Metacognitive Self-management in Developing Students' Rigorous Mathematical Thinking Skills

Abstract

This study aims to describe the metacognitive self-management of students in developing rigorous mathematical thinking. This study uses a qualitative method with a case study approach. The participants were three students from the thirdlevel mathematics education department, who were selected and made a contract with for real analysis lectures. The first student experienced a significant change from the beginning of the meeting, resulting in the metacognitive self-management process being well-conditioned. He completed the task more confidently than the initial presentation, used several references and sources of information to complete the job, and represented each answer in the form of mathematical symbols. This studentscognitive function appears to be of level-1, with qualitative thinking. For the 2nd student, a change was observed in the learning process and the teacher’s motivation and guidance. The results of the interviews showed that the student applied strategies in completing assignments. He answered them systematically, based on experience, and mastered the prerequisite material. This student showed improved thinking skills related to mastery of concepts from new material, analyzing the problems given, being critical and focused when answering, and looking hard to get maximum evaluation results. This 2nd student entered the level of quantitative thinking with precision. Lastly, in the 3rd student, self-management seems stable, but was still lacking in adjusting the understanding of prerequisites with understanding concepts from new material. The development during the learning process shows that he can activate his mathematical knowledge, compose logical proofs of Real Analysis material problems, and build relationships between prerequisite concepts and new material. This type of student enters the level of abstract relational. The results of the study can be a reference for teachers to determine the learning model and the related instruments, so that they can grow the level of mathematical thinking before, during, and after the learning process. Keywords: Metacognitive, self-management, Mathematical thinking skill