kluwer Academic.
- Gözde, A. (2020). Non-routine problem solving performances of mathematics teacher candidates. Educational Research and Reviews, 15(5), 214–224. https://doi.org/10.5897/ERR2020.3907
- Güner, P., & Erbay, H. N. (2021). Metacognitive Skills and Problem-Solving. International Journal of Research in Education and Science, 715–734. https://doi.org/10.46328/ijres.1594
- Henra, K., Budayasa, I. K., & Ismail. (2024). Revealing the dominant metacognitive activities of high school students in solving central tendency and dispersion problems based on gender. Journal on Mathematics Education, 15(4), 1357–1382. https://doi.org/10.22342/jme.v15i4.pp1357-1382
- Hermin, A. P., Pathuddin, Lefrida, R., & Alfisyahra. (2025). Exploring Students’ Metacognition in Numeracy Problem Solving: The Role of Reflective and Impulsive Cognitive Styles. Jurnal Pendidikan MIPA, 26(1), 688–707. https://doi.org/10.23960/jpmipa/v26i1.pp688-707
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- Joshi, R., Hadley, D., Nuthikattu, S., Fok, S., Goldbloom-Helzner, L., & Curtis, M. (2022). Concept Mapping as a Metacognition Tool in a Problem-Solving-Based BME Course During In-Person and Online Instruction. Biomedical Engineering Education, 2(2), 281–303. https://doi.org/10.1007/s43683-022-00066-3
- Magno, C. (2010). The role of metacognitive skills in developing critical thinking. Metacognition and Learning, 5(2), 137–156. https://doi.org/10.1007/s11409-010-9054-4
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- Miles MB, Saldana J, Huberman A 2014. Qualitative Data Analysis: A Methods Soucebook Arizona State. In SAGE Publications, Inc. University Third Edition
- Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2019). HIGHLIGHTS TIMSS 2019: International Results in Maths and Science. 32. https://www.skolporten.se/app/uploads/2020/12/timss-2019-highlights-1.pdf
- Ningsih, N. I. S., Maharani, S., Shofari, M. R., Verlanda, M. A., & Riyanto, O. R. (2023). The Influence of Self-efficacy on Self-Anxiety Based on Students’ Mathematics Learning. Journal of Mathematics Instruction, Social Research and Opinion, 2(3), 273–286. https://doi.org/10.58421/misro.v2i3.193
- OECD. (2019). PISA 2018 Results. In OECD Publishing: Vol. III. https://www.oecd.org/pisa/publications/pisa-2018-results-volume-iii-acd78851-en.htm
- Pathuddin, & Bennu, S. (2021). Metacognitive Skills of Students with High Mathematical Abilities in Solving Contextual Problems. Journal of Physics: Conference Series, 1832(1). https://doi.org/10.1088/1742-6596/1832/1/012048
- Pathuddin, Budayasa, I. K., & Lukito, A. (2018). Metacognitive Knowledge of a Student in Planning the Solution of Limit Problems. Journal of Physics: Conference Series, 1108(1). https://doi.org/10.1088/1742-6596/1108/1/012032
- Pathuddin, Ketut Budayasa, I., & Lukito, A. (2019). Metacognitive Activity of Male Students: Difference Field Independent-Dependent Cognitive Style. Journal of Physics: Conference Series, 1218(1). https://doi.org/10.1088/1742-6596/1218/1/012025
- Polya, G. (1945). How to Solve It A New Aspect of Mathematical Method.
- Prakoso, A. F., Subroto, W. T., Andriansyah, E. H., Sari, V. B. M., Ginanjar, A. E., & Srisuk, P. (2025). How do anxiety and self-efficacy affect the problem-solving skills of undergraduate economics students as prospective teachers in Indonesia? The role of metacognition as a mediating variable. Cogent Education, 12(1). https://doi.org/10.1080/2331186X.2025.2521160
- Ridlo, S., & Lutfiya, F. (2017). The Correlation between Metacognition Level with Self-Efficacy of Biology Education College Students. Journal of Physics: Conference Series, 824(1). https://doi.org/10.1088/1742-6596/824/1/012067
- Schwarzer, R., & Jerusalem, M. (1995). Measures in Health Psychology: A User’s Portfolio. Causal and Control Beliefs (J. Weinman, S. Wright, & M. Johnston, Eds.). NFER-¬‐NELSON.
