<![CDATA[Pembuktian matematis merupakan elemen kunci dalam pendidikan matematika tingkat lanjut dan menjadi fokus utama dalam perkuliahan Pengantar Analisis Real. Namun, banyak mahasiswa mengalami kesulitan dalam memahami konsep dasar, menghubungkan definisi dengan teorema, serta menyusun pembuktian secara runtut, sehingga memengaruhi penguasaan mereka terhadap mata kuliah ini. Penelitian ini bertujuan menelusuri kesulitan mahasiswa dalam memahami soal pembuktian, melaksanakan proses pembuktian, dan menarik kesimpulan dari hasil pembuktian. Jenis penelitian yang digunakan adalah metode campuran (mixed methods), yang menggabungkan pendekatan kuantitatif dan kualitatif. Subjek penelitian adalah satu kelas mahasiswa Jurusan Matematika, Program Studi Pendidikan Matematika, FMIPA, Universitas Negeri Padang yang menempuh mata kuliah Pengantar Analisis Real pada semester Januari–Juni 2024, dengan jumlah 35 mahasiswa. Dari jumlah tersebut, enam orang mahasiswa dipilih sebagai responden wawancara. Instrumen yang digunakan adalah tes soal pembuktian dan lembar wawancara. Data tes (rentang 1-100) dikategorikan dengan nilai 1 sampai dengan 4 berdasarkan rubrik penilaian yang terdapat dalam standar operasional prosedur penilaian UNP. Data wawancara dianalisis menggunakan analisis deskriptif. Hasil penelitian menunjukkan bahwa pada proses pembuktian diperoleh kesulitan mahasiswa: dalam memahami soal pembuktian sebanyak 44,83%, dalam melaksanakan pembuktian sebanyak 52,49%, dan dalam membuat kesimpulan hasil pembuktian sebanyak 65,52%. Analisis jawaban mahasiswa menunjukkan bahwa kesulitan utama terletak pada: kesalahan memahami premis soal, penggunaan definisi irisan yang tidak benar, penyusunan argumen pembuktian yang tidak sistematis, serta penarikan kesimpulan yang tidak didasarkan pada langkah-langkah yang benar. Kata kunci: pembuktian matematis, analisis real, kesulitan mahasiswa. Abstract: Mathematical proof is a key element in advanced mathematics education and is the main focus of the Introduction to Real Analysis course. However, many students experience difficulties in understanding basic concepts, connecting definitions to theorems, and constructing proofs coherently, thus affecting their mastery of this course. This study aims to explore students' difficulties in understanding proof problems, carrying out the proof process, and drawing conclusions from the proof results. The type of research used is a mixed methods study, combining quantitative and qualitative approaches. The subjects were a class of 35 students from the Mathematics Department, Mathematics Education Study Program, Faculty of Mathematics and Natural Sciences, Padang State University, who took the Introduction to Real Analysis course in the January–June 2024 semester. Of these, six students were selected as interview respondents. The instruments used were a proof test and an interview sheet. Test data (range 1–100) were categorized with a score of 1 to 4 based on the assessment rubric contained in the UNP assessment standard operating procedures. Interview data were analyzed using descriptive analysis. The results of the study showed that in the proof process, students found difficulties: in understanding the proof questions as much as 44.83%, in carrying out the proof as much as 52.49%, and in drawing conclusions from the proof results as much as 65.52%. Analysis of student answers showed that the main difficulties lay in: misunderstanding the question premise, using incorrect intersection definitions, compiling unsystematic proof arguments, and drawing conclusions that were not based on correct steps. Keywords: mathematical proff; real analysis; student struggles; proof construction]]>
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