Analisis Kemampuan Berpikir Kombinatorik Siswa Kelas X dalam Menyelesaikan Masalah Barisan dan Deret Ditinjau dari Self-Efficacy dan Anxiety

Abstract

Combinatorial thinking is one of the higher-order thinking skills that students need to solve mathematical problems, particularly those involving sequences and series. This skill is influenced not only by cognitive factors but also by affective factors such as self-efficacy and anxiety. This study aims to describe the combinatorial thinking abilities of 10th-grade students in solving problems involving sequences and series, as viewed through the lens of their levels of self-efficacy and anxiety. This study employs a qualitative approach with a descriptive research design. Research subjects were selected using purposive sampling based on the results of self-efficacy and anxiety questionnaires. Data were collected through self-efficacy, anxiety, and combinatorial thinking ability questionnaires; a combinatorial thinking ability test; and semi-structured interviews. The results of the study show that students’ combinatorial thinking abilities differ across each combination of self-efficacy and anxiety categories. Students with high self-efficacy and moderate or low anxiety when solving sequence and series problems were able to accurately identify known and unknown information, verify the accuracy of information using appropriate patterns, accurately represent patterns using the nth-term formula and mathematical symbols, systematically develop solutions to draw conclusions, and apply the solution to other problems with similar characteristics. Students with high self-efficacy and high anxiety demonstrated only the ability to represent patterns using mathematical symbols. Students with low self-efficacy and moderate anxiety were able to identify information, represent patterns in mathematical form, and construct part of the solution; however, they were not yet able to complete all stages or apply the solution to other problems. Meanwhile, students with low self-efficacy and high or low anxiety were only able to demonstrate abilities in the early stages of problem-solving, such as accurately identifying known and asked information, verifying the accuracy of information using appropriate patterns, and accurately representing patterns using the nth-term formula and mathematical symbols.