- Shimizu, Y. (2022). Relation Between Mathematical Proof Problem Solving, Math Anxiety, Self-Efficacy, Learning Engagement, and Backward Reasoning. Journal of Education and Learning, 11(6), 62. https://doi.org/10.5539/jel.v11n6p62
- Sikdar, P. R. (2024). Development & Use of Progressive Techniques in Mathematics Education. Tech Horizons: Bridging Disciplines in the Era of Emerging Technologies.
- Situngkir, F. L., & Dewi, I. (2022). The view of mathematics education as science. International Journal of Trends in Mathematics Education Research, 5(3), 328–332. https://doi.org/10.33122/ijtmer.v5i3.155
- Subba, B. H., Chanunan, S., & Poonpaiboonpipat, W. (2025). A proposed constructivism-based instructional model to enhance metacognition and mathematical problem-solving skills in Bhutanese grade nine students. Journal on Mathematics Education, 16(1), 51–72. https://doi.org/10.22342/jme.v16i1.pp51-72
- Švecová, V. (2024). Math Anxiety and its Relation to the Success of Mathematical Problems. TEM Journal, 13(1), 207–212. https://doi.org/10.18421/TEM131-21
- Taamneh, M. A., Díez-Palomar, J., & Mallart-Solaz, A. (2024). Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem. Eurasia Journal of Mathematics, Science and Technology Education, 20(12). https://doi.org/10.29333/ejmste/15707
- Tchounwou, M., Okoye, Ebele. C., & Iseguede, F. (2023). Comparison of the Efficacy of Metacognition on Students’ Academic Performance Between Usa, France, Australia, and China. Advances in Social Sciences Research Journal, 10(7), 252–271. https://doi.org/10.14738/assrj.107.14833
- Wutsqa, D. U., Prihastuti, P. P., Fauzan, M., & Listyani, E. (2024). Radial Basis Function Neural Network with ensemble clustering for modeling mathematics achievement in Indonesia based on cognitive and non-cognitive factors. Journal on Mathematics Education, 15(3), 751–770. https://doi.org/10.22342/jme.v15i3.pp751-770
- Zakariya, Y. F. (2022). Improving students’ mathematics self-efficacy: A systematic review of intervention studies. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2022.986622
References
Abdelshiheed, M., Zhou, G., Maniktala, M., Barnes, T., & Chi, M. (2023). Metacognition and Motivation: The Role of Time-Awareness in Preparation for Future Learning. Department of Computer Science. http://arxiv.org/abs/2303.13541
Adhitama, I., Sujadi, I., & Pramudya, I. (2018). Discover the pythagorean theorem using interactive multimedia learning. Journal of Physics: Conference Series, 1008(1). https://doi.org/10.1088/1742-6596/1008/1/012066
Agbata, B. C., Obeng-Denteh, W., Kwabi, P. A., Abraham, S., Okpako, S. O., Arivi, S. S., Asante-Mensa, F., & Adu, G. W. K. (2024). Everyday uses of mathematics and the roles of a mathematics teacher. Science World Journal, 19(3), 819–827. https://doi.org/10.4314/swj.v19i3.29
Anggraini, E., Subanji, S., & Rahardjo, S. (2024). The Role of Self-Efficacy in Enhance Metacognitive and Academic Performance Through Problem-Solving. PRISMA, 13(2), 259. https://doi.org/10.35194/jp.v13i2.4382
Bandura, A. (1977). Self-efficacy: Toward a Unifying Theory of Behavioral Change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191
Birt, L., Scott, S., Cavers, D., Campbell, C., & Walter, F. (2022). Member checking: a tool to enhance trustworthiness or merely a nod to validation? Corresponding author (present address). King’s Research Portal. https://doi.org/10.1177/1049732316654870
Bozgün, K., & Pekdoğan, S. (2018). The Self-Efficacy as Predictors of the Metacognition Awareness in Children. In Journal of Education and Future year (Issue 14). https://doi.org/10.30786/jef.390814
Callan, G. L., Marchant, G. J., Finch, W. H., & German, R. L. (2016). Metacognition, strategies, achievement, and demographics: Relationships across countries. Kuram ve Uygulamada Egitim Bilimleri, 16(5), 1485–1502. https://doi.org/10.12738/estp.2016.5.0137
Clivaz, S., & Miyakawa, T. (2020). Cultural effects on mathematics lessons: through the international collaborative development of a lesson in two countries. HAL Open Science. https://hal.science/hal-02459223v1
Duratun, A. D., & Maryani, I. (2023). The Influence of Self-Efficacy on Metacognition Skills of High Grade Students. International Journal of Elementary Education, 7(3), 403–409. https://doi.org/10.23887/ijee.v7i3.62125
Gjone, G. (1998). Programs For the Education of Researchers in Mathematics Education. In Kluwer Academic.
