Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study

Siti Mawaddah; - Purwanto; Nengah Parta; Sisworo Sisworo

doi:10.17275/per.25.78.12.6

Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study

Abstract

This study aims to explore the metacognitive misdirection experienced by prospective mathematics teachers during mathematical problem solving, with a focus on metacognitive skills such as planning, monitoring, and evaluating. The problem-solving framework adopted in this study is Polya's method. The research participants were selected through purposive sampling based on specific criteria: successful completion of the Calculus 1 course, the demonstrated ability to solve mathematical problems using Polya’s structured problem-solving steps, indications of metacognitive misdirection, and willingness to serve as information sources. Of the sixty-three prospective mathematics teachers enrolled in the mathematics education program at Universitas Lambung Mangkurat, fourteen met the selection criteria, and three were chosen as the main participants. The data were collected through mathematical problem-solving tasks (MPST) and interviews. The MPST focused on the application of functions and derivatives. This study shows that metacognitive misdirection occurs at various steps of the problem-solving process: during the understanding-the-problem step (manifested as an error detection red flag), the carrying-out-the-plan step (characterized by error detection, lack of progress, and anomalous results red flags) and looking-back step (again marked by an error detection red flag). Among these, error detection emerged as the most frequently observed red flag. The study also identifies two distinct types of metacognitive misdirection processes: pseudo-metacognitive misdirection and essential metacognitive misdirection.

Keywords

metacognitive misdirection, mathematical problem solving, Polya's Mehod, Red flag

References

Ader, E. (2019). What would you demand beyond mathematics? Teachers’ promotion of students’ self-regulated learning and metacognition. ZDM - Mathematics Education, 51(4), 613–624. https://doi.org/10.1007/s11858-019-01054-8
Aljaberi, N. M., & Gheith, E. (2015). University students’ level of metacognitive thinking and their ability to solve problems. American International Journal of Contemporary Research,5(3). 121-134. https://www.aijcrnet.com/journals/Vol_5_No_3_June_2015/15.pdf
Ardiyaningrum, M., Retnowati, T. H., Jailani, & Trisniawati. (2019). Online measurement to assess problem-solving skills based on multimedia instrument. Journal of Physics: Conference Series, 1339(1), 1-5. https://doi.org/10.1088/1742-6596/1339/1/012065
Aşık, G., & Erktin, E. (2019). Metacognitive experiences: Mediating the relationship between metacognitive knowledge and problem solving. Egitim ve Bilim, 44(197), 85–103. https://doi.org/10.15390/EB.2019.7199
Becker, F., Wirzberger, M., Pammer-Schindler, V., Srinivas, S., & Lieder, F. (2023). Systematic metacognitive reflection helps people discover far-sighted decision strategies: A process-tracing experiment. In Judgment and Decision Making (Vol. 18). Society for Judgment and Decision making. https://doi.org/10.1017/jdm.2023.16
Carson, J. (2007). A problem with problem solving: Teaching thinking without teaching knowledge. The Mathematics Educator17(2), 7-14. https://files.eric.ed.gov/fulltext/EJ841561.pdf
Faradiba, S. S., & Alifiani, A. (2020). Metacognitive blindness in mathematics problem-solving. Journal of Education and Learning Mathematics Research (JELMaR), 1(2), 43–49. https://doi.org/10.37303/jelmar.v1i2.27
Faradiba, S. S., Sa’dijah, C., Parta, I. N., & Rahardjo, S. (2019). Looking without seeing: The role of metacognitive blindness of student with high math anxiety. International Journal of Cognitive Research in Science, Engineering and Education, 7(2), 53–65. https://doi.org/10.5937/IJCRSEE1902053F
Faradiba, S. S., Sadijah, C., Parta, I. N., & Rahardjo, S. (2019). Metacognitive therapy for mathematics disorder. Journal of Physics: Conference Series, 1157(4), 1-6. https://doi.org/10.1088/1742-6596/1157/4/042079
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

