This study aims to analyze the learning process of introverted students on algebraic operating materials and determine the results of treatment with Problem Based Learning on students' mathematical reasoning abilities. This type of research is an experiment with a single subject or Single Subject Research. The design used is A-B. Data collection techniques through observation, tests, interviews, and documentation. Data analysis uses analysis in conditions and analysis between conditions. Based on the results of the study, the introverted student learning process on algebraic operating material is the subject preparing needs, making designs, identifying, finding and delivering solutions, and conducting evaluations. While the treatment results in the form of Problem Based Learning showed a significant increase, the mean level of test results increased from 48.75 to 92.75 and the percentage of overlap was 0. It was concluded that the use of PBL models had a positive influence on the mathematical reasoning ability of introverted students. It is hoped that the Problem Based Learning model can be used as an alternative learning model to improve the mathematical reasoning ability of introverted students and learning when at school.