Electronic Theses and Dissertation

Penelitian ini bertujuan untuk menganalisis proses berpikir siswa dalam menyelesaikan soal cryptarithm serta menguji pengaruh metacognitive belief terhadap proses berpikir tersebut. Penelitian menggunakan pendekatan mixed methods dengan desain explanatory sequential. Tahap kuantitatif melibatkan 75 siswa kelas XI SMA Inshafuddin Banda Aceh yang mengikuti tes kemampuan menyelesaikan soal cryptarithm dan angket metacognitive belief. Data dianalisis menggunakan statistik deskriptif dan regresi linear sederhana. Tahap kualitatif dilakukan terhadap 7 siswa yang dipilih secara purposive berdasarkan kategori metacognitive belief tinggi, sedang, dan rendah melalui wawancara semi-terstruktur. Hasil penelitian menunjukkan bahwa kemampuan menyelesaikan soal cryptarithm memiliki nilai rata-rata 75,65. Analisis regresi menunjukkan bahwa metacognitive belief berpengaruh positif dan signifikan terhadap kemampuan menyelesaikan soal cryptarithm (R = 0,992; R² = 0,984; p < 0,001). Analisis kualitatif mengidentifikasi tiga pola proses berpikir siswa, yaitu berpikir sistematis-reflektif, berpikir semi-sistematis, dan berpikir trial and error. Siswa dengan metacognitive belief tinggi menunjukkan kemampuan memahami masalah, menyusun strategi, memonitor, dan mengevaluasi penyelesaian secara lebih sistematis dan reflektif. Sebaliknya, siswa dengan metacognitive belief rendah cenderung menggunakan strategi trial and error tanpa monitoring dan evaluasi yang memadai. Temuan ini menunjukkan bahwa metacognitive belief tidak hanya berkontribusi terhadap hasil penyelesaian soal, tetapi juga memengaruhi kualitas proses berpikir siswa dalam menyelesaikan masalah matematika nonrutin seperti cryptarithm.

Keywords: cryptarithm; metacognitive belief; proses berpikir

Abstract This study analyzed students' thinking processes in solving cryptarithm problems and to examine the influence of metacognitive beliefs on these thinking processes. The study employed a mixed-methods approach with an explanatory sequential design. The quantitative phase involved 75 Grade 11 students at one of the Islamic High Schools in Banda Aceh, Indonesia, who took a test of their ability to solve cryptarithm problems and completed a metacognitive belief questionnaire. Data were analyzed using descriptive statistics and simple linear regression. The qualitative phase involved 7 students, purposively selected based on high, moderate, and low levels of metacognitive beliefs, who were interviewed using semi-structured interviews. The results revealed that the average score for solving cryptarithm problems was 75.65. Regression analysis indicated that metacognitive beliefs had a positive and significant effect on solving cryptarithm problems (R = 0.992; R² = 0.984; p < 0.001). Qualitative analysis identified three patterns of students' thinking processes: systematic-reflective, semi-systematic, and trial-and-error. Students with high metacognitive beliefs tend to understand problems, formulate strategies, monitor, and evaluate their solutions more systematically and reflectively. On the other hand, students with low metacognitive beliefs tended to use trial-and-error strategies without adequate monitoring and evaluation. These findings indicate that metacognitive beliefs not only contribute to problem-solving outcomes but also influence the quality of students' thinking processes when solving non-routine mathematical problems such as cryptarithms. Keywords: cryptarithm; metacognitive belief; thinking process