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Learning to know, learning to do, learning to be, and learning to live together are all connected to the four pillars of education. In order to achieve the pillars of education, it is necessary to adapt to the current learning trend of cooperative learning and innovate learning. Using a scientific method and a cooperative learning model similar to STAD, the goal of this study is to make it more likely that students will be able to develop skills relevant to the modern world. With a total sample of 25 students, a quasi-experimental design was used for the research. Tests, questionnaires, observation sheets, and other methods of data collection are utilized. This study's findings demonstrate how STAD-style cooperative learning and a scientific approach support 21st-century students' skills and influence learning achievement. so that students' problem-solving, critical thinking, mathematical communication, and collaboration abilities will all benefit from the STAD learning model's implementation.

Learning trajectory of set is a learning path to get concept of set. However, several teachers did not combine methods, approaches, and ideas in their practical deliveries. This situation becomes a concern for teachers to handle since it will affect the rule without reason so that the accepted concept will not last long in students’ memory. This study aim to describe the learning trajectory using RME models to construct the concept of set. Hypothetical learning trajectory (HLT) was designed using a qualitative method with the realistic mathematics education (RME) of Gravemeijer model as the activity stage begin from preparing for the experiment, pilot experiment, teaching experiment and retrospective analysis. The designed HLT consisted of an objective, activity, and conjecture. This study achieved an understanding of the set concept with applying RME design. By providing examples of contextual mathematics that take place in the learning environment, these outcomes were achieved. Then using media like set cards to model mathematics so that students can advance their own knowledge to the level of formal mathematics. Therefore, the RME-based HLT design can be a solution to obtain the concept of set, primarily in domain definition and set notation to produce a learning trajectory.