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This article is about research on the study of improving students problem solving abilities in the learning process using the Problem Based Learning learning model with the Metacognitive approach. This article also contains a study of the interaction between the learning model and the students mathematical prior knowledge towards problem solving abilities, and the study of student behavior in improving mathematical problem solving skills. Research uses quantitative research methods with research subjects students in the experimental class and the control class. The research instrument consisted of tests of mathematical problem solving abilities, observation sheets and interview guidelines. Research findings include (1) the learning model used does not have a significant effect on improving mathematical problem-solving abilities, both overall and based on mathematical prior knowledge, (2) there is no interaction between learning models and mathematical prior knowledge to improve mathematical problem solving abilities , and (3) there are different behaviors between the experimental class students and control class students in improving mathematical problem solving abilities