Menelusuri Alur Penalaran Siswa dalam Membuktikan Aturan Sinus: Studi Kasus Kualitatif dalam Pembelajaran Berbasis Masalah

Abstract

Mathematical proof plays an essential role in developing students’ reasoning and higher-order thinking skills; however, secondary mathematics instruction often remains procedural, limiting meaningful reasoning development. This study explores students’ reasoning paths in proving the sine rule through Problem-Based Learning. A qualitative case study was conducted in a trigonometry learning context using Problem-Based Learning. Data were collected through classroom observations, analysis of students’ worksheets, and in-depth interviews, and analyzed thematically based on stages of mathematical proof. The results show that students’ reasoning paths develop dynamically through three stages conjecturing, justifying, and concluding. During conjecturing, students formulate initial conjectures based on problem understanding and connections to trigonometric concepts. The justifying stage involves developing and validating conjectures through argumentation, representations, mathematical manipulations, and reasoning supported by social interaction. In concluding, students formulate the sine rule and reflect on the validity of the proof process. Overall, the findings indicate that Problem-Based Learning provides a supportive context for fostering meaningful mathematical proof reasoning.