STUDENTS' PROBLEM-SOLVING ABILITY IN THREE-VARIABLE LINEAR SYSTEMS BASED ON POLYA AND COGNITIVE STYLES

Abstract

Mathematical problem-solving ability is an essential competency in mathematics learning and may be influenced by students’ cognitive characteristics. This study aims to describe students’ mathematical problem-solving ability in solving Systems of Three-Variable Linear Equations (SPLTV) based on Polya’s problem-solving stages: understanding the problem, devising a plan, carrying out the plan, and looking back, viewed from Field-Independent (FI) and Field-Dependent (FD) cognitive styles. The study employed a qualitative approach with a descriptive design. The participants were five students purposively selected, consisting of two FI students and three FD students. The Group Embedded Figures Test (GEFT) was used to identify students’ cognitive styles, while a mathematical problem-solving test was administered to assess initial ability and select representative participants. Data were collected through written problem-solving tests, semi-structured interviews, and documentation. Data credibility was established through time triangulation, while data were analyzed using the Miles and Huberman interactive model, involving data reduction, data display, and conclusion drawing. The findings indicate that FI students tended to successfully complete all four Polya stages systematically. FD students demonstrated more varied abilities; some experienced difficulties in constructing mathematical models, carrying out solution procedures, and checking their answers. However, one FD student successfully completed all Polya stages, supported by regular practice, independent and collaborative learning, and persistence. These findings suggest that cognitive style is associated with students’ problem-solving profiles but is not the sole factor influencing their performance.

Kemampuan pemecahan masalah matematis merupakan kompetensi penting dalam pembelajaran matematika dan dapat dipengaruhi oleh karakteristik kognitif siswa. Penelitian ini bertujuan mendeskripsikan kemampuan pemecahan masalah matematis siswa dalam menyelesaikan Sistem Persamaan Linear Tiga Variabel (SPLTV) berdasarkan tahapan Polya, yaitu memahami masalah, menyusun rencana, melaksanakan rencana, dan memeriksa kembali, ditinjau dari gaya kognitif Field-Independent (FI) dan Field-Dependent (FD). Penelitian menggunakan pendekatan kualitatif dengan desain deskriptif. Subjek penelitian terdiri atas lima siswa yang dipilih secara purposif, yaitu dua siswa FI dan tiga siswa FD. Group Embedded Figures Test (GEFT) digunakan untuk mengidentifikasi gaya kognitif, sedangkan tes pemecahan masalah digunakan untuk mengidentifikasi kemampuan awal dan menentukan subjek penelitian. Data dikumpulkan melalui tes tertulis, wawancara semi-terstruktur, dan dokumentasi. Kredibilitas data diuji melalui triangulasi waktu, sedangkan analisis data menggunakan model interaktif Miles dan Huberman melalui reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa siswa FI cenderung mampu memenuhi keempat tahapan Polya secara sistematis. Siswa FD menunjukkan kemampuan yang lebih beragam; sebagian mengalami kesulitan dalam membangun model matematika, melaksanakan prosedur, dan memeriksa kembali jawaban. Namun, satu siswa FD mampu memenuhi seluruh tahapan Polya karena didukung kebiasaan berlatih, belajar mandiri maupun bersama teman, dan kegigihan. Temuan menunjukkan bahwa gaya kognitif berkaitan dengan profil kemampuan pemecahan