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The purpose of this research is to compare the effectiveness of learning models to develop student critical thinking skills and retention in mathematics through the application of Problem Based Learning (PBL) models and multimedia assisted Direct Instruction (DI) models for students who have different cognitive styles. This research is quasi-experimental type, using non-equivalent control group design. Subject of this research are students in three different senior high school with two class samples in each school. There are 102 students of control class with Direct Instruction learning model by multimedia and 97 students of experiment class with Problem Based Learning model. The instrument of this research are test and questionnaires. The findings of this research are that there are significant differences in student critical thinking skills and retention between groups of student with Field Dependent (FD) and Field Independent (FI) cognitive styles and also between group of student with Direct Instruction model and Problem Based Learning model. Each learning model has interaction with critical thinking skills but not student retention. This research is useful for educators to develop students critical thinking skills processes with an effective learning model approach especially for senior high school students. The educators can know the interaction of cognitive styles with student retention, the extent to which cognitive styles are able to have an impact on student retention. This research provides knowledge an effective learning model to develop critical thinking skills and retention of student both Field Dependent and Field Independent cognitive style. Based on cognitive style, Field Independent students have higher retention and critical thinking skills compared to Field Dependent students.

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