Penelitian ini bertujuan untuk mengetahui cara siswa kelas viii akhwat smp muhammadiyah boarding school tarakan dalam melatih kemampuan berpikir kritis matematis aspek explanation. penelitian ini dilakukan selama 3 bulan, yaitu mulai 5 juni 2020 sampai 4 september 2020 di smp muhammadiyah boarding school tarakan. jenis penelitian ini adalah studi kasus melalui pendekatan kualitatif. subjek penelitiannya adalah siswa kelas viii akhwat sebanyak dua orang yang dipilih dengan purposive sampling. peneliti mendapatkan dari satu kelas viii akhwat di smp muhammadiyah boarding school tarakan, terdapat dua siswa dengan kemampuan berpikir kritis matematis aspek explanation yang bagus. pengumpulan data dilakukan menggunakan wawancara pada subjek dan informan, analisis dokumentasi dengan melihat buku catatan dan observasi kelas online. data yang diperoleh ditulis dalam catatan lapangan lalu dianilisis dengan reduksi data, penyajian data dan penarikan kesimpulan. peneliti mengecek keabsahan data dengan triangulasi sumber, yaitu wawancara subjek dan informan; triangulasi waktu dengan wawancara subjek beserta informan pada suasana berbeda; triangulasi teknik melalui wawancara, analisis dokumentasi dan observasi; melakukan member check; menuliskan secara rinci hasil penelitian; dan dilaksanakannya audit oleh dosen pembimbing secara online. berdasarkan hasil penelitian, maka kedua subjek, yaitu aa dan nz melatih kemampuan berpikir kritis matematis aspek explanation pada indikator menyatakan hasil dengan cara tidak mudah menyerah dalam berusaha mencari jawaban dari soal matematika, indikator menyatakan penjelasan dengan cara memiliki rasa empati dan tidak asal bicara dalam memberikan penjelasan dan indikator menyajikan argumen dengan cara bersedia menerima pendapat teman yang lebih benar. kata kunci: berpikir kritis, explanation, matematika

This study aims to determine how students of class viii akhwat smp muhammadiyah boarding school tarakan in training their mathematical critical thinking skills on the aspect of explanation. this research was conducted for 3 months, from 5 june 2020 to 4 september 2020 at smp muhammadiyah boarding school tarakan. this type of research is a case study through a qualitative approach. the research subjects were students of class viii akhwat as many as two people who were selected by purposive sampling. researchers found that from one class viii akhwat at smp muhammadiyah boarding school tarakan, there were two students with good mathematical critical thinking skills on explanation aspects. data collection was carried out using interviews with subjects and informants, analysis of documentation by looking at notebooks and online classroom observations. the data obtained were written in field notes and then analyzed by data reduction, data presentation and drawing conclusions. the researcher checked the validity of the data by using triangulation of sources, namely interviews with subjects and informants; time triangulation by interviewing subjects and informants in different situations; technical triangulation through interviews, documentation analysis and observation; do a member check; write down in detail the results of the research; and conducting an online audit by the supervisor. based on the results of the study, the two subjects, namely aa and nz trained the ability to think mathematically critical aspects of the explanation on the indicators stating the results by not giving up easily in trying to find answers to math problems, indicators expressing explanations by having a sense of empathy and not just speaking in giving explanations and indicators present arguments in a manner that is willing to accept a friend's opinion which is truer. keywords: critical thinking, explanation, mathematics