From Linearity to Iteration: Navigating Polya's Problem-Solving Stages in an e-PBL Geometry Environment

Haqq, Arif Abdul
Wahid, Sirojudin
Izzati, Nurma
Riyanto, Onwardono Rit
Alves, Dionisio Aquino
Sulistiawati, Sulistiawati
Nugraha, Aditiya Eka

Mosharafa: Jurnal Pendidikan Matematika
Vol. 15 No. 1 (2026): January

Penelitian ini mengkaji bagaimana mahasiswa mengalami dan memaknai tahapan pemecahan masalah Polya saat mengerjakan tugas geometri dalam lingkungan electronic Problem-Based Learning (e-PBL) yang diimplementasikan melalui sistem manajemen pembelajaran berbasis Moodle yang dikustomisasi. Penelitian ini menggunakan desain deskriptif kualitatif dengan sumber data berupa artefak pemecahan masalah tertulis, wawancara semi-terstruktur, dan jejak digital selama e-PBL. Data dianalisis menggunakan analisis tematik Braun dan Clarke dengan pengodean deduktif berdasarkan empat tahap Polya dan pengodean induktif untuk menangkap pola penalaran yang muncul. Hasil penelitian menunjukkan bahwa pemecahan masalah berlangsung secara dinamis dan rekursif. Tahap memahami dan merencanakan melibatkan penafsiran ulang representasi multimodal, sedangkan tahap pelaksanaan ditandai oleh pergeseran representasi yang memperjelas konsep. Prompt reflektif dalam e-PBL mendukung deteksi kesalahan dan penguatan konsep, serta menegaskan peran tahap evaluasi. This study examines how students experience and interpret Polya’s problem-solving stages while working on geometry tasks in an electronic Problem-Based Learning (e-PBL) environment implemented through a customized Moodle based learning management system. Using a qualitative descriptive design, data were collected from written problem-solving artefacts, semi-structured interviews, and digital traces generated during e-PBL activities. The data were analyzed using thematic analysis following Braun and Clarke, combining deductive coding based on Polya’s four stages with inductive coding to capture emerging reasoning patterns. The findings indicate that problem-solving is enacted as a dynamic and recursive process rather than a linear sequence. Understanding and planning involve repeated reinterpretation of multimodal representations, while execution is characterized by representational shifts that support conceptual clarity. Reflective prompts in e-PBL facilitate error detection and conceptual consolidation, highlighting the importance of the evaluative stage.