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The purpose of this study is to analyze the ability of mathematical critical thinking of Mathematics Education students. The subjects are 86 students of one university in Bandung, who took Ordinary Differential Equation Course. The length of the study is about 4 months. In the first two months, the students got the Direct Learning and the other two months, the students got the Indirect Learning. Instruments in this study were two sets of critical thinking test, which consist of each three essay questions. The results showed that the mathematical critical thinking ability of students is low. There are no difference abilities of mathematical critical thinking among the two learning approach, their achievements are still in low categories. Among the three indicators of the tests, ‘identifying the underlying concepts- got the lowest score, ‘answering question with relevant reasons- got the medium score and ‘examining the truth of the statements and explain it- got the highest score, but those three scores are still in low category.