Analysis of Probabilistic Critical Thinking Skills of Students with High Mathematical Resilience

Abstract

Probabilistic critical thinking skills are essential for students to master. Previous studies have generally examined mathematical critical thinking based on cognitive abilities, resulting in a gap in the literature regarding how students’ profiles of probabilistic critical thinking are viewed from an affective perspective, namely, mathematical resilience. The purpose of this study is to analyze the probabilistic critical thinking skills of students with high mathematical resilience. This study is a qualitative research conducted on students of the Mathematics Education Study Program, Faculty of Mathematics and Natural Sciences, Semarang State University, with the research subjects being students of the Mathematics Education Bachelor's Program, Faculty of Mathematics and Natural Sciences, Semarang State University, in the second semester of the 2024/2025 academic year. There were three research subjects with high mathematical resilience. Data collection was conducted through tests, interviews, and questionnaires. Data were analyzed using: (1) data reduction; (2) data display; and (3) conclusion drawing/verification, while data validity was determined through triangulation, namely by comparing test results with interview results, as well as comparing the results of the research subjects. The results of this study indicate that the probabilistic critical thinking ability of subjects with high resilience meets the indicators of focus, situation, inference, and overview. However, they are still unable to meet the indicators of reason and clarity. The suggestion is that students need reinforcement in giving reasons for each step in problem-solving, as well as in providing further explanations when concluding. Theoretically, these findings enrich the literature on probabilistic critical thinking by integrating the affective dimension of mathematical resilience. Practically, these results serve as a guide for educators in designing learning interventions explicitly aimed at training students to articulate their reasoning and clarify their conclusions.

Abstrak

Kemampuan berpikir kritis probabilistik merupakan kemampuan esensial yang harus dikuasai mahasiswa. Kajian terdahulu umumnya meneliti berpikir kritis matematis berdasarkan kemampuan kognitif, sehingga terdapat kesenjangan literatur mengenai bagaimana profil berpikir kritis probabilistik mahasiswa ditinjau dari aspek afektif, yaitu ketangguhan matematis. Tujuan dalam penelitian ini adalah menganalisis kemampuan berpikir kritis probabilistik mahasiswa dengan resiliensi matematis tinggi. Penelitian ini merupakan penelitian kualitatif yang dilaksanakan pada mahasiswa program studi Pendidikan Matematika FMIPA Universitas Negeri Semarang, dengan subjek penelitian mahasiswa Program Studi Sarjana Pendidikan Matematika Fakultas Matematika dan Ilmu pengetahuan Alam Universitas Negeri Semarang semester dua tahun perkuliahan 2024/2025. Subjek penelitian sebanyak tiga mahasiswa dengan resiliensi matematis tinggi. Pengambilan data melalui tes, wawancara, dan angket. Data dianalisis menggunakan: (1) data reduction; (2) data display; dan (3) conclusion drawing/verification, sedangkan keabsahan data dilakukan melalui triangulasi yaitu membandingkan hasil tes dengan hasil wawancara, serta membandingkan hasil subjek-subjek penelitian. Hasil penelitian ini menunjukkan kemampuan berpikir kritis probabilistik subjek dengan resilisensi tinggi mampu memenuhi indikator focus, situation, inference, overview.   Sedangkan untuk indikator reason dan clarity masih belum mampu. Saran yang diberikan perlu adanya penguatan mahasiswa dalam memberi alasan dalam setiap langkah dalam memecahkan masalah, serta dalam memberi penjelasan lebih lanjut dalam membuat kesimpulan. Secara teoretis, temuan ini memperkaya literatur berpikir kritis probabilistik dengan mengintegrasikan dimensi afektif ketangguhan matematis. Secara praktis, hasil ini menjadi panduan bagi pendidik untuk merancang intervensi pembelajaran secara eksplisit untuk melatih mahasiswa dalam mengartikulasikan alasan dan memperjelas kesimpulan.