Metacognitive Processes in Solving Direct and Inverse Proportion Problems: A Qualitative Study of Junior High School Students

Suri Toding Lembang; Rubianus Rubianus; Borotoding Deanti Ernita; Risno Kilala

doi:10.35445/alishlah.v18i2.8980

Metacognitive Processes in Solving Direct and Inverse Proportion Problems: A Qualitative Study of Junior High School Students

Suri Toding Lembang, Rubianus Rubianus, Borotoding Deanti Ernita, Risno Kilala

Abstract

Metacognitive regulation plays a crucial role in mathematical problem solving, yet limited qualitative research has examined how students employ planning, monitoring, and evaluation when solving direct and inverse proportion problems. These concepts require students to interpret proportional relationships rather than merely apply computational procedures, making them highly dependent on reflective thinking. This study aimed to analyze the metacognitive processes demonstrated by students with different levels of metacognitive ability while solving proportional reasoning problems. This qualitative descriptive case study involved three Grade VIII students from UPT SMP Negeri 1 Bittuang, representing high, medium, and low metacognitive ability levels. Participants were selected through purposive sampling based on the results of a Metacognitive Awareness Inventory and a proportional reasoning test. Data were collected using problem-solving tasks and semi-structured interviews and analyzed through thematic analysis involving open, axial, and selective coding, supported by triangulation across written work, interview transcripts, and observations. The findings revealed distinct patterns of metacognitive regulation across the three participants. High-metacognitive students demonstrated systematic planning, continuous monitoring, and comprehensive evaluation. Medium-metacognitive students performed adequate planning and procedural monitoring but showed limited conceptual monitoring and evaluation. Low-metacognitive students relied primarily on trial-and-error strategies with minimal evidence of planning, monitoring, or reflective evaluation. Across all ability levels, evaluation emerged as the weakest metacognitive component. The study concludes that metacognitive components develop unevenly and operate as an integrated regulatory system that substantially influences mathematical problem solving. The findings highlight the importance of explicitly incorporating metacognitive scaffolding into mathematics instruction to strengthen students’ reflective thinking and proportional reasoning.

Keywords

metacognition; problem solving; direct proportion; inverse proportion; mathematics education

References

Aditomo, A., & Klieme, E. (2020). Forms of student engagement in PISA 2015: Exploring the relationship with metacognition. Learning and Instruction, 66, 101299. https://doi.org/10.1016/j.learninstruc.2019.101299

Callan, G. L., & Cleary, T. J. (2018). Self-regulated learning in mathematics: A review. Educational Psychology Review, 30(3), 903–933. https://doi.org/10.1007/s10648-018-9440-8

Chairani, N. (2016). Metakognisi dalam pembelajaran matematika. Deepublish.

Efklides, A. (2011). Interactions of metacognition with motivation and affect in self-regulated learning: The MASRL model. Educational Psychologist, 46(1), 6–25. https://doi.org/10.1080/00461520.2011.538645

Efklides, A. (2020). Metacognition and affect: What can metacognitive experiences tell us about the learning process? Educational Psychology Review, 32, 1–30. https://doi.org/10.1007/s10648-020-09527-4

Elita, S., Habibi, M., Putra, T., & Wulandari, Y. (2019). Students’ metacognitive evaluation skills in mathematical problem-solving. Journal of Physics: Conference Series, 1188(1), 012063. https://doi.org/10.1088/1742-6596/1188/1/012063

Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231–235). Lawrence Erlbaum.

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

Gurat, M., & Medula, C. (2016). Metacognitive strategies in mathematical problem solving: A study among Filipino students. International Journal of Learning, Teaching and Educational Research, 15(5), 104–117.

Jia, X., Li, W., & Cao, L. (2019). The role of metacognitive components in creative thinking. Frontiers in Psychology, 10, 2404. https://doi.org/10.3389/fpsyg.2019.02404

Ledshisa, I. A., & Murtiyasa, B. (2023). Metacognition indicators in mathematics problem solving. JRAMathEdu: Journal of Research and Advances in Mathematics Education, 8(2), 112–126.

Lembang, S. T. (2022). The analysis concept of integers counting operations in traditional Toraja games “Si Goal” and “Si Patte’”. AIP Conference Proceedings, 2600, 020020. https://doi.org/10.1063/5.0113329

Magiera, M. T., & Zawojewski, J. S. (2018). Characterizing shifts in middle school students’ metacognitive functioning during mathematical problem solving. Mathematical Thinking and Learning, 20(3), 203–230. https://doi.org/10.1080/10986065.2018.1474532

Nelson, T. O., & Narens, L. (1990). Metamemory: A theoretical framework and new findings. In G. H. Bower (Ed.), Psychology of learning and motivation (Vol. 26, pp. 125–173). Academic Press. https://doi.org/10.1016/S0079-7421(08)60053-5

Pratiwi, D. (2019). Analysis of student errors in solving mathematical problems based on metacognitive skills. Journal of Physics: Conference Series, 1321(3), 032059. https://doi.org/10.1088/1742-6596/1321/3/032059

Putra, D. (2020). Students’ metacognitive awareness and error detection in mathematical problem solving. International Journal of Scientific & Technology Research, 9(4), 122–128.

Salam, M., Ibrahim, N. H., & Sukardjo, M. (2020). Strategies of metacognition based on behavioural learning to improve students’ mathematics ability. International Journal of Instruction, 13(2), 61–72. https://doi.org/10.29333/iji.2020.1325a

Sumaryanta, S., Isnarto, I., & Wijaya, A. (2023). Students’ mathematical problem-solving difficulties in Indonesian secondary schools. International Journal of Education and Practice, 11(1), 45–59.

Susanti, E., Widodo, A., & Nurhayati, S. (2023). The contribution of metacognitive awareness to mathematical problem solving: A structural equation modeling approach. Thinking Skills and Creativity, 49, 101301. https://doi.org/10.1016/j.tsc.2023.101301

Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2019). Difficulties in solving context-based mathematics problems: Students’ errors and strategies. International Journal of Science and Mathematics Education, 17(4), 829–848. https://doi.org/10.1007/s10763-018-9891-3

DOI: https://doi.org/10.35445/alishlah.v18i2.8980