This naturalistic qualitative research aimed to describe students disposition of mathematical critical thinking in Contextual Socrates learning. The subject of this study were students of VII J class of SMPN 8 Bandarlampung in academic years of 2014/2015 which was obtained by purposive sampling technique. The data of this study was qualitative data about students' mathematical critical thinking disposition which were obtained by observation recording, documentation, and interviews. Before analysing the data, the researcher did the triangulation of data sources. Analysis of the data of this study used four stages, that were coding, reducting, and displaying of data, then getting the conclusion. Based on this study, it was concluded that the mathematical critical thinking disposition indicators which appeared dominantly in Socrates Contextual learning were curiousity and analyticality.Penelitian kualitatif naturalistik ini bertujuan untuk mendeskripsikan disposisi berpikir kritis matematis siswa pada Pembelajaran Socrates Kontekstual. Subjek penelitian ini adalah siswa kelas VII J SMPN 8 Bandarlampung tahun pelajaran 2014/2015 yang diperoleh melalui teknik purposive sampling. Data penelitian ini merupakan data kualitatif mengenai disposisi berpikir kritis matematis siswa yang diperoleh melalui catatan lapangan, dokumentasi, dan wawancara. Sebelum menganalisis data, peneliti melakukan triangulasi sumber data. Analisis data penelitian ini menggunakan 4 tahap, yaitu memberi kode, mereduksi, dan menyajikan data, kemudian menarik kesimpulan. Berdasarkan penelitian ini, diperoleh kesimpulan bahwa indikator disposisi berpikir kritis matematis yang dominan muncul pada Pembelajaran Socrates Kontekstual adalah rasa ingin tahu dan analitis.Kata kunci: berpikir kritis matematis, disposisi, Socrates Kontekstual