Goos, M. (2002). Understanding metacognitive failure. Journal of Mathematical Behavior, 21(3), 283–302. https://doi.org/10.1016/S0732-3123(02)00130-X
Goos, M., Galbraith, P., & Renshaw, P. (2000). A money problem: A source of insight into problem solving action. International Journal for Mathematics Teaching and Learning, 1–21. https://www.researchgate.net/publication/43487463
Güner, P., & Erbay, H. N. (2021). Metacognitive skills and problem-solving. International Journal of Research in Education and Science, 7(3), 715–734. https://doi.org/10.46328/ijres.1594
Habib, M., Amjad, A. I., Aslam, S., Saleem, Z., & Saleem, A. (2024). Navigating Math Minds: Unveiling the Impact of Metacognitive Strategies on 8th Grade Problem- Solvers Abilities. International Electronic Journal of Elementary Education, 17(1), 135–144. https://doi.org/10.26822/iejee.2024.368
Haury, D. L. (2002). What is problem solving? The connected teacher's companion to problem solving in science and mathematics, 1–31. https://www.academia.edu/2484646/What_is_problem_solving
Huda, N., & Marzal, J. (2023). Scaffolding Appropriation for Students’ Metacognitive Failure in Solving Mathematical Problems (pp. 245–254). https://doi.org/10.2991/978-2-38476-012-1_32
Huda, N., Sutawidjaja, A., Subanji, & Rahardjo, S. (2018). The errors of metacognitive evaluation on metacognitive failure of students in mathematical problem solving. Journal of Physics: Conference Series, 1008(1), 1–11. https://doi.org/10.1088/1742-6596/1008/1/012073
Huda, N., Sutawidjaja, A., Subanji, S., & Rahardjo, S. (2019). Investigation of students’ metacognitive failures in mathematical problem solving based on metacognitive behavior. Journal of Physics: Conference Series, 1157(3), 1–7. https://doi.org/10.1088/1742-6596/1157/3/032102
Joseph, N. (2010). Metacognition needed: Teaching middle and high school students to develop strategic learning skills. Preventing School Failure: Alternative Education for Children and Youth, 54(2), 99–103. https://doi.org/10.1080/10459880903217770
Kaya, Z. B., & Kepceoglu, I. (2022). Metacognitive failures of preservice mathematics teachers ın problem solving. Athens Journal of Sciences, 9(4), 273–290. https://doi.org/10.30958/ajs.9-4-4
Knox, H. (2017). Using writing strategies in math to increase metacognitive skills for the gifted learner. Gifted Child Today, 40(1), 43–47. https://doi.org/10.1177/1076217516675904
Krieger, F., Azevedo, R., Graesser, A. C., & Greiff, S. (2022). Introduction to the special issue: the role of metacognition in complex skills - spotlights on problem solving, collaboration, and self-regulated learning. Metacognition and Learning, 17(3), 683–690. https://doi.org/10.1007/s11409-022-09327-6
Krulik, S., & Rudnick, J. A. (1988). Problem Solving: A Handbook for Elementary School Teachers. In Africa’s potential for the ecological intensification of agriculture.
Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20–40. https://doi.org/10.29333/iejme/272
Lai, E. R. (2011). Metacognition: A Literature Review Research Report. http://www.pearsonassessments.com/research.
Lesh, R., & Zawojewski, J. (2007). Problem Solving and Modeling. In: Lester, F., Ed., Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing.
Livingston, J. A. (2003). Metacognition: An Overview. Acedemic Press.
Ozdogan, S. S., Ozçakir, B., & Orhan, B. (2019). A case of teacher and student mathematical problem-solving behaviors from the perspective of cognitive-metacognitive framework. Studia Paedagogica, 24(4), 221–243. https://doi.org/10.5817/SP2019-4-10
Özsoy, G., & Ataman, A. (2009). The effect of metacognitive strategy training on mathematical problem-solving achievement. In International Electronic Journal of Elementary Education (Vol. 1, Issue 2). www.iejee.com
Papleontiou-Louca, E. (2003). The concept and instruction of metacognition. Teacher Development, 7(1), 9–30. https://doi.org/10.1080/13664530300200184
Polya, G. (1985). How to Solve it. In Princeton: University Press. https://doi.org/10.1017/cbo9780511616747.007
Reinhard, A., Felleson, A., Turner, P., & Green, M. (2021). Assessing the Impact of Metacognitive Post-Reflection Exercises on Problem-Solving Skillfulness. https://doi.org/10.1103/PhysRevPhysEducRes.18.010109
Rozak, A., Subanji, Nusantara, T., & Sulandra, I. M. (2018, January). Identification Metacognitive Failure on Mathematics Problem Solving. Paper presented at the University of Muhammadiyah Malang's 1st International Conference of Mathematics Education (INCOMED 2017). https://doi.org/10.2991/incomed-17.2018.23
Schoenfeld, A. H. (1985). Mathematical Problem Solving. In Educational Studies in Mathematics. Academic Press, Inc. https://doi.org/10.1007/BF00305624
Schraw, G., & Graham, T. (2010). Helping gifted students develop metacognitive awareness. Roeper Review, 20(1), 4–8. https://doi.org/ 10.1080/02783199709553842
Schraw, G., & Moshman, D. (1995). Metacognitive theories. Educational Psychology Review, 7(4), 351–371. https://doi.org/10.1007/BF02212307
Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. International Perspectives on the Teaching and Learning of Mathematical Modelling, 1, 165–180. https://doi.org/10.1007/978-94-007-0910-2_18
Stillman, G. (2020). Metacognition. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (Second Ediiont, 608–610).
Tachie, S. A. (2019). Metacognitive skills and strategies application: How this helps learners in mathematics problem-solving. Eurasia Journal of Mathematics, Science and Technology Education, 15(5). https://doi.org/10.29333/ejmste/105364
Whitebread, D., Coltman, P., Pasternak, D. P., Sangster, C., Grau, V., Bingham, S., Almeqdad, Q., & Demetriou, D. (2009). The development of two observational tools for assessing metacognition and self-regulated learning in young children. Metacognition and Learning, 4(1), 63–85. https://doi.org/10.1007/s11409-008-9033-1
Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25–48. https://doi.org/10.1007/BF03217394
Winarti, Ambaryani, S. E., & Putranta, H. (2022). Improving Learners’ Metacognitive Skills with Self-Regulated Learning based Problem-Solving. International Journal of Instruction, 15(2), 139–154. https://doi.org/10.29333/iji.2022.1528a

