The purpose of this study in general is to determine the effect of the implementation of problem-based learning models and independent learning on mathematical problem solving abilities by controlling students' prior knowledge. This research was conducted in class X semester 1 (one) of the 2015/2016 academic year at SMA Negeri 2 Kota Serang and SMA Negeri 1 Ciruas. This study uses an experimental method with a 2×2 factorial design or a treatment by level 2 x 2 design, because of the treatment and the level. The affordable population in this study were all students of class X MIA (Mathematics and Natural Sciences) SMA Negeri 2 Kota Serang and SMA Negeri 1 Ciruas. Sampling was taken by multistage random sampling. The research data include: Data analysis was carried out both descriptively and inferentially. The results of this study indicate that there is an effect of problem-based learning model and independent learning on mathematical problem solving ability by controlling students' prior knowledge with a significance level of 0.00.
                        
                        
                        
                        
                            
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