This article describes a comparison of mathematics learning methods between Japan and Indonesia. In Japan, structured and systematic approaches such as Rikai Kansatsu and Kōryū are applied, with an emphasis on observation, deep understanding, and collaborative work in solving mathematical problems. Teachers in Japan also apply problem solving and open ended approaches, which encourage students to think critically, creatively and independently. In addition, the implementation of lesson study as a scientific activity that involves teachers in developing the theory and practice of mathematics learning is a strong foundation for the method in Japan. On the other hand, in Indonesia, there is a shift towards more inclusive and creative learning approaches, such as the Scientific approach and the Concrete Representational Abstract (CRA) approach. Teachers in Indonesia emphasize more on achieving individual and classical student competencies, with a strong orientation towards learning outcomes. Although the concept of lesson study has been implemented in Indonesia, there are still differences in the development of theories and the application of learning methods. Awareness, support, and collaboration among teachers are key to developing and expanding the application of lesson study and improving the quality of mathematics learning in Indonesia. With increased teacher understanding and participation, the potential of lesson study development and implementation in Indonesia can be optimized to improve students' understanding of mathematics and critical thinking skills.