The ability to think critically and mathematically is strongly needed so that the students are able to face the challenges of 4.0 industrial revolution. By thinking critically, they are expected to be more adaptive in finding solutions to each problem. This study aims to identify the students' mathematical critical thinking skills in solving differential calculus problem solving based on some indicators of mathematical critical thinking skills in learning using cognitive growth model. This is a Classroom Action Research (CAR) which was caried out within four weeks in the odd semester of academic year 2018/2019. The subjects of this study were the first-year students of the Mathematics Education Program in one of higher education institutions in Magelang, Central Java who took the Differential Calculus course. Data collection techniques in this study were test, observation, and interviews. The test results were then analyzed quantitatively, and the indicators of critical thinking skills in each question were also described. Based on the results of the study, it can be shown that about 30% students who begin to think critically is initiated by achieving the indicator of analyzing the arguments. However, not all students who begin to think critically are also able to draw conclusions precisely through deductive and inductive reasoning. There are only five or 16.67% who have been able to draw conclusions correctly.