Details

Primary Language

English

Subjects

Specialist Studies in Education (Other)

Journal Section

Research Article

Authors

Siti Mawaddah ^*
0000-0003-0599-6153
Indonesia

- Purwanto
0000-0003-0974-4068
Indonesia

Nengah Parta
0000-0003-4255-9323
Indonesia

Sisworo Sisworo
0000-0002-1962-082X
Indonesia

Early Pub Date

November 4, 2025

Publication Date

November 1, 2025

Submission Date

December 30, 2024

Acceptance Date

August 6, 2025

Published in Issue

Year 2025 Volume: 12 Number: 6

DOI

https://doi.org/10.17275/per.25.78.12.6

IZ

https://izlik.org/JA67RJ28NH

APA

Mawaddah, S., Purwanto, -, Parta, N., & Sisworo, S. (2025). Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study. Participatory Educational Research, 12(6), 55-73. https://doi.org/10.17275/per.25.78.12.6

AMA

1.Mawaddah S, Purwanto, Parta N, Sisworo S. Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study. PER. 2025;12(6):55-73. doi:10.17275/per.25.78.12.6

Chicago

Mawaddah, Siti, - Purwanto, Nengah Parta, and Sisworo Sisworo. 2025. “Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study”. Participatory Educational Research 12 (6): 55-73. https://doi.org/10.17275/per.25.78.12.6.

EndNote

Mawaddah S, Purwanto -, Parta N, Sisworo S (November 1, 2025) Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study. Participatory Educational Research 12 6 55–73.

IEEE

[1]S. Mawaddah, - Purwanto, N. Parta, and S. Sisworo, “Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study”, PER, vol. 12, no. 6, pp. 55–73, Nov. 2025, doi: 10.17275/per.25.78.12.6.

ISNAD

Mawaddah, Siti - Purwanto, - - Parta, Nengah - Sisworo, Sisworo. “Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study”. Participatory Educational Research 12/6 (November 1, 2025): 55-73. https://doi.org/10.17275/per.25.78.12.6.

JAMA

1.Mawaddah S, Purwanto -, Parta N, Sisworo S. Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study. PER. 2025;12:55–73.

MLA

Mawaddah, Siti, et al. “Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study”. Participatory Educational Research, vol. 12, no. 6, Nov. 2025, pp. 55-73, doi:10.17275/per.25.78.12.6.

Vancouver

1.Siti Mawaddah, - Purwanto, Nengah Parta, Sisworo Sisworo. Metacognitive Misdirection of Prospective Mathematics Teachers in Mathematical Problem Solving - an Explorative Study. PER. 2025 Nov. 1;12(6):55-73. doi:10.17275/per.25.78.12.6