<![CDATA[This study aims to analyze students' rigorous mathematical thinking from three levels of cognitive function structures associated with their contribution to self-assessment metacognitive knowledge in Real Number System lectures. This research is qualitative research with a type of case study. The research subjects were three students of the Mathematics Education Study Program who contracted the Real Number. System course selecting research subjects based on test results identifies students into three rigorous mathematical thinking cognitive function structure levels. This study's results indicate that rigorous mathematical thinking contributes to students' self-assessment metacognitive knowledge. The quality of review of students who have a rigorous mathematical thinking level can lead to thoroughness, intellectual perseverance, critical investigation, and truth-seeking in solving problems appropriately, structurally, and systematically into a direct experience in the learning process is described as metacognitive. Students at the level of abstract relational thinking can assess their own abilities very well, learn independently, and choose with certainty how to solve problems by placing the right method. Qualitative thinking level students focus more on symbols or symbols and represent their knowledge through visualization. He prefers that the type of evaluation problem solving is not in the form of long, detailed sentences but instead immediately transforms the sentences into clear mathematical symbols]]>
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