Exploring Polya's Problem-Solving Stages, Cognitive Components, and Role Change Dynamics in Mathematical Problem-Solving Discussions - Abdul Haris; Muslim Muslim; Mutmainah Mutmainah; Adi Apriadi Adiansha (Jurnal Pendidikan Progresif, 2026)
This study aims to examine the effectiveness of integrating Polya's problem-solving stages with commognitive discourse practices in collaborative learning, and to describe the associations among Polya's stages, commognitive components, and the dynamics of role change in mathematical problem-solving discussions, as well as their contributions to the development of mathematical thinking quality. A quantitative approach with a quasi-experimental Non-Equivalent Control Group Design was employed. Participants were pre-service teacher students at STKIP Taman Siswa Bima, assigned to an experimental class (n = 30) and a control class (n = 30). Data were collected using a mathematics problem-solving test based on Polya's four stages and structured observation instruments that measured cognitive components and changes in discussion roles. Data analysis included Rasch-model-based instrument quality testing, normality and homogeneity prerequisite tests, a paired-samples t-test for each class separately to assess within-group pre-post differences (df = 29 per class), an independent-samples t-test on N-Gain scores to compare treatment effectiveness between classes (df = 58), and an N-Gain analysis to assess treatment effectiveness. Instruments demonstrated strong validity (PTMEA Corr. = 0.40–0.65) and high reliability (person reliability = 0.87–0.88). The experimental class showed significantly greater improvement in mathematical problem-solving ability than the control class (posttest means: 49.5 vs. 43.7). The paired t-test confirmed a significant pre–post improvement in the experimental class [t(29) = 2.435, p = 0.021] but not in the control class [t(29) = 1.295, p = 0.206]. Observational data indicated that activation of commognitive components:  consistent use of mathematical terms, visual mediators, and justification narratives, and the emergence of dynamic role changes during discussion were associated with improvements in problem-solving quality. Mathematical problem solving develops more effectively when Polya's heuristic stages are integrated with cognitive-discursive practices that foster epistemic role changes in collaborative discussions. This integration offers an innovative framework for designing meaningful, discussion-based mathematics learning. Keywords: mathematical problem solving, Polya’s stages, commognitive, collaborative discussion, role change.