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This research is a design research validation studies type that aims to develop a learning trajectory in three-dimensional geometry topics to support students' quantitative thinking skills with the Rigorous Mathematical Thinking (RMT) approach. A Hypothetical Learning Trajectory (HLT) will be refined throughout the lesson carried out in the classroom. The activities are in the form of a student worksheet (LKPD) which consists of 2 problems to support the learning process. The research subjects were 36 students of SMA Negeri 1 Palembang class XII MIPA 7, while the focus of the research was 6 students with low, medium, and high abilities who were selected by purposive sampling. The research method consists of three stages, namely: (1) preparation phase; (2) design experiment which is divided into the pilot experiment and teaching experiments; (3) retrospective analysis. The research was carried out online using the application zoom meeting and combined with an offline classroom. Data collection techniques in this research are student worksheets, written tests, and interviews. Research data is collected and will be analyzed qualitatively. The results showed that the learning trajectory obtained can be useful for supporting students' quantitative thinking skills on three-dimensional material with indicators that appear in this study are conserving constancy, quantifying space and spatial relationships, analyzing and integrating. [ABSTRACT FROM AUTHOR]

This paper aims to describe mathematics teachers' perception of mathematical proof. Proving in mathematics for the teacher is crucial as the foundation of developing students' skills in generating correct proof to some conjectures which require good mathematical reasoning. It has been highlighted in some works of literature that mathematical reasoning which is closely related to proving in mathematics also contributes to the development of a chosen set of 21st-century skills. A total number 152 of Indonesian in-service mathematics teachers were given a survey concerning their perception of mathematical proving. The description of the result consists of five important categories including the process of mathematical proof, thinking ability in mathematical proof, appropriate school level in learning proof, topic, and understanding in a mathematical proof. It is found that Indonesian in-service mathematics teachers had a positive attitude towards mathematical proof as a teaching approach in their classrooms, as the opportunity for students to improve helped students improve their thinking ability. [ABSTRACT FROM AUTHOR]