This research aims to determine the increase in mathematical problem solving abilities in permutation material through the problem based learning (PBL) learning model. This research is classroom action research (PTK) with research subjects being students of class XI TPM 2 SMK Negeri 1 Madiun, totaling 34 students. In this research, the instruments used were problem-solving ability tests and observation sheets. In this research there are two cycles, where each cycle consists of planning, implementation, observation and reflection which follows the Lewin model procedure. In this study, the minimum learning completeness obtained was >75%. The analysis technique used in this research is descriptive qualitative which is adapted to the Hiles and Huberman technique, including data collection, data reduction, drawing conclusions and verification. The results of this research show that there is an increase in problem solving abilities using the problem based learning (PBL) learning model. This can be seen from the number of students who have achieved the very good problem solving ability category, namely 15.63% in the pre-cycle, then increasing to 25 % in cycle 1, and then increased in cycle 2, namely 53%, and in cycle 2 learning completion had reached 84.38%.