Gözde, A. (2020). Non-routine problem solving performances of mathematics teacher candidates. Educational Research and Reviews, 15(5), 214–224. https://doi.org/10.5897/ERR2020.3907
Güner, P., & Erbay, H. N. (2021). Metacognitive Skills and Problem-Solving. International Journal of Research in Education and Science, 715–734. https://doi.org/10.46328/ijres.1594
Henra, K., Budayasa, I. K., & Ismail. (2024). Revealing the dominant metacognitive activities of high school students in solving central tendency and dispersion problems based on gender. Journal on Mathematics Education, 15(4), 1357–1382. https://doi.org/10.22342/jme.v15i4.pp1357-1382
Hermin, A. P., Pathuddin, Lefrida, R., & Alfisyahra. (2025). Exploring Students’ Metacognition in Numeracy Problem Solving: The Role of Reflective and Impulsive Cognitive Styles. Jurnal Pendidikan MIPA, 26(1), 688–707. https://doi.org/10.23960/jpmipa/v26i1.pp688-707
Jameson, M. M., Dierenfeld, C., & Ybarra, J. (2022). The Mediating Effects of Specific Types of Self-Efficacy on the Relationship between Math Anxiety and Performance. Education Sciences, 12(11). https://doi.org/10.3390/educsci12110789
Joshi, R., Hadley, D., Nuthikattu, S., Fok, S., Goldbloom-Helzner, L., & Curtis, M. (2022). Concept Mapping as a Metacognition Tool in a Problem-Solving-Based BME Course During In-Person and Online Instruction. Biomedical Engineering Education, 2(2), 281–303. https://doi.org/10.1007/s43683-022-00066-3
Magno, C. (2010). The role of metacognitive skills in developing critical thinking. Metacognition and Learning, 5(2), 137–156. https://doi.org/10.1007/s11409-010-9054-4
Meher, V., Baral, R., & Bhuyan, S. (2024). Examining impact of metacognitive interventions on self-efficacy of higher secondary school students: A quasi-experimental study. American Journal of Education and Learning, 9(2), 163–176. https://doi.org/10.55284/ajel.v9i2.1171
Miles MB, Saldana J, Huberman A 2014. Qualitative Data Analysis: A Methods Soucebook Arizona State. In SAGE Publications, Inc. University Third Edition
Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2019). HIGHLIGHTS TIMSS 2019: International Results in Maths and Science. 32. https://www.skolporten.se/app/uploads/2020/12/timss-2019-highlights-1.pdf
Ningsih, N. I. S., Maharani, S., Shofari, M. R., Verlanda, M. A., & Riyanto, O. R. (2023). The Influence of Self-efficacy on Self-Anxiety Based on Students’ Mathematics Learning. Journal of Mathematics Instruction, Social Research and Opinion, 2(3), 273–286. https://doi.org/10.58421/misro.v2i3.193
OECD. (2019). PISA 2018 Results. In OECD Publishing: Vol. III. https://www.oecd.org/pisa/publications/pisa-2018-results-volume-iii-acd78851-en.htm
Pathuddin, & Bennu, S. (2021). Metacognitive Skills of Students with High Mathematical Abilities in Solving Contextual Problems. Journal of Physics: Conference Series, 1832(1). https://doi.org/10.1088/1742-6596/1832/1/012048
Pathuddin, Budayasa, I. K., & Lukito, A. (2018). Metacognitive Knowledge of a Student in Planning the Solution of Limit Problems. Journal of Physics: Conference Series, 1108(1). https://doi.org/10.1088/1742-6596/1108/1/012032
Pathuddin, Ketut Budayasa, I., & Lukito, A. (2019). Metacognitive Activity of Male Students: Difference Field Independent-Dependent Cognitive Style. Journal of Physics: Conference Series, 1218(1). https://doi.org/10.1088/1742-6596/1218/1/012025
Polya, G. (1945). How to Solve It A New Aspect of Mathematical Method.
