To face the industrial revolution 4.0, the abilities that should be possessed by students are high-level thinking skills that include mathematical critical thinking skills. Critical thinking is the ability to analyze information obtained based on facts in order to make reasonable conclusions. This is a qualitative descriptive study that aimed to determine and illustrate the critical thinking skill of students with filed dependent (FD) and filed independent (FI) cognitive in solving a single variable linear equation problem. Two students selected based on the GEFT test acted as the subjects of this study. One of them had FD cognitive while the other had the FI cognitive. The instruments used in this study were (1) mathematical critical thinking tests, (2) cognitive style tests in the form of GEFT, and (3) interviews. Data analysis techniques in this study consisted of (1) data reduction, (2) data presentation, (3) verification and conclusion. The indicators of students’ mathematical critical thinking skill included (1) reason and (2) clarity. It was found that (1) student with filed dependent style on reason indicator needed to get used to making an argument or reason, while for clarity indicators, FD subject could change statements into mathematical symbols clearly and precisely. (2) Students with cognitive style FI, chose and gave reasons and drew conclusions correctly, changed statements into mathematical symbols clearly and precisely.