<![CDATA[The Problem Based Learning learning model focuses more on problems so that students can contribute their own knowledge and think at a higher level. The method in this study is quantitative with a quasi-experimental design research type with a population of all eighth grade students at SMP Negeri Bandar Lampung. The sample selection used cluster random sampling. Data collection techniques used learning style questionnaires, conceptual understanding ability tests and mathematical problem solving. The analysis technique used in this study was the Two Way Manova (Two Way Multivariate Analysis of variance) test with a significance level of 5%. The results of this study concluded that (1) There is an influence of the Problem Based Learning (PBL) learning model on students' conceptual understanding and mathematical reasoning. The best ability is mathematical reasoning ability. (2) There is an influence of learning style on students' conceptual understanding and mathematical reasoning. Visual learning style is best compared to auditory and kinesthetic learning styles on conceptual understanding ability. Then the kinesthetic learning style is best compared to visual and auditory learning styles on mathematical reasoning ability. (3) There is an influence of the Problem Based Learning (PBL) learning model and learning styles simultaneously on students' understanding of concepts and mathematical reasoning. (4) There is an influence of the problem based learning (PBL) learning model on students' understanding of concepts and mathematical reasoning partially. (5) There is an influence of learning styles on understanding concepts and there is no influence of learning styles on students' mathematical reasoning partially. (6) There is an influence of the Problem Based Learning (PBL) learning model and learning styles on mathematical reasoning only.]]>
