Guru dituntut mempunyai kemampuan untuk mengajukan permasalahan matematis yang baik serta mempunyai kemampuan berpikir kritis matematis. Hal ini di dukung oleh kebijakan dari Kementrian Pendidikan dan Kebudayaan (Kemendikbud) pada tahun 2018 yang mengharuskan guru untuk berperan dalam pembuatan Ujian Sekolah Berstandar Nasional (USBN) serta kurikulum 2013 yang menekankan pada Higher-Order Thinking Skills. Hal ini tentunya harus ditangani secara maksimal, salah satunya adalah melatih calon guru dalam mengajukan permasalahan, berpikir kritis, serta resiliensi matematis. Penelitian ini memiliki tujuan untuk menganalisis capaian dan peningkatan kemampuan pengajuan masalah (KPM), berpikir kritis (KBK), dan resiliensi matematis mahasiswa dalam pembelajaran berbasis masalah dan Discovery Learning berdasarkan kemampuan awal matematika (KAM) dan keseluruhan. Metode yang digunakan dalam penelitian adalah quasi eksperimen dengan desain pretest-posttest control group design. Populasi dalam penelitian ini adalah mahasiswa Program Studi Pendidikan Matematika S1 pada salah satu PTS di provinsi Jawa Tengah, dan sampel dalam penelitian adalah mahasiswa Program Studi Pendidikan Matematika semester II tahun akademik 2016/2017. Beberapa hasil yang diperoleh dalam penelitian ini adalah: 1) Tidak terdapat perbedaan capaian KPM, KBK dan resiliensi matematis dilihat dari KAM maupun keseluruhan, kecuali pada KBK kategori KAM tinggi. 2) Tidak terdapat perbedaan peningakatan KPM dan resiliensi matematis dilihat dari KAM maupun keseluruhan. 3) Terdapat perbedaan peningkatan KBK pada kategori KAM tinggi, sedang dan Keseluruhan. 4) Terdapat interaksi Pembelajaran Berbasis Masalah dan Discovery Learning dengan KAM terhadap peningkatan KBK matematis mahasiswa. ;---A teacher is demanded to master the ability to pose good mathematical problems and to master critical thinking math. This statement is supported by the policy of Education and Culture Ministry (Kemendikbud) issued on 2018 which obligated teachers to participate in constructing tasks to be included in standardized-national examination (USBN) and implement the curriculum 2013 which is emphasized on HOTS. This is supposed to be done maximally; and one of the ways is by training the prospective math teachers in posing mathematical problems, critical thinking, and mathematical resilience. This study aims to analyze achivement and improvement in posing mathematical problems, critical thinking, and mathematical resilience through problem-based learning and discovery learning based on students’s mathematical basic knowledge. This study employs quasi-experimental with pretest-posttest control group design. The population of this study is the second smester students of Mathematics department at one of the private universities in Central Java. The sample of this study is the second semester students of Mathematics department in the academic year 2016/2017. The results of the analysis in this study are: 1) there is no difference in the achievement and improvement of posing mathematical problems and mathematical resilience of the students who were taught using problem-based learning and those who were taught using discovery learning in three categories of students’ mathematical basic knowledge (high, medium, and low), (2) there is a difference in the achievement of critical thinking of the students who were taught using problem-based learning and discovery learning in high students’ mathematical basic knowledge, (3) there is no difference in the improvement of critical thinking of the students who were taught using problem-based learning and those who were taught using discovery learning in low category of students’mathematical basic knowledge, (4) there is interaction between approach and students’ mathematical basic knowledge in the improvement of the students’ ability to think critically
