Dissecting Students' Strategies: How Do Polya's Steps Reveal Problem-Solving Abilities?

Thalita Husna Fauztina; Sri Sutarni

doi:10.31764/paedagoria.v17i2.37884

Dissecting Students' Strategies: How Do Polya's Steps Reveal Problem-Solving Abilities?

Thalita Husna Fauztina, Sri Sutarni

Abstract

This study aims to analyze junior high school students’ mathematical problem-solving abilities on Geometric Sequences and Series based on Polya’s problem-solving steps. A descriptive qualitative approach was employed involving 27 eighth-grade students. The research stages included administering a contextual problem-solving test, selecting subjects through purposive sampling, conducting semi-structured interviews, and analyzing data using the Miles and Huberman model (data reduction, data display, and conclusion drawing). Four students representing high, medium, and low ability levels were selected as the main subjects. Data were collected using contextual problem-solving tests and supported by semi-structured interviews. The analysis focused on students’ performance across Polya’s four stages: understanding the problem, devising a plan, carrying out the plan, and looking back. Students’ problem-solving performance showed clear differences across Polya’s four stages. High-ability students applied all stages systematically, with only minor notation errors. Medium-ability students demonstrated sufficient conceptual understanding but struggled with planning strategies, maintaining procedural consistency, and interpreting problems, often leading to incorrect formula selection and ratio miscalculations. In contrast, low-ability students faced difficulties from the initial stage, particularly in identifying given information, distinguishing arithmetic and geometric concepts, and selecting appropriate formulas. Their errors commonly included using incorrect models, incomplete procedures, and lack of verification. These findings indicate that successful mathematical problem solving depends not only on formula mastery but also on conceptual understanding, strategic planning, and verification skills. Therefore, instruction should emphasize structured problem-solving processes and strengthen students’ conceptual and metacognitive abilities.

Keywords

Mathematical Problem-Solving; Polya’s Steps; Geometric Sequences and Series; Junior High School Students.

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DOI: https://doi.org/10.31764/paedagoria.v17i2.37884