This study aims to determine the differences in critical thinking skills that are significant in the Basic Concepts of Mathematics course in learning using the Inquiry and Discovery Learning learning models. This type of research is a quasi-experimental study with a nonequivalent control group design. The study population was students of the Elementary School Teacher Education Study Program, Faculty of Educational Sciences, Muhammadiyah University of North Sumatra, with a total of 66 students. The data collection technique uses the integrated critical thinking skills rubric instrument of description questions. The data analysis technique uses the t-test with the Independent Sample T Test technique. The results of this study indicate that the level of critical thinking skills in learning using the Inquiry model is higher than in Discovery Learning. This can be seen from the results of the t-test which shows a probability value of 0.000 because the probability value is ? 0.05, then H0 is rejected and Ha is accepted. This means that there are significant differences in the Inquiry and Discovery Learning learning models for critical thinking skills in mathematics