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

Authors

  • Suri Toding Lembang Universitas Kristen Indonesia Toraja https://orcid.org/0009-0002-1392-0300
  • Rubianus Rubianus Universitas Kristen Indonesia Toraja, Indonesia
  • Borotoding Deanti Ernita Universitas Kristen Indonesia Toraja, Indonesia
  • Risno Kilala Universitas Kristen Indonesia Toraja, Indonesia

DOI:

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

Keywords:

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

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.

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Published

2026-06-30

How to Cite

Lembang, S. T., Rubianus, R., Ernita, B. D., & Kilala, R. (2026). Metacognitive Processes in Solving Direct and Inverse Proportion Problems: A Qualitative Study of Junior High School Students. AL-ISHLAH: Jurnal Pendidikan, 18(2), 2850–2858. https://doi.org/10.35445/alishlah.v18i2.8980

Issue

Vol. 18 No. 2 (2026): JUNE 2026

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