The aim of the research is to examine the conceptual design of learning contectual math based on lesson study. The impact of try out is the changing math study communication. The research used qualitative design. The research location is elementary school after the eruption of Merapimountain at Selo, Boyolali. Teacher grade IV Sekolah Dasar Negeri 1 Seloas a teacher model. Technique of data gathering: observation, in depth interview, and documentation. Tech nique of data analisis, comparative and critical analisis. Data validity used triangulation, method and resource. The research result showed that, contectual math learning based on lesson study can increase math study communication. Lesson Study that is done by the teacher in his/her group cyclely, mainly: (1) learning syllabus and content standard, (2) developing planning of conducting learning, (3) model teacherconducted learning, and (4) result reflection of learning conducting. Contectual math learning based on lesson studyis conducted in five stages. 1) Students' orientation on problem situation. 2) Students coordinate for studying. 3) Investigation guiding both individual or group. 4) Developing and presenting creativity result. 5) to analyse and evaluate problem solving process.