ANALYSIS OF UNDERSTANDING OF MATHEMATICAL CONCEPTS IN HOTS QUESTIONS ON CIRCLES AT ISLAMIC BOARDING SCHOOLS

Abstract

This study aims to explore in depth students’ mathematical conceptual understanding in solving Higher Order Thinking Skills (HOTS) problems on the topic of circles and to identify the error patterns and problem-solving strategies that emerge in an Islamic boarding school context. Mathematics learning in Islamic boarding schools presents unique challenges because students are required to balance academic learning with intensive religious and boarding-school activities, which may influence their learning experiences and conceptual understanding. The study employed a qualitative descriptive design supported by quantitative descriptive statistics. The participants were nine twelfth-grade students from a pesantren-based senior high school in Indramayu, who completed a HOTS-based conceptual understanding test and semi-structured interviews. Data were analyzed through the stages of reduction, presentation, and conclusion drawing, with source triangulation used to ensure data credibility. The results showed that 22% of students were classified in the high category, 56% in the medium category, and 22% in the low category, with an average score of 53 and a standard deviation of 26. Students in the high category were able to determine circle equations, center points, radii, intersection points, and visual representations accurately. In contrast, students in the medium category experienced difficulties in elimination, factorization, and visualization processes, while students in the low category struggled with algebraic operations and substitution procedures. These findings indicate that most students still require support in applying conceptual understanding to HOTS-based contextual problems. This study contributes to mathematics education by providing an in-depth description of students’ conceptual understanding, error patterns, and problem-solving strategies when solving HOTS-based circle problems in an Islamic boarding school setting.

Penelitian ini bertujuan mengungkap tingkat pemahaman konsep matematis siswa pesantren dalam menyelesaikan soal Higher Order Thinking Skills (HOTS) pada materi lingkaran serta memetakan karakter kesalahan dan strategi penyelesaian yang digunakan. Penelitian menggunakan pendekatan deskriptif kualitatif yang didukung analisis deskriptif kuantitatif dengan subjek sembilan siswa kelas XII pada salah satu SMA berbasis pesantren di Indramayu. Pengelompokan siswa ke dalam kategori tinggi, sedang, dan rendah dilakukan berdasarkan indikator pemahaman konsep matematis yang meliputi kemampuan menyatakan kembali konsep, merepresentasikan konsep, menerapkan prosedur, dan menyelesaikan masalah. Data dikumpulkan melalui enam soal uraian kontekstual dan wawancara semiterstruktur. Instrumen penelitian telah melalui proses validasi ahli sebelum digunakan. Data dianalisis melalui tahap reduksi, penyajian, dan penarikan kesimpulan dengan triangulasi sumber. Hasil penelitian menunjukkan bahwa 22% siswa berada pada kategori tinggi, 56% kategori sedang, dan 22% kategori rendah, dengan rata-rata skor 53 dan simpangan baku 26 yang menunjukkan adanya variasi kemampuan dan heterogenitas pemahaman konsep di antara siswa. Siswa kategori tinggi mampu menentukan persamaan lingkaran, pusat, jari-jari, posisi titik, dan titik potong kurva secara tepat. Siswa kategori sedang masih mengalami kesulitan pada proses eliminasi, pemfaktoran, dan visualisasi, sedangkan siswa kategori rendah mengalami kesulitan pada operasi aljabar dasar dan substitusi. Temuan ini menunjukkan bahwa sebagian besar siswa masih memerlukan penguatan pemahaman konsep untuk menyelesaikan soal HOTS secara efektif. Oleh karena itu, diperlukan strategi pembelajaran yang dapat memperkuat penalaran aljabar, kemampuan visualisasi, dan pemahaman konsep matematis guna meningkatkan kemampuan siswa dalam menyelesaikan soal HOTS.