Identifikasi proses berpikir siswa dalam menyelesaikan masalah aljabar dengan menggunakan representasi graf

Representasi graf banyak digunakan, salah satunya untuk menggambarkan proses berpikir siswa. Caranya dengan melihat hubungan antara langkah penyelesaian satu dengan lainnya dalam menyelesaikan masalah matematika. Penelitian ini bertujuan untuk merepresentasikan proses berpikir siswa dalam menyelesaikan masalah aljabar dengan bantuan representasi graf. Subjek penelitian ini adalah 3 dari 38 siswa kelas IX-A SMP Negeri 26 Surabaya, yang diambil dengan teknik snowball sampling . Teknik pengumpulan data menggunakan metode wawancara berbasis tugas. Tugas atau masalah yang diberikan berupa dua soal open onded dan hasilnya dianalisis serta direpresentasikan melalui graf: graf pohon biner, graf pohon rentang, dan graf pohon keputusan. Hasil penelitian menunjukkan bahwa melalui graf pohon biner, representasi proses berpikir siswa masih sederhana dan tidak sistematis dengan langkah-langkah penyelesaian yang dilakukan masih sedikit. Melalui graf pohon rentang, proses berpikir siswa direpresentasikan secara praktis, lengkap, dan tepat. Melalui graf pohon keputusan, proses berpikir siswa direpresentasikan secara teratur, rinci, dan terurut. Abstract One of the uses of graph representation was to describe students’ thinking. Processes by identifying the relationship between one completion step and another completion step in doing mathematics problems. This qualitative descriptive research aimed to describe the representation of students’ thinking processes in solving algebraic questions with the help of graph representation. The subjects of this study were 3 from 38 students of class IX-A at SMP Negeri 26 Surabaya, Indonesia selected through snowball sampling. Data was collected from task-based interview methods. The task or problem given was two open-ended questions and the results were analyzed as well as represented through graphs: binary tree graph, spanning tree graph, and decision tree graph. The results showed that through the binary tree graph, the representations of students’ thinking processes were still simple and not systematic with few steps to complete. Through the spanning tree graph, students’ thinking processes were represented practically, completely, and precisely. Through the decision tree graph, students’ thinking processes were represented in an orderly, detailed, and consecutive.