Analisis Pemecahan Masalah Sudut pada Topik Trigonometri oleh Siswa SMA Berkemampuan Tinggi Ditinjau dari Tahapan Polya

Abstract

Problem-solving ability is one of the essential competencies in mathematics learning, particularly in trigonometry, which requires students to understand concepts, determine appropriate solution strategies, and perform accurate calculations. This study aimed to describe the process of solving angle-related problems in trigonometry by high-ability senior high school students based on Polya’s problem-solving stages. This study employed a qualitative approach with a descriptive research design. The research was conducted at SMA Negeri 2 Jember, involving three tenth-grade students categorized as high-ability learners based on their trigonometry achievement and mathematics teacher recommendations. Data were collected through trigonometric problem-solving tests and semi-structured interviews. The data were analyzed through data reduction, data display, triangulation, and conclusion drawing. The results show that all participants were able to complete the stages of understanding the problem and devising a plan effectively. At the understanding stage, students identified the known and unknown information and comprehended the context of the problems accurately. At the planning stage, students selected appropriate strategies by applying trigonometric ratios according to the characteristics of each problem. During the implementation stage, one participant solved all problems correctly, while the other two participants made computational errors despite applying appropriate strategies. At the looking-back stage, all participants reviewed their solutions; however, they were not always able to identify the mistakes made in previous steps. The findings indicate that high-ability students demonstrate a systematic problem-solving process in accordance with Polya’s stages, although calculation accuracy and evaluative skills still influence the success of problem resolution.