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This research aimed at analyzing the differences students- critical thinking skills that learning Basic Chemistry II through discovery learning based on constructing concept mapping and mind mapping. It was a quasi-experimental research with nonequivalent pretest-posttest control group design. The research subject was students who programmed Basic Chemistry II in Science Education Study Program, the Ganesha University of Education on even semester in academic year 2018/2019. The subject consists of 34 students that were divided into two classes, those were class A and class B that consisting of 17 students respectively. Class A as the experiment-1 group learned through discovery learning based on constructing concept mapping and class B as the experiment-2 group learned through discovery learning based on constructing mind mapping. The research object was students- critical thinking skills that collecting by a critical thinking skills test. Data of students- critical thinking skills were analyzed through descriptively and inferential analysis, namely the Mann-Withney U-test with 5% significance level. The results showed that there is no significant differences in students- critical thinking skills that learning through discovery learning based on constructing concept mapping and mind mapping with the average score are 56.7 and 54.1 respectively. However, there are differences in each indicator of students- critical thinking skills. Critical thinking skills profile of students who constructing concept mapping and mind mapping are 71.8 and 57.7 for interpretation, 54.1 and 34.1 for analysis, 47.1 and 28.2 for evaluation, 71.6 and 82.4 for inference, 69.1 and 64.7 for explanation respectively.