Jurnal Pendidikan Progresif
Vol 16, No 2 (2026): Jurnal Pendidikan Progresif

Exploring Polya's Problem-Solving Stages, Cognitive Components, and Role Change Dynamics in Mathematical Problem-Solving Discussions

Abdul Haris (Department of Mathematics Education, STKIP Taman Siswa Bima)
Muslim Muslim (Master'
s Program in Pedagogy Education, STKIP Taman Siswa Bima)

Mutmainah Mutmainah (Department of Mathematics Education, Universitas Nggusuwaru)
Adi Apriadi Adiansha (Department of Primary School Teacher Education, STKIP Taman Siswa Bima)



Article Info

Publish Date
30 May 2026

Abstract

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.

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Journal Info

Abbrev

jpp

Publisher

Subject

Education

Description

urnal Pendidikan Progresif is an academic journal that published all the studies in the areas of education, learning, teaching, curriculum development, learning environments, teacher education, educational technology, educational developments from various types of research such as surveys, research ...