The low ability of students to solve mathematical problems at SMP N 1 Abung Tinggi is due to the difficulty of the students in solving problems and it seems that only a few have above average scores. This study aims to see the differences in learning outcomes of students who use the TAPPS learning method with the quick on the draw strategy and the direct instruction method on the mathematical problem solving ability in terms of differences in the cognitive styles of students. The type of research used is quasi experimental design. The data collection technique used was a test. Hypothesis testing uses two-way Anova analysis. Previously, the prerequisite test was carried out which included the normality test using the Liliefors test and the homogeneity test using the Barlett test. The result obtained in this study that (1) there are differences in the learning outcomes of students who use the TAPPS learning method with the quick on the draw strategy and the direct instruction method for mathematical problem solving abilities, (2) there is no difference between students with independent cognitive style and cognitive style dependent on ability in solving mathematical problems, (3) there is no interaction between the TAPPS learning method with the quick on the draw strategy and the direct instruction method in terms of differences in cognitive styles on the ability to solve mathematical problems.