Prakoso, A. F., Subroto, W. T., Andriansyah, E. H., Sari, V. B. M., Ginanjar, A. E., & Srisuk, P. (2025). How do anxiety and self-efficacy affect the problem-solving skills of undergraduate economics students as prospective teachers in Indonesia? The role of metacognition as a mediating variable. Cogent Education, 12(1). https://doi.org/10.1080/2331186X.2025.2521160
Ridlo, S., & Lutfiya, F. (2017). The Correlation between Metacognition Level with Self-Efficacy of Biology Education College Students. Journal of Physics: Conference Series, 824(1). https://doi.org/10.1088/1742-6596/824/1/012067
Schwarzer, R., & Jerusalem, M. (1995). Measures in Health Psychology: A User’s Portfolio. Causal and Control Beliefs (J. Weinman, S. Wright, & M. Johnston, Eds.). NFER-¬‐NELSON.
Shimizu, Y. (2022). Relation Between Mathematical Proof Problem Solving, Math Anxiety, Self-Efficacy, Learning Engagement, and Backward Reasoning. Journal of Education and Learning, 11(6), 62. https://doi.org/10.5539/jel.v11n6p62
Sikdar, P. R. (2024). Development & Use of Progressive Techniques in Mathematics Education. Tech Horizons: Bridging Disciplines in the Era of Emerging Technologies.
Situngkir, F. L., & Dewi, I. (2022). The view of mathematics education as science. International Journal of Trends in Mathematics Education Research, 5(3), 328–332. https://doi.org/10.33122/ijtmer.v5i3.155
Subba, B. H., Chanunan, S., & Poonpaiboonpipat, W. (2025). A proposed constructivism-based instructional model to enhance metacognition and mathematical problem-solving skills in Bhutanese grade nine students. Journal on Mathematics Education, 16(1), 51–72. https://doi.org/10.22342/jme.v16i1.pp51-72
Švecová, V. (2024). Math Anxiety and its Relation to the Success of Mathematical Problems. TEM Journal, 13(1), 207–212. https://doi.org/10.18421/TEM131-21
Taamneh, M. A., Díez-Palomar, J., & Mallart-Solaz, A. (2024). Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem. Eurasia Journal of Mathematics, Science and Technology Education, 20(12). https://doi.org/10.29333/ejmste/15707
Tchounwou, M., Okoye, Ebele. C., & Iseguede, F. (2023). Comparison of the Efficacy of Metacognition on Students’ Academic Performance Between Usa, France, Australia, and China. Advances in Social Sciences Research Journal, 10(7), 252–271. https://doi.org/10.14738/assrj.107.14833
Wutsqa, D. U., Prihastuti, P. P., Fauzan, M., & Listyani, E. (2024). Radial Basis Function Neural Network with ensemble clustering for modeling mathematics achievement in Indonesia based on cognitive and non-cognitive factors. Journal on Mathematics Education, 15(3), 751–770. https://doi.org/10.22342/jme.v15i3.pp751-770
Zakariya, Y. F. (2022). Improving students’ mathematics self-efficacy: A systematic review of intervention studies. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2022.986622